City School Expenditures The Variability and Interrelation of the Various Items By George Drayton Stray er, A.B. Submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in the Faculty of Philosophy Columbia University 1905 LB 2829 .S8 Copy l City School Expenditures The Variability and Interrelation of the Various Items By George Drayton Stray er, A.B. Submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in the Faculty of Philosophy Columbia University 1905 Gift Carnegis last. CONTENTS PAGE Introduction I The Problem . 3 Data 10 Variability 42 Relationships . 80 Conclusion 100 Acknowledgment . 103 Vita . 104 City School Expenditures THE VARIABILITY AND INTERRELATION OF THE PRINCIPAL ITEMS By GEORGE DRAYTON STRAYER, A.B., Johns Hopkins University ; Fellow in Education, Teachers College, 1904-05 INTRODUCTION The importance of the subject-matter of Mr. Strayer's in- vestigation needs no comment. The methods, being in some respects new in the literature of education, deserve some com- ment. It is impossible to gain adequate insight into facts as com- plex as those of school expenses and school achievements with- out some use of technical statistical methods. If Mr. Strayer's report puzzles some readers by its tables of frequency, its con- stant use of the median rather than the average as a measure of central tendency, its coefficients of correlation and their correc- tions, it is of necessity. The facts could not otherwise be handled properly — in some cases not at all. The one matter of technique which needs explanation and perhaps apology is the use of the Pearson Coefficient of Correla- tion. This measure of the general relation of a deviation of the amount of one item in the budget from the typical amount of that item to the deviation in the same city of some other item from its typical amount, is indispensable but necessarily obscure. It is indispensable: (1) because it presents to the mind in a single figure a mass of individual relationships which 2 City School Expenditures in their detailed form leave no definite impress on even the most skilled examiner of statistics (e. g., let any one try to measure accurately the facts of the relation of teachers' salaries to janitors' salaries without its aid); (2) because it makes all relationships between any one and any other of the same order of facts comparable and commensurate (e. g., let any one without its use say whether the total cost per pupil is more or less closely followed by the cost per pupil of text-books and supplies than by that for janitors' salaries). It is necessarily obscure; (1) because the general tendency for which it stands represents a result which an indefinite number of different arrangements of relationships could all equally give, and (2) because the variability of the individual relationships, from which it rescues us in part, still remains to prevent any prophecy of the coefficient's implication concerning any special case other than a most complicated statement of probabilities. Readers who are familiar with modern statistics will have gained a con- crete acquaintance with coefficients which will make tables XXXVII, XXXIX, etc., clear and emphatic. To others they cannot be. On the whole, although the arithmetical labor of calculating these coefficients is enormous, they should be used in all studies of relationships of mental and social traits. Those calculated by Mr. Strayer will increase in importance as we obtain from the budgets of private schools, colleges, business cor- porations, and the like, similar coefficients to compare with them. One other feature of Mr. Strayer's method of presentation needs comment — his careful arrangement of the individual measures from which all his later results are derived. The pub- lication of these in full enables any critic to verify the conclu- sions, any investigator of the same problem to combine new data with them so as to get better advantages from both, and any investigator of other problems to use in his own way a body of facts which could be obtained now only at a cost of hundreds of hours, and in a few years could not be obtained at all. The reader who is irritated, as well as awed, by the pages of indi- vidual records must remember that in the social sciences lump- ing facts into averages and totals conceals far more truth than it reveals, and destroys half the value of the record to the expert. Edward L. Thorndike April, 1905 City School Expenditures THE PROBLEM The financial problem in connection with our public schools is fundamental. We may devise improved courses of study, we may provide for the proper training of teachers, our aim may be sound and our method well grounded, and still we must have the money to build and properly equip and maintain buildings, to provide the necessary books and supplies, to hire the competent supervisors and teachers, or all will count for naught. We believe that our schools have advanced in this country during the past fifty years, and we know that along with this advance the amount of money spent for public educa- tion has increased in a ratio altogether out of proportion to the number of people educated. Still further, we believe that those sections of our country which to-day spend the most money for public education are the sections which are doing the best work. Especially with the growth of cities and the great increase of urban population has the amount of money spent for public schools grown larger. But even the great increase in expendi- ture, amounting in some cases to ten- or even twenty -fold during the past fifty years, has not been sufficient to satisfy the de- mands of those who believe in the efficacy and necessity of public education in our modern democracy. President Eliot, in his address before the Connecticut State Teachers' Association in 1902, argued for more liberal expendi- tures for public education, in order that we might accomplish by this means certain desirable ends which we have as yet failed to attain. He sums up his argument in one part of his address as follows: "My first argument in support of this proposition is that, as a nation and on the whole, in spite of many successes, we have met with many failures of various sorts in our efforts to educate the whole people, and still see before us many unsurmounted difficulties. It is indisputable that we have experienced a profound disappointment in the results thus far obtained from a widely diffused popular educa- tion. It was a stupendous undertaking at the start, and the difficulties have increased with every generation. Our fore- fathers expected miracles of prompt enlightenment; and we are seriously disappointed that popular education has not defended 4 City School Expenditures us against barbarian vices like drunkenness and gambling, against increase of crime and insanity, and against innumerable delusions, impostures, and follies. We ought to spend more public money on schools, because the present expenditures do not produce all the good results which were expected and may reasonably be aimed at." l In a second address to the New Hampshire State Teachers' Association in the same year, President Eliot maintained that more money should be given to the public schools, because of the great gains that have been made in public education. Some of the improvements to which he called attention were the establishment of kindergartens, improvement in the curricula of elementary schools, increase in the number of high schools, improvement in school buildings, new kinds of schools (manual training, the mechanic arts high school, the evening school, and the vacation school), improvement in normal schools, improved methods of selecting and ap- pointing teachers, pensions for teachers, increased employment of educational experts in supervising and executive functions of urban school systems, the increased use of high schools, the introduction of the costly elective system, better university teachers, improved professional training, increased opportunity for the higher education of women, and increased attention given to the welfare of the body. Every one of these educa- tional improvements, says President Eliot, "has been costly; but every one has justified itself in the eyes of the tax-payers, or of those who voluntarily pay for it; not one would now be recalled, and the total result encourages the expectation that large new expenditures would commend themselves to the people at the start, and in the end would prove to be both profitable in the material sense and civilizing in the humane sense. "You have doubtless noticed that the gains I have reported are chiefly in education above fourteen years of age. There has been improvement in the first eight grades since 1870, but it is relatively small. Yet the great majority of American chil- dren do not get beyond the eighth grade. Philanthropists, social philosophers, and friends of free institutions, is that the fit educational outcome of a century of democracy in an unde- 1 Eliot, More Money for the Public Schdols, p. 23. City School Expenditures 5 veloped country of immense natural resources? Leaders and guides of the people, is that what you think just and safe? People of the United States, is that what you desire and intend?" 1 There is nothing unusual nor radical in this appeal of Presi- dent Eliot. In almost every educational journal one can find arguments for increased expenditures for teachers' salaries. In many states laws have been passed or proposed which declare that all text-books shall be furnished free to children. In every community new school buildings are built better than the old. More attention is given to proper heating, lighting, and ven- tilating. All this means an increase in school expenditures. Along with this great increase in expenditure and with the de- mand for still greater sums of money for public education, there has arisen the necessity for greater ability in the handling of school moneys, and, on the part of the tax-payers who furnish the money, a desire to know how the money is spent and what results are obtained. Those who have controlled our free public schools have always had the double function of attending to the business affairs of the school system, as well as looking after the matter of instruction. In the early days, when the chief expenditure was for the teacher's salary and there were very few other items of expense, it was a comparatively simple matter to administer the finances of the then small school systems. With the great growth of cities and school systems, together with the enormous increase in amount and variety of expenditures, the problem of business administration has become very complex. This de- mand for expert ability in dealing with the business affairs of the schools has been met in different ways. In some instances a special committee of the school board or committee has been given charge of the financial affairs of the schools. In many cases the superintendent has not only supervised instruction, but has also been the business manager for the school system. In other cases, notably in Cleveland and Indianapolis, a special executive officer has been provided to look after the business affairs. There is a growing feeling that the business affairs of the large school systems demand expert ability, and that it is financially profitable for a large city to employ a business 1 Eliot, More Money for the Public Schools, pp. 125-127. 6 City School Expenditures director to look after the financial interests of the school system. The Chicago Commission, appointed in 1898, recommended that the f miction of the school board "be chiefly legislative, the executive work being delegated to the superintendent and busi- ness manager." x However desirable it may be to have a special executive officer whose duty it shall be to look after the business affairs of the schools, the fact remains that in vastly the greater majority of cities of over ten thousand inhabitants this work is now done by the school board, by the superintendent of schools, or by the board and the superintendent in co-opera- tion with each other. In the year 1899 there reported to the Department of Super- intendence of the National Educational Association the Com- mittee on Uniform Financial Reports, which had been appointed at the previous meeting. Something of the purpose for which this Committee was appointed, as well as their recommendations, may be found in the following quotation: "While local conditions enter into the necessities for ex- pense in any public school system, yet one of the most useful means of estimating proper expenditures should be afforded by a study of the financial school reports of other similar cities or districts. As these reports are at present made, they are of little use in this respect. Items given in one report are omitted from another. Items of income and outgo are differently grouped in different reports, and the statement is made in such a way that it is impossible to separate the items for the purpose of re-classification. In getting the cost of education per child, different items are put into the total cost of education, which forms the dividend, while the divisor is sometimes the number enrolled, sometimes the average number in daily membership, sometimes the average number in daily attendance. "One of the chief studies of a wise administrator of schools is to make the cost of education per child as low as is consistent with the best service. Attention to this and to the compara- tive study of the reports for a period of years, now that most of our school systems are established on a somewhat similar plan, should give an idea of the average or normal cost of edu- cation per child. Having this, the manager of schools may know how expense in his system differs from this normal stan- 1 Report of the Chicago Educational Commission. City School Expenditures 7 dard, and, if not normal, why it is above or below. This knowl edge cannot be arrived at, however, until the same items are included when comparing cost of education, and the same divi- sor is used when obtaining the average. By careful compara- tive study, railroad men know the average cost of hauling freight per ton per mile, and the cost per mile of transporting a passenger. Those administering schools should be as well in- formed upon the cost of education." * Concerning the form of report recommended by this Committee, we shall have some- thing to say later. Just at this point it is interesting to verify their statement with regard to the non-uniformity of reports. Unfortunately, the work of this Committee seems to have had little effect upon the reports which have been issued since 1899. The sources of information concerning school expenditures are: the Report of the Commissioner of Education for the United States, the sev- eral State Reports, and the City Reports. In the Report of the Commissioner of Education, school expenditures for cities of over 8000 inhabitants are classified under four heads, namely: (1) permanent investment and lasting improvements, (2) teach- ing and supervision, (3) current and incidental expenses, and (4) evening schools. It is hardly necessary to state that if any comparison among different cities is to be made, a further dis- tribution of these items is necessary. The item "teaching and supervision" contains several items of expenditure which should be compared with each other; while the item "current and incidental expenses" is so general that we are unable to tell anything about the use which is made of the money. If we turn to State Reports we are again disappointed. The Massachusetts State Report classifies city school expenditures under the following heads: teachers' salaries; conveyance of pupils; fuel and care of premises ; school committee, including clerical aid and truant service ; superintendent of schools ; text- books and school supplies; school sundries; alterations and permanent repairs; new schoolhouses ; and ordinary repairs. This classification is superior to that found in the Report of the Commissioner of Education, because of the more detailed infor- mation which it gives. One might wish, however, that fuel and • Proceedings of the National Educational Association, i8qq, p. 345. 8 City School Expenditures the care of school premises could be given as separate items; and when we remember the difference in the salaries paid to high school teachers and to elementary school teachers, it would seem that these items should be further subdivided. In the Pennsylvania State Report expenditures are classified as follows: schoolhouses, purchasing, building, renting, etc.; teachers' wages; cost of school text -books; cost of school sup- plies other than text -books including maps, globes, etc. ; fuel, contingencies, fees of collectors, and all other expenses. It is easily seen that the Pennsylvania Report gives less definite in- formation than the Massachusetts Report, and that a comparison of the expenditures for cities of the two States could not be made from the material available. The New Jersey State Report classifies expenditures as fol- lows: teachers' salaries ; fuel and janitors' salaries; building and repairing; debt and interest ; manual training; text-books, ap- paratus, and supplies; transportation of pupils; other school purposes. Again it is hardly necessary to suggest that the item "teachers' salaries" is not sufficiently specific for the purpose of comparison. It may be well enough for the information of patrons to account for fuel and janitors' salaries under one head, but if one were interested in the relation between janitors' sal- aries and the amount of fuel consumed, this classification would scarcely answer the purpose. In the New York State Reports there is still less information given concerning the money expended by cities for school purposes. The City Reports, so far as I have been able to examine them, are little more satisfactory than the State and National Reports. Items which are given in one report, are omitted or combined with other items in another report in such manner as to make comparisons impossible. Frequently there is included under a single head an item of expenditure which properly belongs to current expense for maintenance and operation, and another which might better be classified as falling under the head of permanent equipment. In about half of the reports which I have examined, teachers' salaries are given as a single item. Miscellaneous expenses, that is, the money which is spent but not definitely accounted for, amounts to from one to twenty-five per cent, of the entire City School Expenditures g expenditure. In one report, school furniture and rent are given as one item. In another, janitors' and truant officers' salaries are given as a single item, without any explanation as to whether the janitor acts as truant officer or not. Text-books, supplies, permanent equipment or apparatus make one item of another report. Fuel and repairs are grouped together in another, and so on through the entire list. Mr. Jesse D. Burks, in an unpub- lished study, found three thousand different heads under which information concerning city school systems was given in the annual reports. It was because of this state of affairs that the Committee of the National Educational Association on Uniform Financial Reports was appointed; and it was with the same problem in view that President Butler, in a discussion of a paper on "Taxa- tion and Teachers' Salaries" before the National Educational Association in 1902, said: "What we need and need very badly in this country, is not only a more scientific system of taxation, but more adequate and exact information as to what should be the relative cost of various elements in the disbursements of our cities, towns, and villages. For example, no one knows just what ought to be the normal cost of the public school system of a city of 250,000 people. We know how rapidly such popula- tion increases, and how many children of school age come under the care of the community each year, but we do not know what the school system should normally cost, or what should be the proportion of its cost to the total cost of maintaining the local government. Nor do we know what proportion of a city school system should be charged to teachers' salaries, what to supplies, what to supervision, and what to the other items which make up the total bill of expense. Here is a field of investigation which is of surpassing interest, not only to school officer and superintendent, but to every intelligent citizen. It cannot be entered upon too soon, for the subject is one that goes to the very bottom of our public life." » The problem which we have undertaken in this investiga- tion is a part of that which President Butler so clearly outlined. This study will deal with the distribution of the money spent for schools among the various items of the budget. Whether or not we may hope to determine the norm which 1 Proceedings of the National Educational Association, 1902, p. 329. IO City School Expenditures should be followed, of this we are certain, that some informa- tion concerning current practice can be secured, and that a solution to some of the problems which arise may be suggested because of this more adequate knowledge of present conditions. DATA The data which furnish the basis of this study were secured from fifty -eight cities of between ten and fifty thousand inhabi- tants, located in Massachusetts, Rhode Island, Connecticut, New York, and New Jersey. To the Superintendent of Schools in each city the following blank form was sent : ©jcrlwrabia WLnivRV&itvi Hew ffavfc. Data for research in Educational Administration. tures for the year igo and igo , in the city of state of School Expendi- No. I. Current Expenses : i. Salaries for supervision (Superintendent, Assistant, Dep- uty, or Associate Superintendents, and Principals) 2. Salaries for business administration (salaries of members of the Board of Education, Business Manager, Superinten- dent of Buildings and Grounds, Clerks to Board of Edu- cation, etc., etc.) 3. Salaries of Janitors (number and aggregate of their salaries) 4. Salaries of Matrons or Maids in connection with Kin- dergartens and Baths (number and aggregate of their salaries) 5. Salaries of Truant Officers (number and aggregate of their salaries) 6. Salaries for Teaching: Number of Elementary School (Primary and Gram- mar) Teachers and aggregate of their salaries. . . Number of High School Teachers and aggregate of their salaries Number of Kindergarten Teachers and aggregate of their salaries Number of Evening School Teachers and aggregate of their salaries City School Expenditures ii ii. 12. 13- 14. IS- 16. i7- 18. 19. 20. 21. Salaries for Teaching: (Continued.) No. Number of Truant School Teachers and aggregate of their salaries Number of Teachers' Training School Teachers and aggregate of their salaries Number of Special Teachers or supervisors of spe- cial subjects (Manual Training, Cooking, Sewing, Drawing, Music, Nature Study, Penmanship, Physical Education, etc.) and aggregate of their salaries Number of Vacation School and Play Ground Teachers and aggregate of their salaries What are the daily wages of (1) Carpenters, $ (2) Bricklayers, $ (3) Day Laborers, $ in your city? Text-books, including copy- and drawing-books and re- pairs to books Supplies consumed by pupils (paper, pencils, ink, chalk, pens and pen-holders, erasers, laboratory, manual train- ing, cooking, and kindergarten supplies, etc., etc.) Janitors' Supplies (brooms, brushes, towels and washing of towels, toilet paper, soap, etc., etc.) Supplies for Board of Education, Superintendents', and Principals' offices Fuel .' Light and Power Water Ordinary repairs to Buildings and Grounds Rent School Census Transportation of Pupils Insurance Freight and Expressage Printing and Advertising Telegraph, Postage, etc 22. Telephone 23. Other Current Expenses: Are books furnished free to indigents ? to all stu- dents? What supplies are furnished free to in- digents? .to all students?. «a 12 City School Expenditures II. Plant and Permanent Equipment: i. New buildings and sites, furniture and furnishings for new buildings, and permanent improvements to buildings 3. Permanent equipment or apparatus (scientific apparatus, tools or apparatus for manual training and cooking, type- writers for commercial departments, maps, charts, globes, VI. All other Expenditures : (If important expenditures have been omitted in the above classification, will you kindly itemize such expendi- tures below.) Total Expenditures for the year: VIII. Paid for Evening Schools [total current expenses, included in IX. Paid for Teachers Training Schools [total current expenses, in- Cities of between ten and fifty thousand inhabitants were chosen because this is the type city in the United States. Of 562 cities of over eight thousand inhabitants, according to the census of 1900, 481 cities are between eight and fifty thousand. Not only is the city above fifty thousand much less common than the city of fewer inhabitants, but it is more apt to present problems peculiar to itself, and hence does not admit so well of comparison. Even if it had been possible to secure information from as many of the larger cities, they would necessarily have been so scattered, and conditions of climate, rate of growth in population, general economic welfare, tradition with regard to public education, etc., would have been so different that a comparison could not so well have been made. After having chosen the size of city to be studied, the terri- City School Expenditures 13 tory was limited to the states named above because it was felt that in this region conditions were very similar. In the territory covered there are 117 cities of between ten and fifty thousand. For the school year 1902—1903 the blank form given above was filled out by fifty-eight cities. For the school year 1 903-1 904 similar data were secured from thirty of these cities before this investigation was completed. The form of report used was drawn up with two purposes kept constantly in mind, namely: first, that the several items of expenditure should be so reported that they would admit of comparison; second, that as far as possible the whole expendi- ture should be reported under proper heads — that the item generally termed "miscellaneous expenses" should, so far as possible, be eliminated. It will be noticed, however, that a place for reporting such expenditures was allowed to remain on the blank. In preparing this form, we considered carefully the form of report recommended by the Committee of the National Educational Association, and have in some parts followed their classification. On the other hand, it seemed to us that in more than one instance their classification was not the best, because it did not provide for sufficient detail. The first item under expenditures in that report is salaries of teachers and super- visors. Now, if a comparison is to be made, it seems to us that this item needs to be further subdivided. It may be that one city is paying entirely too much for supervision. We may want to discover if there is any relation between a large amount of money spent for supervision and the amount spent for school supplies. In order to discover these things, it will be necessary for us to subdivide the item of "salaries." Again, in order that we may be able to make a valid com- parison, it has seemed wise to divide the salaries for teaching into several items, namely: the amount paid elementary school teachers; high school teachers; kindergarten, evening school, truant school, and teachers' training school teachers; special teachers, or supervisors of special subjects; and teachers in vacation schools and play grounds. As stated above, we can only compare the item of salaries when we know in what way that money was spent. In the report of the National Educational Association Com- mittee, supplies are classified under two heads — stationery and 14 City School Expenditures other supplies for schools. We have thought it best to classify- all supplies consumed by pupils under a single head, including in this item paper, pencils, ink, chalk, pens, pen-holders, black- board erasers, laboratory, manual training, cooking, and kinder- garten supplies, etc. In order that we may be able to use this item and that of text-books intelligently, our form contains the following questions : Are text -books furnished free to indigents ? Are they furnished free to all pupils? What supplies are fur- nished free to indigents ? to all students ? Other supplies are classified under two heads: janitors' sup- plies and supplies for the board of education, superintendents', and principals' offices. Besides the item of janitors' salaries, we include, as a separate item, salaries of matrons or maids in connection with the kindergartens or baths. In addition to the item of fuel and light (which we classify under two heads, namely, fuel, and light and power) and or- dinary repairs to buildings given in the National Educational Association Report, we have seen fit to classify current expenses under the following additional heads: water; rent; school census; transportation of pupils; insurance; freight and ex- pressage; printing and advertising; telephone, telegraph, postage, etc.; and other current expenses. We did not expect that all would report expenditures under each of the above heads, but we do think that if there are such expenses it is best that they be reported separately. Our second large heading we have designated as "plant and permanent equipment." Under this head we make four sub- divisions, namely: (i) new buildings and sites, furniture and furnishings for new buildings, and permanent improvements to buildings and grounds; (2) furniture exclusive of that put in new buildings; (3) permanent equipment or apparatus, includ- ing scientific apparatus, tools and apparatus for manual train- ing and cooking, typewriters for commercial departments, maps, charts, globes, etc.; (4) reference and library books. In asking for the amount paid on principal of bonded debt, on principal of loans, for interest, the total current expenses for evening schools, and for teachers' training schools, we have fol- lowed the recommendation of the National Educational Asso- ciation Committee. In another part of the report, we ask for the wages of car- City School Expenditures 15 penters, bricklayers, and day laborers in the city from which information is received, hoping in this case to be able to infer something concerning the cost of living in that city, which will in turn enable us to form a correct idea concerning the salaries paid to teachers. Of the fifty-eight cities reporting the first year, thirty were able to report their total expenditure under the classification given, without resorting to the use of the ambiguous heading "miscellaneous." Of the remaining twenty-eight cities, sixteen reported less than 2 % under the head "miscellaneous"; ten others reported less than 5 %; and the remaining cities re- ported 5.14 % and 6.75 % for unclassified expenditures. For the second year, of the thirty cities reporting, eighteen report nothing under "miscellaneous"; and of the remaining twelve, eight re- port 1 % or less, three 2 %, and one 3.76 % under this head. In order to compare the expenditures in the different cities with but two years' data, it seemed best to base all compari- sons upon the cost of maintenance and operation, that is, the ex- penditures which are absolutely necessary in order to keep the schools going, together with the amount spent for keeping the plant in proper repair. Under this head we included furniture put into old buildings, that is, new furniture put in to replace old ; and also money spent for apparatus and for reference and li- brary books. These expenditures, we believe, are properly classi- fied as expenditures for maintenance and operation, since they seldom represent any very large increase in permanent equip- ment. In the printed form given above, they were placed under "plant and permanent equipment," because the writer be- lieved that it was customary to place them there and that proper returns could be most easily secured by classifying them in this way. To have taken into consideration the amount spent for new buildings or grounds, or for permanent improve- ments, would have been unfair to some cities, because in some cases a much larger proportion of such expenditures is met by an issue of bonds than in others. The item of interest is not included in the cost of maintenance and operation for a similar reason. This item is sometimes included in the public school budget, while in other cases it is paid by the city. On this point the National Educational Association Committee on Uni- form Financial Reports says : "Expenditures seem to fall into three classes: the usual 1 6 City School Expenditures current expenditures necessary for the maintenance of schools ; expenditures for sites, buildings, permanent improvements and equipment; other expenditures which, for various reasons, are not put in either of the two preceding classes. ' ' For the purpose of this report the first of these classes is by far the most important, for it would probably be conceded that from this item of current expense should be determined the cost of education per child, the most important item to be shown." x After having determined the classification to be used, and that the total expenditures for maintenance and operation should serve as the basis for comparison, the question which next arises is, "How shall the separate items be compared as among the different cities?" It has been common to compare the expenditures for different cities on the basis of the cost per pupil in daily attendance. We shall use this method, and, in addition, it seems well to compare the different items on a slightly different basis, namely, the cost per pupil based upon a figure half-way between the average daily attendance and the average daily enrolment. In discussing this point, the National Educational Association Committee on Uniform Financial Re- ports says: "For many reasons No. 39" (average number in daily mem- bership, all schools) "seems the most suitable divisor. If com- puted in a uniform manner, the figures showing number in average daily membership would most nearly show the require- ments for school rooms, furniture, supplies, and teachers. But it is not true that these figures are obtained by the same pro- cess, or based upon the same facts, in the different school sys- tems. Usage varies so in computing membership in different schools — pupils in some cases being counted as members of the schools, when in other cities the same state of facts would cause the child to be considered as no longer a member of the school — that fair comparison is apparently not practicable by the use of this divisor. "Your committee is of the opinion that a divisor as little subject to misunderstanding as possible, and one based upon facts which are obtained in the same way everywhere, is of the first importance. The members believe that this is provided by item 40, average number in daily attendance, all schools, 1 Report of the National Educational Association, i8gg, p. 347. City School Expenditures 17 and we have, therefore, made that item the divisor to be used, in connection with items 12 and 13, to obtain what shall be known as the 'cost of education.' " 1 The school must provide teachers, buildings, and equipment for more than the average daily attendance, and yet it is seldom that provision is made for a number equal to the average daily enrolment. It seems, therefore, that the figure half-way be- tween the two is a better figure than either of the others. It was impossible to secure the figures for the average daily enrol- ment in some cases, and for this reason the average cost per pupil for the first and second year will be based upon the average daily attendance, even though we do not believe it is so good a figure as the other. Still another basis for comparison recommends itself — the apportionment of money spent for specific purposes expressed in per cents of the total expenditures for maintenance and operation. This last classification offers a particularly interest- ing basis for comparison and is entirely free from obscurity. The question is simply one of distribution of the money that is spent among the several items of the budget. Just as an in- dividual may spend too much for clothes, for food, for books, or for amusement, in the same manner it is possible for a city to spend too great a proportion of its money for janitors, for fuel, for school supplies, or even for supervision. The information which has been collected is given in the tables which follow. Throughout the study each city is known by the number which is given it in the first table. These tables (Tables I to IX) contain every fact with which we work. Any one can, from the data here given, repeat all our calculations. Moreover, it may happen that some one else may wish to use the information which furnishes the basis of this study for a different purpose. It is unfortunate that many studies, involving the use of data which were secured with con- siderable difficulty, have been published without giving the data upon which the conclusions were based. Such an omission makes it impossible for any one else to verify the conclusions which the author has reached, and denies to others the use of valuable data which they might use for purposes quite as im- portant as those for which the information was first collected. 1 Report of the National Educational Association, i8gg, pp. 349-352. TABLE I Gross expenditures for maintenance and operation for the school year 1902-03. Fifty-eight cities of from 10,000 to 50,000 inhabitants in Massachusetts, Rhode Island, Connecticut, New York, and New Jersey. The amounts are scored in dollars. >, o o "3 M a u 0> O Books, plies. "p. p. W c -M u d O ■eg.s 3 U 1 PL, *d ,2 H P. a x 3 u fe CI) H 3 W 1—1 '5 ni 1—1 'd-d i 3 I. 76,252 47,712 2,200 392 5,033 300 3,919 2,531 664 83 3,473 359 2. 60,492 38,015 2,000 150 350 2,690 662 300 10,163 286 3- 52,708 35,918 2,100 3,725 3,235 530 2,481 2,399 4- 153,729 98,028 16,570 550 10,950 400 5,194 4,449 1,078 7,357 353 5- 121,400 89,100 2,700 650 8,000 950 7,300 200 300 7,400 600 6. 50,613 36,860 2,100 2,660 3,315 100 50 2,079 130 7- 85,975 57,320 7,600 500 9,113 810 2,401 3,596 816 3,560 8. 60,473 35,150 8,200 8,675 750 3,000 900 100 200 3,528 100 9- 100,484 66,883 2,800 1,080 7,520 500 6,749 9,414 IO 217,991 160,832 3,683 1,482 12,886 1,000 5,011 7,052 583 913 9,285 572 ii. 82,100 40,800 9,490 900 7,500 900 5,500 5,000 500 12. 71,281 45,775 6,500 5,402 168 2,075 2,660 5,000 13- 95,802 51,578 16,660 614 6,587 900 2,493 2,706 234 6,309 179 14. 39,960 24,828 2,000 2,717 100 1,243 993 109 3,271 200 15. 116,039 82,062 2,500 550 7,019 200 4,607 4,607 310 7,801 314 16. 25,639 17,290 2,000 1,641 350 742 849 1,297 17. 99,717 62,645 7,800 600 7,000 400 2,901 3,061 30 7,320 815 18. 43,570 30,700 1,950 2,960 100 3,300 2,800 19. 52,870 33,250 1,800 350 3,600 70 2,500 1,500 3,800 20. 59,772 42,730 1,275 3,080 400 1,422 929 95 5,896 78 21. 52,178 36,080 6,575 100 3,070 100 800 200 100 2,000 100 22. 17,368 12,856 205 727 1,018 259 37 714 60 23. 45,745 13,150 13,450 300 6,839 300 4,531 24. 29,787 19,296 2,750 450 1,861 200 422 30 30 2,000 136 25. 30,398 21,250 2,400 1,500 100 100 30 50 2,000 35 26. 95,064 53,487 15,920 550 5,580 100 1,922 2,899 123 91 4,220 143 27. 40,622 22,812 4,250 2,951 2,473 725 1,899 28. 46,041 30,001 1,800 590 3,328 300 1,732 3,474 29. 56,374 34,745 1,640 3,944 175 3,847 640 2,870 ■~20 TABLE I {Continued) Gross expenditures for maintenance and operation for the school year 1902-03 Fifty-eight cities of from 10,000 to 50,000 inhabitants in Massachusetts, Rhode Island, Connecticut, New York, and New Jersey. The amounts are scored in dollars. 3 c ■a "gei bo 3 . .2 31? nd ools tems n). . 3 3 1-1 as en u ■3 P. a) Pi 3 jj CD 3 "U r-l 0£ O " O O CO '■£ t/i "tTa 3 u 3 nJ u 3 3 a! tn 60.2 .si Ph< O A . . O .3 ** ft" of u CD 3 ,3 P. H O CO a cu 3 « j5 § "u ft X .213 3 cS u of ft ft < of 2 £,■" it £ >> (art >> *3 w|^ I. 4,018 15 528 1,570 337 245 53 220 1,248 308 1,008 35 1,503 2. 141 3,249 100 100 1,800 35 300 150 1,821 3- 2,044 275 839 4- 581 5,087 264 100 237 ISO 50 441 546 1,306 1,556 5- 1,200 400 1,260 40 400 600 300 3,200 6. 2,000 750 94 79 25 20 350 762 7- 6,356 100 2,000 833 140 492 43 12 283 8. 200 2,278 100 1,088 369 75 150 50 60 250 150 100 760 9- 550 150 150 86 4,602 794 10. 1,144 11,542 250 974 528 44 ii. 3,500 400 750 750 100 110 10 150 1 5,540 200 1,800 12. 2,500 163 98 690 100 150 ' 1,153 13- 520 2,496 140 100 455 1,560 158 156 35 5 1,211 451 204 48 874 14. 2,811 48 36 646 134 76 239 298 140 70 IS- 3,173 800 125 997 159 260 33 37 100 325 16. 300 1,030 50 89 635 17. 3,974 85 1,000 190 333 40 75 225 332 690 200 1,924 18. 1,200 60 300 50 100 25 25 19. 200 3,000 125 1,500 90 100 15 20 300 650 20. 531 2,192 225 190 138 32 557 522 21. 80 2,000 305 50 30 20 18 400 150 250 22. 1,148 22 33 25 108 5 150 23- 280 3,216 213 120 1,440 15 675 276 940 24. 277 873 54 618 91 15 49 377 250 25- 250 1,800 75 250 10 250 10 138 50 100 26. 523 3,254 556 281 100 1,280 76 300 50 43 500 3,065 808 27. 181 957 818 155 50 116 369 669 412 28. 2,092 216 194 76 1,350 355 532 1,690 29. 158 6,008 126 696 266 220 669 350 19 TABLE I (Continued) Gross expenditures for maintenance and operation for the school year 1902-03. Fifty-eight cities of from 10,000 to 50,000 inhabitants in Massachusetts, Rhode Island, Connecticut, New York, and New Jersey. The amounts are scored in dollars. r » V • ST H w ■ o « 75. w wfe^l 30. 110,846 74,946 3,000 800 7,013 1,000 1,892 3,087 765 5,481 206 31. 70,593 39,850 2,000 700 4,650 800 3,957 8,826 225 32. 80,361 44,437 3,000 700 4,500 400 852 1,500 301 1,500 5,249 592 33- 21,515 14,525 2,750 300 1,320 78 149 38 25 1,072 35 34- 49,993 32,176 2,160 600 4,060 780 25 458 300 200 5,025 108 35- 104,414 76,142 2,100 717 6,811 750 90 411 260 5,916 282 36. 38,677 22 809 6,700 300 1,340 120 250 80 20 2,000 271 37. 50,462 29,874 8,502 1,017 2,656 250 1,043 3,024 38. 24,278 15,686 1,800 934 400 50 100 155 50 1,336 39. 51,887 32,305 5,750 500 2,700 400 909 400 3,416 40. 54,614 34,362 2,225 694 2,172 450 945 2,282 177 4,804 41. 87,209 56,574 3,662 1,626 4,004 84 4,952 126 20 5,294 418 42. 89,467 48,525 13,900 1,000 4,684 1,000 4,500 3,500 500 5,000 43- 62,348 40,642 2,200 397 4,143 500 1,166 1,053 431 67 5,520 236 44. 48,410 30,852 2,200 300 2,930 420 569 61 750 4,844 234 45- 88,459 59,334 2,000 150 4,730 600 4,815 1,071 250 150 3,343 806 46. 107,537 66,153 12,200 800 4,930 540 3,076 1,854 1,008 500 4,229 128 47- 58,427 16,294 9,500 2,108 4,931 500 1,950 1,620 9,411 347 48. 18,402 10,745 1,800 200 1,100 244 787 250 40 30 1,131 41 49- 14,877 9,512 1,800 100 600 200 771 150 100 52 814 50. 81,954 51,099 5,700 1,400 2,775 500 3,685 1,303 150 5,128 214 51. 64,465 42,350 8,950 650 3,525 425 1,200 300 150 50 3,600 70 52. 100,305 52,500 6,625 725 7,000 600 3,000 3,500 625 450 4,500 53-144,783 96,925 17,700 1,000 9,990 7,057 1,397 4,034 54- 75,700 42,225 8,100 950 4,200 2,900 3,450 600 250 3,750 800 55- 35,800 22,000 1,200 200 1,900 400 2,000 2,000 200 56. 50,192 27,415 8,175 400 4,200 150 800 929 600 844 2,195 203 57. 114,800 74,375 11,400 2,150 5,425 3,000 5,000 250 250 4,500 500 58. 77,200 48,650 7,455 500 4,180 5,000 1,000 500 2,500 200 TABLE I (Continued) Gross expenditures for maintenance and operation for the school year 1902-03. Fifty-eight cities of from 10,000 to 50,000 inhabitants in Massachusetts, Rhode Island, Connecticut, New York, and New Jersey. The amounts are scored in dollars. o "o U u e 3 55 u a) Is w u '3 a u a Pi 3 in G 01 O "0 O 'o c .0 t!"ft 3 a u H Insurance. Freight and Express. bo- 2 .St P*< Telegraph, Postage, etc. Telephones. Miscellaneous Expenses. 3-~. P" bo g'J "e v E a fe-S 3 u a P, a < Reference and Library Books. Evening Schools (included in items already given). 30. 8,157 75 931 660 351 1,021 201 1,261 675 3i. 4,522 250 270 194 370 96 2,551 886 446 2,047 32. 8,541 300 424 151 644 240 3,014 2,000 500 1,516 33- 1,011 62 50 9 55 21 15 34- 730 266 250 730 615 96 239 850 325 35- 2,915 185 370 75 678 80 249 4,202 590 696 903 36. 218 877 125 400 75 25 25 100 494 230 326 37- 1,179 100 291 1,646 878 38. 2,386 50 279 25 148 21 319 50 189 300 39- 2,200 98 949 60 4 2,200 40. 396 1,909 72 799 47 1,102 703 283 1,190 41. 763 156 1,585 201 91 616 193 229 138 194 100 523 1,277 42. 1,000 2,500 1,006 75 260 50 150 1,000 500 317 43- 369 1,546 100 259 171 31 25 310 52 39 1,734 417 528 407 44- 393 2,079 1,116 595 94 130 30 284 335 194 45. 6,139 982 108 780 100 1,452 395 150 443 46. 360 2,787 3,870 277 197 571108 485 108 1,500 600 656 619 47- 120 7,706 382 1,048 662 188 1,196 100 364 844 48. 96 275 450 50 84 30 291 10 591 68 41 50 49- 27 198 35 87 26 17 6 41 135 133 73 50. 5,642 1,000 318 193 50 508 150 10 1,729 369 51. 1,200 50 595 35 125 25 90 75 500 500 52. 15,000 1,200 700 800 100 1,800 ] L.000 180 53- 4,681 1,999 2,495 54- 3,175 350 600 275 350 50 275 915 350 1,675 280 1,950 55- 1,000 3,500 500 500 400 56. 2,683 284 152 119 443 300 100 200 57. 5,000 250 250 300 150 1,000 500 500 650 58. 350 4,000 850 100 5 100 10 200 100 1,500 TABLE II Gross expenditures for maintenance and operation for the school year 1903-04, thirty of the cities which reported for 1902-03 reporting. The amounts are scored in dollars. 8 £ • H S i« pq 5. 124,160 90,100 2,700 640 8,400 920 3,500 1,200 200 200 10,000 800 6. 44,648 26,957 2,100 2,970 50 1,000 2,000 150 3,500 175 8. 63,749 44,554 2,100 3,675 750 3,000 600 100 100 3,500 13. 114,634 70,099 15,455 500 6,518 1,000 2,663 3,434 7,548 14. 41,793 26,935 2,000 3,306 101 1,043 1,319 47 3,565 15. 116,108 70,129 18,020 675 7,390 200 2,490 3,928 168 98 6,783 229 16. 26,918 18,381 2,000 1,819 200 442 897 1,899 20. 59,423 43,106 1,800 3,256 400 2,000 1,181 123 5,011 61 27. 40,637 22,59S 5,686 3,217 2518 902 74 28. 47,036 31,195 1,800 570 3,328 300 1395 6,303* 29. 50,616 32,349 1,547 250 4,263 146 4,037 _ 3,087 45 30. 117,263 78,771 3,000 850 7,342 31. 77,025 50,751 2,000 700 5,075 32. 68,924 38,100 11,300 750 5,000 34. 45,412 29,105 2,000 600 4,S57 35. 123,116 89,360 6,775 5,870 36. 38,904 26,070 6,500 300 1,424 37. 53,161 31,107 9,283 1,121 2,790 39. 46,859 29,000 5,950 480 2,580 40. 54,556 27,563 9,850 1,200 1,980 41. 90,956 51,597 12,830 1,637 4,123 42. 92,550 50,050 14,600 4,784 43. 71,995 51,961 2,200 491 4,527 45. 91,573 61,140 5,800 1,200 5,255 48. 23.806 13,454 3,425 250 1,290 52. 106,235 63,885 " 5,950 2,300 8,400 54. 70,496 36,716 8,450 600 3,736 55. 32,000 21,525 2,000 200 1,900 56. 49,888 33,525 2,200 400 4,150 57. 120,163 77,915 11,500 2,150 6,725 * Including repairs 1,100 1,978 536 3,263 5,055 188 800 7,766 113 400 1,100 800 500 348 4,150 541 780 52 663 1,070 1,639 810 100 500 407 300 7,808 149 200 250 75 20 2,500 192 250 664 100 4,198 24 400 1,454 626 1,113 3065 450 1,475 2,080 274 3248 68 5,035 280 191 6,684 282 1,000 4,690 3,803 606 1,051 4,400 221 500 1,500 653 585 100 2,210 239 600 3,573 1,500 500 400 3,709 900 300 854 830 30 200 1,215 25 1,000 4,200 3,500 500 350 4,000 1,000 5,450 7,275 150 4,086 1,800 150 50 1,500 400 100 900 1,200 500 100 2,195 203 3,000 4,375 4,750 800 TABLE II (Continued) Gross expenditures for maintenance and operation for the school year 1903-04, thirty of the cities which reported for 1902-03 reporting. The amounts are scored in dollars. n G tn +3 '6 o 14 S t-c a! t/i u '3 p. 0) Ph 43 a n tn a vx ct .2 + 3 tn u ft 3 ftp* a ci u T3 9 fi m 3 bog" bo c M tn s.S Sg ft u •S3; S &< g> 1) ft 1 tn P . O tn v s 2-° a a u fa a ft ft £ >, bed >, 11X1 ftS c *3 £|-a 5- 1,200 400 1,400 125 150 75 50 1,300 200 500 100 2,300 6. 4,000 75 750 450 116 75 50 30 200 852 8. 180 2,200 100 1,211 500 50 200 75 205 50 600 400 13- 600 2,733 117 360 939 168 2,500 756 14. 1,972 130 39 675 193 173 111 24 18 110 30 15- 3,287 800 125 893 100 354 36 35 267 100 16. 300 786 50 144 612 20. 1,415 158 185 345 692 628 27. 182 1,500 500 526 17 1,494 645 330 131 28. 6,303 198 : L.228 718 2,733 29. 176 2,592 125 788 184 211 434 400 30. 10,822 75 985 355 427 1,995 1,057 31- 7,025 290 543 214 99 447 667 1,277 32. 2,500 240 850 201 251 240 600 800 250 34- 2,326 250 1,500 25 96 50 200 200 35- 6,069 795 50 300 100 240 1,273 1,566 744 800 36. 210 50 60 168 60 75 15 100 410 75 150 37- 2,415 504 379 100 225 39- 1,871 209 60 40. 403 2,051 50 1,318 60 2,036 518 41. 568 3,252 200 182 139 367 59 26 2,280 572 585 42. 604 3,120 751 99 213 110 1,068 750 630 43- 559 2,095 100 730 50 437 100 141 1,705 552 277 384 45- 4,634 350 200 762 100 438 388 175 350 48. 40 920 30 100 540 40 60 100 103 52. 5,000 2,500 650 700 100 1,000 1,000 200 54- 2,000 350 443 50 100 25 200 614 256 55- 400 100 10 75 790 600 500 56. 1,800 283 200 152 50 119 310 1,000 200 300 1,000 57- 5,000 900 250 500 200 100 500 900 400 200 750 23 TABLE III The amounts spent for each item expressed as per cents of the total amount spent for maintenance and operation. Fifty-eight cities, for the school year 1902-03. Number of City. Teaching. a .0 'w ■> 14 ft 3 Ih 10 u 'S rt >— > w Ih ft) O 56 c 1-1 co ft ft < S m.2 fcW £< 09 •d oi 3 . O.bo c ^ s 0] o c <2 §3 u 0. o SPQ 3« S fe' S E c P^J 30. .8 .6 .3 .9 .2 1.1 31- .4 .4 .3 .5 .1 3.6 1.3 .6 32. .4 .5 .2 .8 .3 3.7 2.5 .6 1.9 33- .3 .2 .1 .3 .1 .1 34- .5 .5 1.5 1.2 .2 .5 1.7 .7 35- .2 .4 .1 .7 .1 .2 4.0 .6 .7 .9 36. .3 1.0 .2 .1 .1 .3 4.9 1.3 .6 .8 37- .2 .6 3.3 1 .7 38. .2 1.2 .1 .6 .1 1.3 .2 .8 1.2 39. .2 1.8 .1 4.2 40. .1 1.5 .1 2.0 1.3 .5 2.2 41. 1.8 .2 .1 .7 .2 .3 .2 .2 5.1 .6 1.5 42. 1.1 .1 .3 .1 .2 1.1 .6 .4 43- .2 .4 .3 .1 .1 .5 .1 .1 2.8 .7 .9 .7 44. 2.3 1.2 .2 .3 .1 .6 .7 .4 45- 1.1 .1 .9 .1 1.6 .4 .2 .5 46. 3.6 .3 .2 .5 .1 .5 .1 1.4 .2 .6 47- .7 1.8 1.1 .3 2.0 .2 .6 48. 2.5 .3 .5 .2 1.6 .1 3.2 .4 .2 .3 49. .2 .6 .2 .1 .1 .3 .9 .9 .5 50. 1.2 .4 .2 .1 .6 .2 2.1 Si. .1 .9 .1 .2 .1 .1 .1 .8 .8 52. 1.2 .7 .8 1.8 1.0 .2 53. 1.4 54- .5 .8 .4 .5 .1 .4 1.2 .5 2.2 .4 55- 9.8 1.4 1.4 1.1 56. .3 .2 .9 .6 .2 .4 57- .2 .2 .3 .1 .8 .3 .4 58. .1 .3 .1 1.9 27 TABLE IV The amounts spent for each item expressed as per cents of the total amount spent for maintenance and operation. Thirty cities, for the school year 1903-04. >. tn to .52 a 0. '2 £2 1-.' CD o o 2 .2 '> u u u u in O O PQ GO "ft "p. a 3 C3 xn . w £"3. *3 3 1 •a c CO at .a S 3 (8 O a 3 5 'a C() 1—1 •** a Xi CD .2 '> u u CD a 3 to u CD S3 '5 1— > CD O ifi O a 2 .2 "Vd CD O g 1 u CD is £ H 3 ct) 5 O rt 3 i. 34.18 21.38 .99 .17 2.26 .14 1.75 1.13 .30 .03 1.56 .16 2. 26.48 16.69 .88 .07 .15 1.17 .29 .13 4.39 .12 .06 3. 27.09 18.47 1.08 1.91 1.66 .27 1.27 4. 30.91 19.73 3.33 .11 2.21 .08 1.05 .89 .22 1.48 .07 .12 5. 32.30 23.70 .72 .17 2.13 .25 1.94 .05 .08 1.97 16 6. 26.80 19.50 1.12 1.41 1.75 .05 .03 1.10 .07 7. 21.19 12.65 1.68 .10 2.01 .18 53 .79 .18 .78 8. 29.80 17.29 4.04 1.81 .37 1.48 .44 .05 .10 1.74 .05 .10 9. 29.29 19.50 .82 .32 2.19 .15 1.96 2.75 .16 io. 41.21 3040 .70 .28 2.44 .19 .95 1.34 .10 .17 1.75 .08 .22 n. 27.90 13.90 18.12 3.23 2.58 .31 2.56 2.14 .31 .07 1.88 1.70 1.99 .17 12. 28.28 .82 1.06 13. 28.53 15.33 4.96 .18 1.96 .27 .74 .81 .07 1.88 .05 1.6 14. 27.35 17.02 1.37 1.86 .07 .85 .68 .07 2.24 .14 15. 24.33 17.20 .52 .12 1.47 .04 .9r .97 .06 1.64 .07 16. 27.67 18.65 2.16 1.77 .38 .80 .92 1.40 17. 34.88 21.90 2.73 .21 2.45 .14 1.02 1.07 .01 2.56 .28 18. 34.59 24.39 1.55 2.35 .08 2.62 2.23 19. 27.78 17.50 .95 .18 1.90 .04 1.32 .79 2.00 .11 20. 22.53 16.13 .48 1.16 .15 .54 .35 .04 2.23 .03 .20 28. 28.44 18.55 1.11 .36 2.05 .18 ; 1.07 2.14 1.29 29. 27.91 17.20 .81 1.95 .09 1.91 .32 1.43 .01 .08 3i TABLE VI {Continued) The cost per pupil expressed in dollars and cents. The number used as a divisor is the figure half-way between the average daily attendance and the average daily enrollment. Forty-eight cities, for the school year 1902-03. <3 u a 3 03 U '3 P. Pi a Pi 3 a 6 *o CO a _o O 3 a d u H u a ni 1-1 3 *T3 (jj C bo ho u '£* "Sub s.s 60-2 .at id bo C3 en O fc . . J3 +* cS lH 60 a> CO a) s P. CO 3 . O en tu O Is +> • 3^ P. (JO *> S ^3 3 i. "a; 3 u a. -a a a ■s u a) z H en 1—1 5 pqcs 3 I. 35.64 22.30 1.03 .18 2.35 .14 1.83 1.18 .31 .04 1.63 17 2. 28.00 17.60 .93 .07 .16 1.24 .31 .14 4.70 .13 .07 3- 28.06 19.10 1.12 1.98 1.72 .28 1.32 4- 31.90 20.35 3.44 .11 2.27 .08 1.08 .92 .22 1.53 .07 .12 5- 33.27 24.41 .74 .18 2.19 .26 1.99 .06 .08 2.03 .16 6. 27.65 20.10 1.15 1.45 1.81 .05 .03 1.14 .07 7- 21.61 12.91 1.71 .11 2.05 .18 .54 .81 .18 .80 8. 31.16 18.10 4.23 1.89 .39 1.55 .46 .05 .10 1.82 .05 .10 9- 31.01 43.23 20.63 31.91 .86 .73 .33 .29 2.32 2.56 .15 .20 2.08 .18 2.91 1.84 .11 .17 10. .99 1.39 .12 .23 ii. 29.01 29.20 29.56 14.42 18.75 15.90 3.35 2.66 5.14 .32 .19 2.65 2.21 2.03 .32 .07 .28 1.94 1.77 2.Q5 1.95 .18 .05 12. .85 .77 1.09 13- .83 .07 .16 14. 28.75 17.89 1.44 1.95 .07 .89 .71 .08 2.50 IS- 25.35 17.91 .55 .12 1.53 .04 1.01 1.01 .07 1.71 .07 16. 28.41 19.17 2.22 1.82 .39 .82 .94 1.44 .33 17- 36.00 22.60 2.82 .22 2.53 .14 1.05 1.11 .01 2.64 .29 18. 35.70 28.90 25.17 18.16 1.60 .98 .19 2.43 1.97 .08 .04 2.71 2.30 2.08 19. 1.37 .82 .11 20. 23.16 16.58 .49 1.19 .15 .55 .36 .04 2.29 .03 .21 21. 24.50 16.90 3.08 .05 1.44 .05 .38 .09 .05 .94 .05 .04 22. 8.94 6.63 .11 .37 .53 .13 .02 .37 .03 23. 12.85 3.69 3.78 .08 1.92 .08 1.27 .08 24. 15.26 9.87 1.41 .23 .96 .10 .22 .01 .01 1.03 .07 .14 25. 31.00 21.67 2.45 1.53 .11 .11 .03 .05 2.04 .04 .25 26. 32.67 18.37 5.47 .19 1.92 .03 .66 .99 .04 .03 1.45 .05 .18 27. 26.96 30.30 15.11 19.77 2.82 1.19 .39 1.95 2.19 .20 1.64 1. .48 1.25 2.28 - .12 28. 14 1.38 29. 29.50 18.21 .86 2.06 .09 2.01 .33 1.51 .01 .08 35 TABLE VII {Continued) The cost per pupil expressed in dollars and cents. The average number of pupils in daily attendance is used as the divisor. Fifty-seven cities for the school year 1902-03. •M CO be 3o >• o tO 3 10 .2 0) "2» C bo "2> c8 c O to CO 3 . O to += c to 3 •O to* oS O u u | 3 $5 u ■3 0. CD a Pi a 6 "s .s CO u ft O 3 ftn. co" C as u bo 0. 3 CO to "to u '3 a i— > H Sft >*J Sft gS C O rt m 1 fa •a 1 3 V is 30. 37.32 25.25 1.01 .27 2.36 .34 .64 1.04 .26 1.85 .07 31. 27.90 15.75 .79 .28 1.84 .32 1.56 3.49 .09 32. 34.49 19.07 1.29 .30 1.93 .17 .37 .64 .13 .64 2.25 .25 33- 24.85 16.78 3.18 .35 1.52 .09 .17 .04 .03 1.24 .04 34- 35.96 23.15 1.56 .44 2.92 .56 .02 .33 .22 .09 3.61 .08 35- 24.52 17.87 .49 .17 1.60 .18 .02 .10 .06 1.39 .07 36. 31.94 18.88 5.54 .25 1.11 .10 .21 .07 .02 1.66 .22 .18 37. 19.26 11.40 15.21 3.25 1.75 .39 1.01 .91 .09 .40 .40 .05 1.15 1.30 38. 23.56 .05 .10 .15 39. 32.01 19.94 3.55 .31 1.67 .25 .56 .25 1 2.11 40. 34.79 21.90 1.42 .44 1.38 .29 60 1.45 .11 3.06 .25 41. 24.65 15.99 1.03 .46 1.13 .02 1.40 .04 .01 1.49 .12 .22 42. 28.50 15.47 4.43 .32 1.49 .32 1.43 1.12 .16 ■ L.59 .32 43. 26.09 17.00 .92 .17 1.73 .21 .49 .45 .18 .03 2.31 .10 .15 44- 26.18 16.69 1.19 .16 1.58 .23 .31 .03 .40 2.62 .13 .21 45- 28.53 19.14 .64 .05 1.53 .19 1.55 .35 .08 .05 1.08 .26 46. 41.52 25.53 4.71 .31 1.91 .21 1.19 .72 .39 .19 1.63 .05 .14 47- 20.71 5.78 3.37 .75 1.75 .18 .69 .57 3.34 .12 .04 48. 22.75 13.29 2.23 .25 1.36 .30 .97 .31 .05 .04 1.39 .05 .12 49. 22.20 14.20 2.69 .15 .89 .30 1.15 .22 .15 .08 1.22 .04 51. 32.05 21.05 4.45 .32 1.76 .21 .59 .15 .15 .02 1.79 .04 52. 26.39 13.81 20.49 30.60 1.75 3.74 5.87 .19 .21 .69 1.84 2.11 3.05 .16 .79 .92 1.49 .16 .12 .29 .18 1.19 53- 30.61 .85 54- 54.72 2.11 2.50 .43 2.72 .58 55- 20.50 12.61 .69 .11 1.09 .23 1.14 1.14 .11 56. 28.01 15.33 4.56 .22 2.35 .08 .45 .52 .33 .47 1.22 .11 57- 51.25 33.20 5.09 .96 2.42 1.34 2.23 .11 .11 2.01 .22 58. 21.51 13.55 2.08 .14 1.17 L.39 .28 .14 .69 .06 .10 37 TABLE VII {Continued) The cost per pupil expressed in dollars and cents. The average number of pupils in daily attendance is used as the divisor. Fifty-seven cities, for the school year 1902-03. « -*j . ^ *o M 3^ Number of Cit; Repairs. •4-> a V Pi 3 a 01 "0 c .0 3 B u o>> a cd u 3 to T3 ■U 11 aw •guo 5.9 •£ a 0, V CO 3 . O to 41 01 c u a a 5 to .2 cfl "3 w "w u '3 a! 1— 1 a § 1 m §• X H 3 fa 8 '3 a 0) 5- 33.67 25.33 24.59 .74 2.25 1.64 2.39 .33 6. 25.95 18.52 17.38 1.14 1.53 1.72 1.52 1.63 8. 31.76 22.99 20.34 2.65 1.87 1.92 1.80 1.14 13- 31.88 23.28 18.40 4.88 1.98 1.71 2.10 .79 14. 28.77 19.64 18.23 1.41 2.11 1.62 2.48 1.69 15. 25.00 18.58 16.39 2.19 1.55 1.69 1.57 .69 16. 28.39 21.35 19.20 2.15 1.86 1.63 1.71 .98 20. 23.11 17.23 16.64 .59 1.22 1.06 2.12 .70 27. 26.10 18.08 14.84 3.25 2.01 1.63 .91 .85 28. 29.84 20.79 19.63 1.16 2.13 1.00 29. 27.11 17.80 16.99 .81 2.07 1.99 1.50 1.26 30. 38.01 26.62 25.62 1.00 2.39 1.76 3.16 3i. 29.41 18.85 18.06 .79 1.94 3.30 2.30 32. 31.24 20.23 17.29 2.94 1.98 .89 1.97 2.34 34- 33.75 25.16 21.69 1.47 3.14 2.37 1.06 35- 27.22 20.88 19.81 1.07 1.51 1.14 1.07 36. 31.82 25.45 20.04 5.41 1.13 1.85 .38 37- 19.98 15.20 11.77 3.43 1.04 1.39 .69 39- 30.39 22.47 18.87 3.60 1.63 1.99 1.25 40. 32.96 22.33 18.81 3.52 1.26 2.03 2.45 1.19 41. 24.99 17.48 15.18 2.30 1.14 1.40 1.67 .47 42. 28.79 17.09 15.58 4.51 1.49 2.61 1.45 .89 43. 28.29 20.42 19.50 .92 1.82 .93 1.62 .77 45- 28.80 20.50 19.26 1.24 1.60 1.75 1.13 1.72 48. 25.26 17.59 14.48 3.11 1.43 1.62 1.40 .70 52. 27.70 17.32 15.63 1.69 2.07 1.91 1.00 2.66 54. 51.47 33.72 27.90 5.82 2.86 6.15 2.32 1.83 55- 19.20 13.24 12.34 .90 1.07 1.11 .99 .39 56. 29.47 21.05 18.09 2.96 2.46 1.13 1.29 1.31 57- 51.86 38.69 33.63 5.06 2.68 3.39 2.04 2.20 40 City School Expenditures 41 EXPLANATION OF TABLES Table I gives the gross amount spent for maintenance and operation for each city, and the amounts spent for each of the several items of the budget. The amounts spent for all items of expenditure should, of course, when added, give the gross amount spent, which is scored on the table as "Total." The blanks which are found indicate that the city reported nothing under this head, or that this item is included under one head with some other, in which case they are underscored, if possible. The first line of Table I reads as follows: City number one spent $76,252 for main- tenance and operation, of which $47,712 were spent for teaching, $2200 for supervision, $392 for a clerk, $5032 for janitors' salaries, $300 for truant officers, $3919 for text-books, etc. The data given in Table I is for the school year 1902-1903 for fifty-eight cities of from 10,000 to 50,000 inhabitants, located in Massachusetts, Rhode Island, Connecticut, New York, and New Jersey. Table II gives the same information as Table I for thirty of the same cities for the school year 1903-1904. Table III reduces each item of the budget to per cent, of the total. The first line reads: In city number one 62.6 per cent, is spent for teach- ing, 2.9 per cent, for supervision, .5 per cent, for clerk, 6.6 per cent, for janitors' salaries, etc. If the sum of the per cents for all of the items is taken, they should give 100 per cent. This table gives information for fifty-eight cities for the school year 1902-1903, as noted in Table I. Table IV gives the same information as Table III for thirty of the same cities for the school year 1903-1904. Table V is derived from Tables III and IV by finding the average for two years. Thus, for city number five, for the first year, teaching and supervision amounted to 75.9 per cent, of the total (see Table III, line 5, first and second items) ; for the same city for the second year this item was 74.9 per cent, of the total (see Table IV, first line, items one and two); the average of the two, 75.4 per cent., gives the first figure of Table V. In like manner, janitors' salaries, for the first and second years respectively, for city number five amount to 6.6 and 6.8 per cent. This gives us our figure, 6.7 per cent., for janitors' salaries for city number five in Table V (see Table V, first line, column three). Table VI gives the cost per pupil expressed in dollars and cents. The number used as a divisor here is the figure half-way between the average number of pupils in daily attendance and the average daily enrolment, or average number belonging, as it is sometimes expressed. As stated elsewhere in the text, it is my opinion that this is a better figure than either average daily attendance or average daily enrolment. The only reason that this basis is not used throughout the study is because the figures for average daily enrolment could not be secured for a number 42 City School Expenditures of the cities. In the section giving coefficients of correlation will be found a number of coefficients which were worked out on this basis from this table. This table gives data for forty-eight cities for the school year 190 2-1 903. The first line reads as follows: City number one spent $34.18 per pupil for the maintenance and operation of schools, of which $21.38 per pupil was spent for teaching, $0.99 per pupil for supervision, $0.17 per pupil for clerk, $2.26 per pupil for janitors' salaries, etc. Table VII gives the cost per pupil expressed in dollars and cents. The average number of pupils in daily attendance is used as the divisor in this case. The first line reads as follows: City number one spent $35.64 per pupil for the maintenance and operation of schools, of which $22.30 per pupil was spent for teaching, $1.03 per pupil for supervision, etc. This table gives data for. fifty-seven cities for the school year 1902- 1903. Table VIII gives the same information as Table VII, calculated on the same basis for thirty of these cities for the school year 1903-1904. This table is read the same as Table VII. Table IX gives the average cost per pupil for thirty cities for two years, the school years 1902-1903 and 1903-1904, for the principal items of expense. This table is derived from Tables VII and VIII, which are based on the average number of pupils in daily attendance. The first line reads as follows: In city number five the average for two years of the cost per pupil for maintenance and operation of schools was $33.67 (1902-1903, $33.27; and 1903-1904, $34.08); for teaching and super- vision the average was $25.33; f° r teaching alone, $24.59, etc - Throughout the tables a number written across the space between the columns indicates that this number applies to the two adjoining columns taken together, and similarly an underscore running across three or more columns indicates that the number applies to these col- umns collectively. VARIABILITY In the tables given above, which compare the different items of the school budget on a common basis, the most striking thing to be noticed is the variability which exists among the cities. It is the purpose of this section to consider somewhat minutely the problem of variability in connection with the apportionment of school moneys among the several items of the budget. It may not be out of place here to call attention to the ambiguity if not the positive misrepresentation of facts which results when, as in most cases where such data have been collected, the average alone is given to represent the facts. Of course, if one accepts City School Expenditures 43 the average as meaning simply that the sum of all the cases is divided by their number, no harm is done ; but if one takes the average as indicative of the general tendency or as a measure applicable to the majority of the cases, he may be most com- pletely deluded. The average expenditure per pupil for cities Nos. 22, 23, 54, and 57 for the first year (see Table VII) is $31.94. They spent $8.94, $12.85, $54.72, and $51.25 respectively per pupil. The average in this case does not correctly represent the group nor any particular city within the group. The thing that interests us in the measurement of any trait in a group is the range or limits within which all of the cases lie, and the grouping of the cases within these limits. If we consider the facts found in the tables already given (Tables I to IX), we find that cities differ greatly not only in the amount per pupil which they spend for the maintenance and operation of their schools, but also that even where cities spend about the same amount per child, the distribution of this money among the several items of the budget is very different. Again, when we consider simply the distribution of the money that is spent, regardless of the amount, as is done in the table which gives the per cent, which each item is of the total cost of main- tenance and operation, we find that there is the greatest vari- ability in practice. One city spends 44 % of the cost for maintenance and operation (see Table III) for teaching and supervision, while another spends 82 % for the same purposes; the janitors receive from 3 % to 14 % of the money used to run the schools; supervision costs one city 1 % and another city 17 % of the whole amount spent; salaries for teaching vary from 27 % to 73 % of the budget. It would seem impossible that the money is properly distributed in every case when we consider this remarkable variability in practice. The undistributed expenditure reported under the head "Miscellaneous" needs to be considered in any argument con- cerning the variability in any item as reported by several cities. It is possible that a very large part of the amount thus reported properly belongs to some one of the items for which a report has been made. It may be that the item teaching, supervision, fuel, janitors' salaries, repairs, or some other would be greatly increased if the report had properly distributed the money. It was to guard against any such obscurity that the attempt was 44 City School Expenditures made in this study to secure a complete distribution of expen- ditures in the cities from which information was received, and, as has been noted above, this attempt was to a remarkable degree successful. Thirty cities out of fifty-eight for the first year report nothing under this head ; sixteen reported less than 2 %, ten others less than 5 %, and the two remaining reported 5.14 % and 6.75 %, respectively, as unclassified expenditures. For the second year, of thirty cities reporting, eighteen report nothing under "Miscellaneous"; and of the remaining twelve, eight report 1 % or less; three, 2 %; and one, 3.76 % under this head. It is quite evident, I believe, that the miscellaneous item is so small, even where it occurs, that it may not be used as an explanation of the variability which occurs in all items of expenditure ; and I feel that it is safe to say that the accurate distributions of the amounts reported under this head would not alter the conclusions reached in this paper. It might be argued that the great variability is due to the fact that the cities for which data are given are not comparable, that one has at its command a much larger amount of money in proportion to the number of children to be educated than an- other, and hence the variability. It is true that rightly or wrongly some of these cities are much better provided with money than others, but that does not seem to be the cause of the great variability in the apportionment of the money which they do have. Take, for example, cities Nos. 3, 6, 19, 21, 44, and 56. From the information given in Tables I and III, the following table may be built up : No. of Total No. of pupils in Cost City. Expense. daily attendance. per pupil. 3. $52,708 1,876 $28.06 6. 50,613 1,826 27.65 19. 52,870 1,831 28.90 21. 52,178 2,127 24.50 44. 48,410 1,850 26.18 56. 50,192 1,794 28.01 Per cent, spent for each item: No of _ ^. • • t -x. t^ 1 Text-books _ City Teaching. Supervision. Janitors. Fuel. an( j Supplies. Repairs. 3- Teaching. Supervision. Janitors. Fuel. 68.2 4. 7.1 4.7 72.9 4.2 5.3 6.1 62.9 3.4 6.8 7.2 69.1 12.6 5.9 3.8 63.8 4.6 6.1 10. 54.6 16.3 8.4 4.4 6.1 3.9 6. 72.9 4.2 5.3 6.1 6.6 4. iq. 62.9 3.4 6.8 7.2 7.5 5.7 1.5 3.8 21. "44 56'. 54.6 16.3 8.4 4.4 3.4 5.3 1.2 4.3 City School Expenditures 45 The variation found cannot be due in these cases to a large undistributed amount, for five of these cities distributed their expenditures in the special reports received from them accord- ing to the classification given, without finding it necessary to report anything under the head "Miscellaneous," and the other (No. 56) reports only nine-tenths of 1 % under this head (see Table III). In these cities the amount of money available and the num- ber of pupils to be provided for do not differ very much. We might expect that if there were any principle which controlled the apportionment of money, or if the money were apportioned in the best way, the proportion of the whole cost of main- tenance and operation spent for any of the principal items would be approximately the same in these cities. By glancing at the table, however, we see here the same marked variability which is found when the whole number of cities is considered. Not that there is quite so great a range, which would be very unusual because of the limited number of cases, but that the distribution of money among the several items seems not to be determined by any common principle. It seems strange that of two cities (No. 6 and No. 56) which spend respectively $50,613 for 1826 pupils and $50,192 for 1794 pupils, one should spend 72.9 % of its money for teaching while the other spends 54.6 % for the same purpose. Of course, if we combine the items of teaching and supervision, they do not differ so much (77.1 % and 70.9 %), but if this combination of items is made throughout for the cities of this table , we have a variation in the proportion spent for teaching and supervision of from 66.3 % to 81.7 % of the total (see Nos. 19 and 21). For the other items in these cities in which the conditions seem to be so much alike, the table shows the same variability. Jani- tors' salaries vary from 5.3 % to 8.4 %; fuel, from 3.8 % to 10 % (in cities which spend respectively $24.50 and $26.18 per pupil); text-books and supplies, from 1.2 % to 7.5 %; and repairs from 3.8 % to 5.7 % of the total. It is, indeed, strange if 44 % of the cost of maintenance and operation can in one city provide for proper teaching and super- vision (see Table III.), that in another city, which spends more per pupil, it requires 82 % of the total for this item. It would seem that owing to tradition, to poor business management, or 46 City School Expenditures to some other more invidious cause, the money spent is not always spent to the best advantage. It seems possible, also, that the superintendent whose attention is called to the wide variation in any one item of his budget, might be led to investi- gate the matter, in order to determine whether there is any good reason for such deviation from the ordinary or normal condi- tion of affairs. A more careful study of the variability of the several items of the budget shows that in many cases a large expenditure for one item is accompanied by a small expenditure for another. Again, in other cases large expenditures in one item seem to be accompanied by large expenditures in others and small ex- penditures in some by small expenditures in others. One has but to examine carefully the tables to have suggested the pos- sibility of significant relationships. In another section I shall consider this matter more fully and measure a number of these relationships exactly by means of the Pearson Coefficient of Correlation. There are three ways in which we shall express the variabil- ity in order to get as clear an idea as is possible of the lack of uniformity and in order to suggest the problems which arise because of this variability. From the tables already given (see Tables I to IX), it is possible for us to make out frequency tables like those which follow. In these tables the first column gives the amount of money spent, or the per cent, of the total which the item is, and the second column gives the number of instances where this is true. They give all the facts concerning variability; not only the range or limits within which all of the cases lie, but also the exact placing of every case. EXPLANATION OF TABLES Tables X, XI, XII, and XIII give information for the cities reporting for the school year 1 902-1 903. Table X reads as follows: one city spends 27 % for teaching; one, 49 %; one, 52 %; one, 53 %; two, 54 %, etc. Table XI reads as follows : two cities spend 1 % for supervision ; eleven spend, 2 %; seven, 3 %, etc. Reading the first lines of Tables XII and XIII, we find that four cities spent 3 % of the budget for janitors' salaries, and that six cities spent 3 % for fuel. TABLES OF FREQUENCY The per cent, of the total expenditure for maintenance and operation which is spent for teaching, supervision, janitors' salaries, and fuel. Fifty-eight cities, re- porting for the school year 1902-03. Table X Table XI Table XII Table XIII Teaching. Supervision. Janitors ' Salaries. Fuel. Per Cent. Frequency. Per Cent. Frequency. Per Cent. Frequency. Per Cent. Frequency. 27 1 1 2 3 4 3 6 28 1 2 11 4 6 4 12 29 3 7 5 15 5 10 30 4 6 6 19 6 11 31 5 1 7 7 7 4 32 6 2 8 3 8 3 33 7 5 9 2 9 3 34 8 10 10 2 35 9 5 11 11 36 10 3 12 12 1 37 11 4 13 13 38 12 3 14 1 14 39 13 2 15 40 14 16 2 41 15 1 42 16 4 43 17 2 44 45 46 47 48 49 1 50 51 52 1 53 1 54 2 55 2 56 3 57 58 3 59 2 60 61 3 62 6 63 6 64 6 65 3 66 2 67 3 68 2 69 2 70 1 71 2 72 1 73 4 47 TABLES OF FREQUENCY The per cent, of the total expenditure for maintenance and operation which is spent for teaching, supervision, janitors' salaries, and fuel. Average for two years, thirty cities reporting for the school years 1902-03 and 1903-04. Table XIV Table XV Table XVI Table XVII Teaching. Supervision. Janitors' Salaries. Fuel :. Per Cent. Frequency. Per Cent. Frequency. Per Cent. Frequency Per Cent. ] Frequency. 54 3 2 4 3 2 3 4 55 2 3 4 4 1 4 3 56 1 4 5 5 10 5 8 57 2 5 6 11 6 9 58 6 1 7 4 7 2 59 2 7 1 8 1 8 2 60 2 8 2 9 1 9 61 1 9 2 10 62 3 10 2 11 1 63 1 11 3 64 4 12 2 65 2 13 66 2 14 67 2 15 2 68 1 16 69 17 2 70 71 72 2 73 1 4 s TABLES OF FREQUENCY Cost per pupil expressed in dollars, the average daily attendance being used as the basis of calculation. Fifty-eight cities, reporting for the school year 1902-03. Table XVIII Tab LE XIX Table XX Table XXI Table XXII Total Cost per Pupil. Teaching and Supervision. Janitors' Salaries. Fuel. Text-Books and Supplies. Dollars. Frequency. Dollars. Frequency. Dollars. Frequency. Dollars. Frequency. Dollars. Frequency. 8 1 6 1 .4 1 .4 1 .2 2 9 7 1 .5 .5 .3 1 10 8 .6 .6 .4 1 11 9 1 .7 .7 1 .5 12 1 10 .8 .8 1 .6 13 11 1 .9 2 .9 1 .7 1 14 12 1.0 3 1.0 2 .8 15 1 13 1 1.1 4 1.1 3 .9 2 16 14 2 1.2 1.2 5 1.0 2 17 15 3 1.3 2 1.3 4 1.1 2 18 16 3 1.4 3 1.4 3 1.2 1 19 1 17 6 1.5 5 1.5 2 1.3 3 20 2 18 3 1.6 2 1.6 3 1.4 1 21 2 19 8 1.7 3 1.7 3 1.5 2 22 2 20 3 1.8 4 1.8 3 1.6 4 23 2 21 5 1.9 8 1.9 1 1.7 3 24 4 22 1 2.0 3 2.0 5 1.8 1 25 1 23 5 2.1 3 2.1 1.9 3 26 4 24 4 2.2 2 2.2 3 2.0 5 27 2 25 3 2.3 4 2.3 2 2.1 2 28 8 26 2 2.4 2 2.4 2.2 29 4 27 2.5 2 2.5 2.3 1 30 2 28 2.6 1 2.6 2 2.4 31 5 29 2.7 2.7 1 2.5 1 32 3 30 1 2.8 2.8 2.6 33 1 31 2.9 1 2.9 1 2.7 34 2 32 1 3.0 1 3.0 2.8 35 3 33 3.1 2.9 36 1 34 3.2 3.0 1 37 1 35 3.3 1 3.1 38 36 1 3.4 1 3.2 39 37 3.5 3.3 40 38 1 3.6 1 3.4 41 1 3.7 3.5 1 42 3.8 3.6 43 1 3.9 3.7 44 4.0 3.8 45 4.1 3.9 46 4.2 4.0 47 4.3 4.1 48 4.4 4.2 49 4.5 4.3 50 4.6 4.4 51 1 4.7 1 4.5 52 4.6 1 53 54 1 49 TABLES OF FREQUENCY Cost per pupil expressed in dollars, average for two years, the average daily at- tendance being used as the basis of calculation. Thirty cities, reporting for the school years 1902-03 and 1903-04. Table XXIII Table XXIV Table XXV Table XXVI Table XXVII Total Cost per Teaching and Janitors' Salaries. Fuel. Text-Books and Pupil. Supervision. Supplies. Dollars. Frequency. Dollars. Frequency. Dollars. Frequency. Dollars. Frequency. Dollars. Frequency. 19 2 20 13 1 1.0 2 .9 2 .8 1 21 14 1.1 2 1.0 1 .9 1 22 15 1 1.2 2 1.1 1 1.0 2 23 1 16 1.3 1.2 1 1.1 2 24 1 17 6 1.4 2 1.3 1 1.2 25 3 18 4 1.5 3 1.4 2 1.3 26 1 19 1 1.6 2 1.5 3 1.4 1 27 3 20 5 1.7 1.6 3 1.5 28 5 21 2 1.8 3 1.7 2 1.6 6 29 3 22 3 1.9 3 1.8 2 1.7 3 30 1 23 1 2.0 3 1.9 2 1.8 31 4 24 2.1 2 2.0 1 1.9 3 32 1 25 3 2.2 1 2.1 2 2.0 1 33 2 26 1 2.3 1 2.2 2.1 34 27 2.4 1 2.3 3 2.2 35 28 2.5 2.4 2 2.3 36 29 2.6 1 2.5 2.4 37 30 2.7 2.6 2.5 38 1 31 2.8 1 2.7 2.6 1 39 32 2.9 2.8 2.7 40 33 1 3.0 2.9 2.8 41 34 3.1 1 3.0 2.9 42 35 3.1 3.0 43 36 3.2 3.1 44 37 3.3 1 3.2 45 38 1 3.3 1 46 3.4 47 3.5 48 3.6 49 3.7 50 3.8 51 2 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 1 City School Expenditures 51 Tables XIV to XVII, inclusive, are frequency tables based upon the average of the first and second years' figures from thirty cities. It will be noticed that the range is somewhat less, due largely to the fact that there are fewer cases. These tables are read precisely as Tables X to XIII, illustrated above. The tables for the first year's figures alone are, of course, less reliable than those which give the average for two years, so far as any one city is concerned. However, the greater vari- ability found in these figures for the first year which does not appear when the average for the two years is taken is due largely to the fact that many of the cities which give the extreme varia- tion have not yet reported for two years. In Table No. X, for example, the cities reporting 27%, 28%, 49%, and 52 %, respectively, for teaching, are cities Nos. 47, 23, 11, and 52, none of which reported for the second year (see Tables III and IV). The variability for the first year's figures is, simply be- cause there are more cases, more nearly a correct representation of the facts of variability, we believe, than the average of the two years where many of the extreme cases are not found. It is remarkable that so small a proportion as 27 % should be devoted to teaching in one case, when other cities use 73 % of their funds for this purpose, — that some cities should give 2.7 times as great a proportion for teaching as others. The variation in the proportion which is spent for super- vision is not less remarkable. Here the cities seem to divide themselves into groups — those which spend a comparatively large proportion of their money for supervision, and those in which this item is allowed a smaller share of the money. One feels that supervision which costs 1 7 % of the money available for schools should produce remarkable results in the way of saving time and energy for teachers and pupils, if it is to be justified when compared with other cities in which 2 % of the budget seems to secure satisfactory supervision. The range for janitors' salaries (Table XII) may indicate a real difference in the care of school buildings, or, in rare in- stances, perhaps some connection between ward politics and the janitors' position. Leaving out the most extreme case, it seems rather remarkable that in some instances one dollar out of every eleven available for the maintenance and operation of the schools should be spent for the care of buildings. 52 City School Expenditures That fuel should be allowed in some cities three times as great a proportion of the money spent as in others (see Table XIII) would not seem strange if our cities were found in sec- tions of the country with very different climatic conditions ; but that four or even five times as much should be necessary under conditions which are not greatly different seems prepos- terous. Tables XIV to XVII, which are based on the average for two years, give the most accurate information we have for the thirty cities which reported two years. The limits within which the cases lie are, as has already been noted, somewhat smaller than in the case of the first year's figures considered alone. This is due largely to the fact that we have a smaller number of cases. The variability is, nevertheless, sufficiently striking with a range of from 54 % to 73 % for teaching, from 2 % to 17 % for supervision, from 3 % to 9 % for janitors' salaries, and from 3 % to 11 % for fuel. Tables XVIII to XXII give the variability for the cost per pupil for some of the principal items of the budget. The cost per pupil as given here is based on the average daily attendance (see Table VII). Table XVIII reads as follows: one city spent for main- tenance and operation per pupil in attendance, $8.00; one city, $12.00; one city, $15.00; one city, $19.00; two cities, $20.00; two cities, $21.00, etc. Tables XXIII to XXVII give the variability for some of the principal items of the budget on the cost per pupil basis, the average amount spent per pupil for two years being used (see Table IX). Table XXIII, for instance, reads as follows: the average amount for two years spent for maintenance and opera- tion per pupil in attendance for two cities was $29.00; one city, $23.00; one city, $24.00; three cities, $25.00, etc. In the tables given above, we have an expression of the variability in terms of the amount of money spent. We some- times think of the cities in the region covered by this study as spending a very large amount for public education. The average inhabitant, if not the school officers themselves, of any of these cities will probably say that their school system is quite as good as any other, or at least as good as the average. As a matter of fact, we find a great variability in the total amount per pupil City School Expenditures 53 spent, as well as in the amount spent for various items. No one believes that the city which spends $54.00 per pupil furnishes an education six and three-quarter times as good as the city which spends only $8.00 per pupil. On the other hand, it hardly seems possible that the opportunity for education in the eight-dollar city can be equal to that found in the fifty-four- dollar city. Teaching and supervision which cost $6.00 per child are hardly likely to be as good as those which cost three, four, five, or even six times as much. No argument based upon the difference in the cost of living could account for so great a difference in the cost of instruction. Either the teachers re- ceive a very much smaller salary in the cities which pay a rela- tively small amount per pupil, or they have much larger classes to instruct, or both conditions taken together explain the variability. One may infer that the number of children determines the number of seatings which must be furnished, if not the number and size of buildings ; and yet janitors' salaries may cost from 40 cents to $3.00 per pupil, and fuel from 40 cents to $4.70 per pupil. If we neglect the cases where a very little is spent for text- books and supplies, — the cases where they are not furnished free to pupils, — we still find that some cities spend three or four times as much per pupil as others for these articles. It seems rather remarkable that the real value of books and supplies fur- nished to pupils should vary so much; and even if this were the case, one might question whether the money is spent to best advantage in those cities which spend the larger amounts. Might not a part of this money have been spent to greater ad- vantage in some other way? The limits within which all of the cases lie are significant, but are not so true a measure of the variability of the group as are the limits within which the middle 50 % of the cases lie. A single exceptional case may double the range within which all of the cases lie, but manifestly this does not double the variability of the group. This figure, which we call 2 Q, is found by counting in from both the upper and lower limits until 25 % of the cases have been covered, and then finding the range within which the remaining 50 % of the cases lie. For instance, in Table X, in which there are 58 cases, we count off from the 54 City School Expenditures lower limit fifteen cases (25 % = 14J), which brings us to the group of three cities which spend 58 % of their money for teaching; in like manner, counting from the other extreme, 25 % of the cases are found to spend more than 67 % of their money for teaching. The limits within which the middle 50 % of the cases lie are, then, 58 and 67, and 2 Q equals (67 — 58 =9) nine. After we have found the 2 Q, the relation which it bears to the median gives us a still better idea of the variability of the group. If it is desired to compare the variability of the group in several traits, the relation of the 2 Q to the square root of the median is more exact than either of the figures before suggested because this measure will be less affected by errors due to inaccuracy of measurements, or to the small number of measurements made. In the table below, 2 Q, the per cent, which 2 Q is of the median, and the per cent, which 2 Q is of the square root of the median are given. This table is derived from the frequency tables, Tables X to XXVII inclusive. o Per cent, of total spent for each item. First year's figures. See Tables X to XIII inclusive : Teaching 9 Supervision 8 Janitors' Salaries. 1 Fuel 3 Per cent, of total spent for each item. Average of two years' figures. See Tables XIV to XVII inclusive: Teaching 9 Supervision 8 Janitors' Salaries 4 Fuel 1 Cost per pupil. First year's figures. See Tables XVIII to XXII inclusive: Total cost per pupil 7 Teaching and Supervision 6 Janitors' Salaries .7 Fuel 8 Text-Books and Supplies .9 a Mr 2s u O O u 03 tit,. •3 a) 5 -S 3-2 & cr-a . M a> ca a a. 14 113 105 290 16 40 50 123 14 112 100 283 65 166 16 42 25 132 33 136 37 50 50 61 53 69 City School Expenditures 55 ?a III 8*8 8^2 Oost per pupil. Average of two years' figures. See Tables XXIII to XXVII inclusive : Total cost per pupil 5 Teaching and Supervision 5 Janitors' Salaries Fuel Text-Books and Supplies 17 93 25 111 7 37 50 7 41 53 8 50 61 In the diagrams which follow, the variability is expressed graphically. The heavy line gives the distribution based on the average of the first and second years' figures, while the dotted line gives the distribution for the first year's figures from those cities which reported both years. Along the horizontal axis is indicated the per cent, of the total (or cost per pupil), while the vertical distance indicates the number of cases. This method of indicating variability enables one who is accustomed to this mode of representation to take in at a glance at least the more striking features. It will be noticed that in the main the distribution for the first year's figures, taken alone (the dotted line), conforms to that for the average of the two years. This is significant in that it shows that the conclusions which may be drawn from the one year's figures are fairly reliable, and that we were justified in our treatment of variabil- ity above to make use of the first year's figures with the greater number of cases. 56 City School Expenditures FIG. 1. 53 55 5? 5t 60 FIG. 2. 2 4 64 ! i n^ 8 « I... 15 FIO.3. 70 78 80 FIG.4 1 J 3 4 6 9 Surfaces of Frequency on the Per Cent, of Total Basis. Fig. i. — Teaching. Fig 'a. — Supervision. Fig. 3. — Teaching and Supervision, Fig. 4. — Janitors' Salaries City School Expenditures 57 F I G. & 1 3 5 11 13 F I Q. 6. i — r ~ i 3 4 12 PI O. 7. ~n X 12 3 7 K) 14 Surfaces of Frequency on the Per Cent, of Total Basis Fig. 5. — Text-Books and Supplies. Fig. 6.— Fuel. Fig. 7. — Repairs. 58 City School Expenditures ■£=2 FIG. 8. 13 IS 19 27 33 39 FIG. 9. -. : • 1 : 1 ; -. i i 11 13 IS 19 29 33 1 1 FIG. 10. ; : 1 J ! .. | 1 i •50 1 1.5 4. 5.5 FLFL* FIG. 11. im r=u 1. 1.2S 1.75 FIG. 12. ■9 1.1 1.3 U 2.5 W Surfaces of Frequency on the Cost per Pupil Basis Fig. 8. — Teaching and Supervision. Fig. 9. — Teaching. Fig. 10. — Supervision. Fig. 11. — Janitors' Salaries. Fig. 12. — Text-Books and Supplies. City School Expenditures 59 QfZ pig. ia h=, .9 1.1 1.3 1.7 2.7 3.3 i ■ ■ FIG. 14. .... n-r — i r-~) n 50 .75 t 2. 3. Surfaces of Frequency on the Cost per Pupil Basis Fig. 13. — Fuel. Fig. 14. — Repairs. Still another method of indicating variability is by means of giving the deviation for each of the items from some central figure which may be agreed upon. In the tables which follow, the deviations are calculated from the median. The median, which is simply the point above and below which fifty per cent, of the cases lie, is, we believe, the best figure to use in this case as representing a central ten- dency. It is unambiguous and is not so much influenced by ex- treme cases nor by error as the average would be. EXPLANATION OF TABLES Table XXVIII gives the medians and deviations from them for the cost per pupil based on the average number of pupils in daily attendance . The data are from fifty-seven cities reporting for the school year 1902- 1903 (see Table VII). The first line of the table gives the medians. One half of the cities spend less than $28.50 or just $28.50 per pupil, while the other half spend more than $28.50 or just that amount per pupil for maintenance and operation of their schools. In like manner, $19.96 marks the point above and below which half of the cities lie in their expenditure for teaching and supervision; $18.10 is the median for teaching alone; $1.75 is the median for supervision, and so on for the other items given. In the body of the table, deviations below the me- dian are marked with a minus sign, those above are not marked. 60 City School Expenditures Line number nine reads as follows: City number eight spends $2.66 per pupil more than the median ($28.50) for the maintenance and opera- tion of schools; $2.37 per pupil more than the median ($19.96) for teach- ing and supervision; the median amount, $18.10 per pupil, for teaching; $2.48 per pupil more than the median for supervision, etc. Table XXIX gives the medians and deviations from them for the per cent, which each item is of the total cost of maintenance and opera- tion. The data from which this table is derived are found in Table III, which gives information for fifty-eight cities for the school year 1902- 1903. The first line of the table gives the medians for the several items of expenditure expressed as per cents and hundredths of a per cent. As in Table XXVIII, the deviations below the median are marked with a minus sign while those above are left unmarked. Line two reads as follows: City number one spent 5.5 % less than the median (71.15 %) for teaching and supervision; i. e., 65.65 % of the total cost of mainten- ance and operation was spent for teaching and supervision. If we skip the next two items, we find that this city spent .42 % more than the median (6.19 %) for janitors' salaries; 2.24 % more than the median (2.91 %) for text-books, etc. Table XXX gives medians and deviations on cost per pupil basis for thirty cities, reporting for the school year 1 903-1 904. The figures refer to dollars and tenths of a dollar. This table is derived from Table VIII. The explanation given for Table XXVIII makes this table clear, since this table differs from Table XXVIII only in that it is based on the second year's data and in that it gives the deviations for fewer items. Table XXXI gives medians and deviations for per cent, which each item is of the total cost of maintenance and operation. The data are from thirty cities for the school year 1903-1904 (see Table IV). The figures refer to per cents and tenths of one per cent. The explanation for Table XXIX, which gives the same information for the school year 1902-1903, may be referred to by any one who has difficulty in under- standing this table. Tables XXXII and XXXIII give medians and deviations from medians on both cost per pupil and per cent, of total basis, which are based on two years' figures. These tables are made up by taking the average of the cost per pupil, or the per cent, of total of each item for two years. From these tables, giving the average for each item for two years, medians are calculated and deviations found as in the tables based on a single year's figures. These tables are read precisely as Tables XXX and XXXI. From these tables we can get again the distribution of the cases by grouping those which vary by the same amount. If City School Expenditures 61 this were done we would get frequency tables similar to those given above, or if we represented the distribution graphically, surfaces of distribution like those already given. By examining these tables carefully, it will be seen that cer- tain variations in one item are accompanied by like variations in some other item, or that a plus deviation in one item is ac- companied by a negative deviation for the other, or vice versa. Take, for example, the items of janitors' salaries and salaries for teaching and supervision, as given in Table XXIX (per cent, of total first year's figures). In these items one is struck by the fact that a plus deviation in salaries paid janitors is often ac- companied by a negative deviation for teaching and supervision, and vice versa. Picking out the cases, a table like the following may be made: No. of City. Janitors' Salaries. Salaries for Teaching and Supervision. I. + 4. -5.5 7- + 3.3 -3.4 9- + 1.3 -1.5 11. + 3. -9.9 14. + .7 -3.6 17. + .8 - .5 19. + .6 -5.9 23. + 8.7 -13.0 27. + 1.1 -4.5 28. + 1.0 -2.0 29. + .8 -6.6 30. + .1 - .1 3i. + .4 -11.8 34- + 1.9 -2.4 43- + 1.5 -2.4 47. + 2.3 -26.9 52. + .8 -12.2 56. + 2.2 - .2 6 - .9 + 5.9 8. - .1 + .5 10 - .3 + 4.3 20. -1.0 + 2.4 21. - .3 + 10.5 22. -2.0 + 3.9 25. -1.3 + 6.7 26. - .3 + 1.8 33. - .1 + 11.1 36. -2.7 + 5.2 37- - .8 + 4.9 38. -2.4 + 2.8 39- -1.0 + 2.2 46. -1.6 + 1.4 49. -2.2 + 4.8 5i. - .7 + 8.4 57. -1.5 + 3.4 58. - .8 + 1.6 TABLE XXVIII Medians and deviations from medians for cost per pupil based on the average number of pupils in daily attendance, expressed as dollars and cents. Fifty-eight cities, for the school year 1902-03. i? Medians. 28.50 19.96 18.10 1.75 1.87 .82 .64 I. 7.14 3.37 4.20 — .72 .48 1.01 .54 2. - .50 — 1.43 — .50 — .82 .42 -.33 3- — .44 .26 1.00 — .63 .11 4- 3.40 3.83 2.25 1.69 .40 .26 .28 5. 4.77 5.19 6.31 — 1.01 .32 6. - .85 1.29 2.00 — .60 — .42 7- -6.89 — 5.34 — 5.19 — .04 .18 - .28 .17 8. 2.66 2.37 2.48 .02 .73 .18 9- 2.51 1.53 2.53 — .89 .45 10. 14.73 2.68 13.81 — 1.02 .69 .17 .75 II. .51 — 2.19 — 3.68 1.60 .78 12. .70 1.45 .65 .91 .34 .03 13- 1.06 1.08 — 2.20 3.39 .16 — .05 .19 14- .25 — .63 — .21 — .31 .08 .07 .07 15. -3.15 — 1.50 — .19 — 1.20 — .34 .19 .37 16. - .09 1.43 1.07 .47 — .05 • 30 17. 7.50 5.46 4.50 1.07 .66 .23 .47 18. 7.20 6.18 7.07 — .15 .56 19. .40 — .82 .06 — .77 .10 .55 .18 20. — 5.34 — 2.89 — 1.52 — 1.26 — .68 — .27 - .28 21. — 4.00 .02 — 1.20 1.33 — .43 — -26 22. — 19.56 — 13.22 — 11.47 — 1.64 — 1.40 — .11 23. — 15.65 — 12.49 — 14.41 2.03 .05 24. — 13.24 — 8.68 — 8.23 — .34 — .91 — .72 — .42 25. 2.50 4.16 3.57 .75 — .34 - .71 — .53 26. 4.17 3.88 .27 3.72 .05 - .16 .35 27. 1.54 — 2.03 — 2.99 1.07 .08 .82 28. 1.80 1.00 1.67 — .56 .32 62 TABLE XXVIII {Continued) Medians and deviations from medians for cost per pupil based on the average number of pupils in daily attendance, expressed as dollars and cents. Fifty-eight cities, for the school year 1902-03. 22. J2J Medians. 1.68 1.63 1.09 .18 .18 .39 .29 2 - —.1.3 3.07 .41 -.03 -.11 3- -04 —.31 —.02 4- -32 -.10 -.03 —.06 .09 5- -31 .40 -.73 -.06 -.02 -.05 6. 7. —.33 —.83 .34 —.11 26. 27. 28. 1.33 .79 - .13 3.07 .41 .04 — .31 .32 — .10 — .03 .31 .40 — .73 .13 — .49 - .33 — .83 .34 .33 .19 .08 1.28 — 1.04 .70 .21 1.20 .14 .15 .42 — .06 - .08 .32 — .32 - .08 .93 .34 .08 — .40 .08 — .19 — .05 .48 1.01 .34 .67 — .11 .51 .45 .55 - .77 .66 — .24 — .69 — .15 — 1.26 — .50 — .36 — .19 1.36 — .60 — .64 1.46 .41 .74 - .03 — .18 .03 — .38 — .46 .46 .65 T3 m M c ^ 3 . rt O « ° 8« .S2 B > . 13 +3 c *3 tA 3 . 8 3 OJ O 3 . O VI o u 1 .M.8 81: CQ ft "3 B fa u '3 0. 3 s "3 v -Q -. X> S 3 «« O 2 > J V3 ■> u a> & C/3 C a) c3 03 "m u O 4» °E ■a O O °? « 10 .8 "a 0. 3 03 CQ D- ■"CO 0) 2 a) 1-5 H Medians. 71.15 7.62 63.44 6.19 2.91 1.85 5.98 30. — .05 — 4.91 4.95 .13 — 1.19 .93 — 1.49 31- — 11.76 — 4.78 — 6.99 .40 — .37 32. — 12.12 -3.88 — 8.15 — .59 — 1.84 .02 — 3.05 33. 11.17 5.18 4.08 — .05 -1.16 34- — 2.37 — 3.19 1.01 1.94 — 2.85 -.93 -5.01 35- 4.05 — 5.60 9.74 .36 — 2.82 36. 5.20 9.65 — 4.46 — 2.73 — 1.20 37. 4.92 9.27 — 4.26 — .83 38. 2.80 — .21 1.10 — 2.35 -2.69 — 1.43 — 5.35 39. 2.19 3.47 — 1.19 — .99 — .10 40. — 3.92 — 3.58 — .25 — 2.25 — 1.17 2.29 — .11 41. — 2.07 — 4.42 1.44 — 1.60 — .30 42. — 1.46 6.86 — 9.23 — .96 2.13 2.06 2.96 43- — 2.37 — 3.99 1.81 1.46 — 1.03 — .16 — 2.42 44- — 2.85 — 2.97 .31 — .14 — 1.72 45. -1.81 — 5.36 3.64 — .85 2.54 - .64 .67 46. 1.41 3.68 — 2.18 — 1.63 — .05 - .13 — 1.41 47- — 26.94 8.69 — 35.54 2.25 .44 48. — 4.97 2.16 — 5.04 — .21 1.38 — .49 — .34 49. 4.83 4.48 .44 — 2.16 2.28 - .84 .21 50. — 1.30 — .66 — .55 — 2.80 1.60 — .26 .11 51. 8.39 6.26 2.22 — .72 — 1.04 — 1.38 — 3.65 52. — 12.21 — 1.02 — 11.10 .81 .08 1.63 .48 53- 7.52 4.17 3.44 .70 54- — 4.42 3.12 — 7.45 — .53 .94 2.72 2.43 55. — 6.30 — 4.17 — 1.94 — .88 2.69 56. — .24 ' 8.67 — 8.82 2.18 — 1.30 — 2.53 57. 3.42 2.30 1.21 — 1.47 — .29 2.50 .98 58. 1.60 2.03 — .34 — .78 .50 68 TABLE XXIX (Continued) Medians and deviations from medians for the per cent, which each item is of the total cost of maintenance and operation. Fifty-eight cities, for the school year 1902-03. The figures refer to per cents and hundredths of per cents. ^ T3 w •4-3 M* CM 3 . u to a "3 8 0, Pi 1 1 2 0) u tt a a < a 0)J3 C w Is s 2 *3 S Medians. 5.91 3.92 .6 .06 .49 1.64 30. — .97 3.43 .32 — .42 .65 31- 6.59 2.49 .66 1.98 32. .62 6.69 1.89 .02 2.11 33- — .92 .79 — 1.57 34- 4.09 — 2.46 1.09 .05 -1.16 35- — .22 — 1.12 — .04 .07 .38 .24 36. — .74 — 1.65 .68 — .01 .35 3.25 37- .08 — 1.58 1.62 38. 5.90 -.39 .18 .74 — .33 39- .32 3.85 40. 2.81 — .45 -.09 -.36 41. .16 — 3.74 .35 42. — .32 — 1.12 .52 - .04 — .14 43- 2.95 — 1.42 .07 .25 .16 1.17 44- 4.09 .38 - .02 .09 — .09 45- -3.13 3.02 — .16 - .43 .01 46. — 2.00 — 1.34 .79 — .05 .11 -1.54 47. 10.18 9.28 1.44 ' — .43. .13 48. .25 — 2.43 - .23 — .38 - .22 1.57 49- — .45 — 2.59 .30 .30 — 1.36 50. .35 2.97 1.51 51. - .33 — 2.06 - .48 .18 .29 52. 11.03 .39 - .31 .15 53- — .59 .78 54- — .94 .29 — .14 1.62 .12 — .44 55- — .32 — 1.12 .80 .80 — .63 56. — 1.54 1.42 — .40 — .09 - .76 57- — 1.99 .43 .27 — .17 — .06 58. — 1.67 1.26 - .47 1.45 69 TABLE XXX Medians and deviations from medians for cost per pupil based on the average number of pupils in daily attendance, expressed as dollars and cents. Thirty cities, or the school year 1903-04. The figures refer to dollars and tenths of dollars. s? oft iians. 29.08 21.19 18.90 1.74 1.91 1.61 1.67 1.12 5- 5.0 4.3 5.9 — 1.0 .4 — .3 1.1 — .7 6. — 4.8 — 5.4 — 4.2 — .6 — .3 .2 1.1 8. 3.3 2.5 3.7 2.5 .2 .1 13- 5.1 4.3 2.0 3.4 .2 .6 — .3 14. — .3 — 1.2 — .3 — .4 .4 .2 15. — 4.4 — 2.5 — 4.2 2.1 — .4 — .2 — .2 — .4 16. — .9 .1 .3 .4 — .1 .3 — .3 20. — 6.0 — 3.8 — 2.2 — 1.1 — .6 .4 .3 — .6 27. — 2.8 — 3.0 — 4.3 1.9 .1 — 1.1 — .1 28. .3 — .6 .6 — .6 .2 — .7 29. — 4.4 — 5.6 — 1.1 — 1.0 .2 .4 — .2 .1 30. 9.6 5.8 7.1 — .8 .5 2.4 3i. 1.8 1.5 — .9 .1 .4 1.7 32. — 1.1 — 1.1 — 3.4 2.9 .1 — .8 — .1 34- 2.5 .4 1.3 — .4 2.5 — .5 .5 35- .8 2.2 2.8 — .1 — .5 — 1.5 .3 .3 36. 2.6 5.3 2.3 3.6 — .7 .4 — 1.2 37- — 8.4 -5.4 — 6.7 1.9 — .8 — .2 39- — .3 .3 — 1.1 1.9 — .3 40. 2.1 .2 — 3.2 3.9 — .8 .4 .1 41. -3.7 — 3.2 — 4.5 1.8 — .8 - .2 .2 — .2 42. — .9 — 3.2 2.9 — .4 1.1 — .3 — .1 43- 1.4 1.7 3.2 — .8 — .7 — .7 — .2 45- .5 .1 — .2 — .5 .4 48. — 1.4 — 1.5 — 3.2 2.3 — .4 .4 — .3 — .1 52. — .1 — 2.1 — 1.5 — .1 .4 .5 — .6 . 3 54- 19.1 9.8 6.3 4.0 .7 7.1 .2 55- — 11.2 — 8.0 — 6.8 — .6 — .9 — .5 — .8 — .7 56. 1.9 1.0 2.0 — .4 .7 — .3 — .3 57. 23.4 17.9 15.2 .33 1.0 1.6 .4 1.1 70 TABLE XXXI Medians and deviations from medians for the per cent, which each item is of the total cost of maintenance and operation. Thirty cities, for the year 1903-04. The figures refer to per cents and tenths of per cents. .5 > I m to o 0< CO p. . n Medians. 71.7 64.2 6.3 6.1 5.5 5.8 3.8 5- 3.2 8.5 — 4.1 6 — 1.7 2.3 — 2.8 6. — 6.5 — 3.7 — 1.6 .5 1.2 2.0 5.2 8. 1.6 5.8 — 3.0 — .4 .1 — .3 — .3 13- 2.8 — 3.3 7.1 — .5 — .2 .8 — 1.4 14. — 2.4 .2 — 1.4 1.8 .1 .9 15. 4.4 — 3.7 9.3 .3 — 1.0 16. 4.2 4.1 1.1 .6 — .5 1.3 — .9 20. 4.0 8.8 — 3.3 — .6 — .1 1.6 — 1.4 27. — 1.9 — 8.6 7.7 1.8 .7 — 3.6 1.1 28. — 1.4 2.2 — 2.5 1.0 — 2.5 29. — 4.7 — .3 — 3.2 2.3 .3 1.3 30. — 1.7 3.1 — 3.7 .2 — 1.5 5.5 3i. — 3.1 1.7 -3.7 .5 4.3 5.3 32. — 8.9 10.1 1.2 -2.7 .2 — .2 34- — 3.1 — .1 — 1.9 4.6 — 2.2 1.3 35. 6.6 8.4 — .8 — 1.3 -5.0 .5 1.1 36. 13.7 4.0 10.8 — 2.4 .7 — 3.7 37- 4.7 — 5.4 11.3 — .8 2.1 .8 39. 2.9 — 2.2 6.4 — .6 .2 40. — 2.6 — 13.3 11.9 — 2.4 1.0 41. — .7 — 7.4 7.8 — 1.6 1.6 — .2 42. — 1.7 — 10.1 9.7 — .9 3.7 — 1.0 — .4 43- 3.6 8.0 — 3.2 .2 — 2.5 — 2.7 — .9 45. 1.5 2.6 — .4 — 1.7 1.3 48. — .7 — 7.7 8.1 - .7 1.5 — .7 .1 52. — 5.7 — 4.0 — .7 1.8 2.7 — 2.0 .9 54- — 5.5 — 12.1 5.7 — .8 12.5 — 1.0 55. 1.9 3.1 — .2 .5 — .8 — 2.5 56 3.0 — 1.9 2.2 — 1.3 — 1.4 — .2 57 2.9 .7 3.3 — .5 — 1.8 .4 71 TABLE XXXII Medians and deviations from medians for average cost per pupil for two years based on the average number of pupils in daily attendance. The figures refer to dollars and tenths of dollars. Thirty cities, reporting for two school years, 1902-03 and 1903-04. ■a . <£ O s H 3 -co « 3 H w w '3 2 03 H Medians. 28.8 20.5 18.3 2.2 1.9 1.6 1.7 1.1 5- 5.9 4.9 6.3 -1.4 .4 .7 — .7 6. — 2.8 — 1.9 — .9 -1.0 - .3 .1 — .2 .6 8. 3.0 2.5 2.0 .5 .3 .1 .1 13- 3.1 2.8 .1 2.7 .1 .1 .4 — .3 14. — .8 — .1 — .8 .2 .8 .6 IS- — 3.3 — 1.9 — 1.9 - .3 — .1 — .4 16. — .4 .9 .9 — .1 20. — 5.7 — 3.2 — 1.7 -1.6 — .6 — .6 .4 — .4 27. — 2.7 — 2.4 — 3.5 1.1 .1 - .8 — .2 28. 1.0 .3 1.3 — 1.0 .3 — .6 29. — 1.7 -2.7 — 1.3 — 1.4 .2 .3 — .2 .2 30. 9.2 6.2 7.3 — 1.2 .5 2.1 31. .6 1.6 — .2 — 1.4 .1 1.6 1.2 32. 2.4 — .2 — 1.0 .8 .1 - .7 .3 1.3 34- 4.9 4.7 3.4 — .7 1.3 .7 35- — 1.6 .4 1.5 — 1.1 — .3 — .1 36. 3.0 5.0 1.7 3.2 — .7 .1 — .7 37- — 8.8 — 5.3 — 6.5 1.3 — .8 — .3 — .4 39- 1.6 2.0 .6 1.4 — .2 .3 .2 40. 4.2 1.9 .5 1.3 - .6 .4 .8 .1 41. — 3.8 -3.0 — 3.1 .1 — .7 — .2 — .6 42. — 3.4 — 2.7 2.3 — .4 1.0 — .2 — .2 43. — .5 1.2 — 1.2 — .7 — .3 45- 1.0 — .9 — .3 .1 — .5 .6 48. -3.5 — 2.9 -3.8 .9 — .4 — .2 — .4 52- — 1.1 — 3.1 — 2.7 — .5 .2 .3 — .6 1.6 54. 22.7 13.3 9.6 3.6 1.0 4.5 .6 — .8 55- -7.6 — 7.2 — 6.0 — 1.3 - .8 — .5 — .7 — .7 56. .7 .6 .2 .8 .6 — .5 — .3 .2 57. 23.1 18.2 15!3 2.9 .8 1.7 .3 1.1 72 TABLE XXXIII Medians and deviations from medians for per cent, of total which each item is, based on average for two years. Thirty cities, reporting for the school years 1902-03 and 1903-04. The figures refer to per cents and tenths of per cents. S3 %£ & "is § £c0 rt o 60 O •— to w aca ■§ 3 & -g| Medians. 70.7 63.1 8.0 6.1 5.7 5.9 3.5 5- 4.7 10.1 -5.8 .6 — .5 1.2 — 2.6 6. .3 3.6 -3.6 — .1 .9 .1 3.0 8. 1.8 .9 .4 — .1 .3 — .2 .1 13. 2.1 — 3.7 7.4 .2 — .4 .7 — 1.0 14. — 2.3 .3 — 3.1 1.3 — .1 2.2 2.4 IS- 4.0 2.7 .9 .2 1.0 .3 -.7 16. 4.8 4.8 — .4 .5 — .1 .2 20. 3.9 9.1 — 5.4 — .8 — 1.3 2.7 — .5 27. — 2.6 — 7.2 4.6 1.5 1.3 — 2.4 .1 28. — 1.0 2.7 — 4.1 1.0 — 2.3 29. — 5.0 — .3 — 5.0 1.6 1.2 - .3 — 1.4 30. — .2 4.7 — 5.4 .2 — 1.3 4.8 31. -6.7 — 1.9 — 5.3 .5 5.3 4.3 32. — 5.3 — 8.8 2.1 .3 -2.9 .4 3.6 34- — 2.1 1.1 — 3.6 3.3 .7 — .2 35- 6.0 9.8 — 4.2 - .4 -5.4 .3 36. 10.1 — -5 9.2 — 2.5 — 5.0 — .1 — 2.3 37- 5.5 — 3.9 9.2 — .9 1.0 — .1 39- 3.2 — 1.0 3.9 - .7 .6 .6 40. — 2.6 — 6.1 3.1 -2.3 .4 1.4 .1 41. — .7 — 2.2 1.1 — 1.6 — .1 .8 -1.7 42. — .9 — 9.0 7.7 — .9 3.4 — .8 — .4 43- 1.3 5.6 — 4.7 .3 — 2.4 — .8 45- .5 3.8 — 3.7 — .6 .4 — 2.0 2.4 48. — 2.2 -5.7 4.1 — .4 .6 — .3 — .8 52- -8.3 — 6.9 — 1.9 .3 1.6 -2.3 6.3 54. — 5.3 — 9.1 3.3 — .7 7.5 — 1.1 55. — 1.5 1.3 — 3.2 — .5 .1 — .8 — 1.5 56. .5 — 2.2 2.3 2.2 — 1.9 — 1.5 .9 57. 3.8 1.7 1.7 -1.0 — 2.0 .7 73 74 City School Expenditures There are thirty-six cases in which a positive deviation for one item is accompanied by a negative deviation for the other, and only twenty -one cases where like deviations occur for both items. One might seem justified in declaring that a negative relationship exists. It is not possible from the table to tell how large this negative relationship is, much less to express it in a single significant figure. It is just here that the great value of the Pearson Coefficient of Correlation x comes in. In the next set of tables (see Tables XXXIV and XXXV) the deviations are given as a per cent, of the median. The gross deviations from the median are significant, especially when deviations for different items are compared with each other as indicated above, but the range of variability is better indicated, I believe, by giving the per cent, of the median or other single figure indicating a central tendency. For example, the median for janitors' salaries (first years' figures, per cent, basis) is 6.2 %, and for salaries for teaching and supervision it is 71.2 %. Now, a deviation of .6 % in the case of janitors' salaries seems insignificant when compared with a deviation of 7.1 % for teaching and supervision — the one is almost twelve times the other ; but when we remember that each one represents a devia- tion equivalent to about 10 % of the median, we are nearer recognizing their real significance, I believe, than when we con- sider them merely in gross. Even this method of comparison is, however, misleading, since it is absolutely impossible for the items "teaching and supervision" or "teaching" to vary as much as 100 % above or below the median when the per cent, of the total is taken as the basis of comparison, because the median for teaching and supervision amounts to 70.7 %, and for teaching to 63.1 % of the total. On the cost per pupil basis, while it is not impossible to have a variation equal to 1 00 % of the median, or greater, for these larger items, yet, even if such variations occur, they are not comparable to variations which give the same per cent, of the median where this item represents a very much smaller part of the total expenditure. 2 Even after 1 The reader not versed in statistical methods is referred to Thorn- dike's Mental and Social Measurements (The Science Press, 1904), where he will find a most satisfactory treatment of this and other statistical methods. 2 For discussion of this point, see Thorndike, Mental and Social Measurements, pp. 102 and 103 City School Expenditures 75 these qualifications (which show us that we must be on our guard in comparing variabilities for different items) have been made, I am still of the opinion that these tables are very help- ful in giving us a correct idea of the variability of all items, as well as permitting us to compare the variability of items whose medians represent about the same proportion of the total or nearly the same cost per pupil. In Table XXXIV the items which apparently show the least variability are "total," "teaching and supervision," and " teach- ing." As noted above, any deviation above the median is pos- sible; i. e., the deviation above the median may be 100 % or more of the median. It is striking to note that the deviations expressed as per cents of the median for the total amount spent range from — 30.6 % to + 80.2 %; while for teaching and supervision the range is from —35.1 % to + 88.8 %. Appar- ently the amount paid per child for teaching and supervision is even more variable than the total amount of money spent per child. Possibly this is what we might have expected when we remember that teachers of some sort can^be had for almost any salary, while some of the other commodities or utilities which must be had to run the school have a much more definite market value. The great range for supervision from — 73-7% to + 166 % is at least partially to be accounted for, I believe, by the fact that no very clear distinction exists between teachers and supervisors or principals in some systems. Those who should have been reported as teachers are, doubtless, in some instances reported as supervisors, and vice versa. The items "janitors' salaries," "text-books and supplies," and "fuel" furnish the best opportunity for comparison of variability. The medians for these items are respectively $1.90, $1.60, and $1.70. The range of deviations for janitors' salaries is from — 42.8 % to + 53.5 % of the median; for text-books and supplies, from — 42. 7 % to +274%; and for fuel, from — 40.9 % to 93.6 %. That the smallest proportional plus varia- tion should be found in the item of janitors' salaries, and the largest for the item of text-books and supplies seems to me to indicate that, in some cities at least, more money means more of those things which make possible efficient work in the schools. The deviations for the item of repairs show a range of from — 74-8 % to + 196.6 % of the median. There would probably TABLE XXXIV Deviations from the medians; average cost per pupil for two years (see Table XXXII), reduced to per cents of the medians. The figures refer to per cents and tenths of per cents. 39 40 41 42 43 45 52 54 55 go, £W Medians. 28.8 20.5 18.3 2.2 1.9 1.6 1.7 1.1 5 20.5 23.9 34.4 —64.5 21.4 40.9 —65.5 6 —9.7 —9.3 —4.9 —46.1 —16.1 6.1 —11.7 56.1 8. 10.4 12.2 10.9 23.1 18.3 5.8 9.4 1* 10.8 13.7 .6 124.0 5.4 6.1 23.4 —28.1 14 —3.9 —.6 —36.9 10.7 46.8 56.1 i<. —11.5 —9.3 —10.4 —16.1 —5.8 —37.4 l6 —1.4 4.4 4.9 —9.4 20 —19.8 —15.6 —9.3 —73.7 —32.1 —36.6 23.4 —37.4 27 _9.4 —11.7 —19.1 50.7 5.4 —46.8 —18.7 28. 3.5 1.5 7.1 —46.1 16.1 —36.6 2Q _ 5 .9 -13.2 —7.1 —64.5 10.7 18.3 —11.7 18.7 00 32.0 30.2 39.9 —55.3 26.7 196.6 3i 2.1 7.8 —1.1 —64.5 5.4 93.6 112.2 32' 8.3 —1.0 —5.5 36.9 5.4 —42.7 17.6 121.6 34 . 17.0 22.9 18.6 —32.3 69.5 40.9 35 —5.6 1.9 8.2 —50.7 —16.1 —5.8 36 10.4 24.4 9.3 148.0 —37.4 5.8 —65.5 „' —30.6 —25.9 —35.5 59.9 —42.8 —17.6 —37.4 5.6 9.8 3.3 64.5 —10.7 17.6 18.7 14.6 9.3 2.7 59.9 —32.1 24.4 46.8 9.4 13.2 —14.6 —17.0 4.6 —37.4 —12.2 —56.1 —16.6 —14.8 106.0 —21.4 61.0 —11.7 —18.7 .7 6.6 —55.3 —42.7 —28.1 5.5 —41.5 —16.1 6.1 —29.2 56.1 48. —12.2 —14.1 —20.8 41.5 —21.4 —11.7 —37.4 — 3.8 —15.2 —14.8 23.1 10.7 18.3 —35.1 149.0 78.8 64.9 52.5 166.0 53.5 274.3 35.1 —74.8 — 26.4 —35.1 —33.3 —59.9 —42.8 —30.5 —40.9 —65.5 eg" 2.4 2.9 1.1 36.9 32.1 —30.5 —17.6 18.7 57' 80.2 8S.8 83.6 134.0 42.8 104.0 17.6 102.8 76 TABLE XXXV Deviations from the medians; average for two years of per cent, of total which each item is (see Table XXXIII), reduced to per cents of the medians. The figures refer to per cents and tenths of per cents. ■6 "8 u ,- g >,.+» fe 2 °o SSO a 0£g,0 OOM Oijia U yB £ Total Cost per Pupil correlated with Teaching and Super- vision +1.015 1 + .97 +.96 +.99 +.88 Total Cost per Pupil correlated with Janitors' Salaries + .716 +.66 +.70 +.56 +.73 Total Cost per Pupil correlated with Text-Books and Sup- plies + .955 +.85 +.85 +.67 +.64 Total Cost per Pupil correlated with Fuel...!... + .522 2 +.45 +.50 +.34 +.40 Total Cost per Pupil correlated with Repairs + .246 +.24 +.47 +.56 +.35 Teaching and Supervision correlated with Janitors' Salaries + .746 +.64 +.63 +.44 +.53 Teaching correlated with Text- Books and Supplies + .737 +.63 +.76 +.35 +.65 Supervision correlated with Text : Books and Supplies. .. + .869 +.69 +.57 +.51 +.27 Supervision correlated with Repairs - .128 -.14 +.18 -.09 +.07 Supervision correlated with Teaching + .366 +.27 +.31 +.05 +.12 Supervision correlated with Fuel + .11 +.06 +.02 +.04 +.01 Janitors' Salaries correlated withFuel + .531 +.30 +.61 -.08 +.45 Janitors' Salaries correlated with Repairs + .219 +.32 +.32 +.39 +.24 Repairs correlated with Fuel . . + . 147 + . 12 + . 21 - . 001 + . 20 1 That this coefficient as corrected gives over ioo % is due to the fact that the third decimal place is lacking in the coefficients from which the correction was made. 2 The item "fuel" as reported for the two years is less definite than most of the other items, because fuel bought, or at least fuel paid for, one year is often used the next year; consequently, only the second method given by Spearman for the correction of the Pearson coefficient is used. This method is based on the fact that an increase in the num- ber of measures of each of the facts originally measured increases its accuracy. 82 City School Expenditures 83 first year's figures alone were used, when the second year's figures alone were used, and when the average for the two years was used (see columns 3,4, and 2). The second column gives the coefficients derived from the average of two years' figures; the third, the coefficients derived from the first year's figures from cities reporting two years; the fourth, the coefficients de- rived from the second year's figures; and the fifth, the co- efficients found when the figures for the fifty-eight cities reporting the first year were used. In the discussion which follows, the coefficients referred to are always the corrected coefficients, unless it is specifically stated that other coefficients are meant. I believe that the corrected coefficient more nearly expresses the relationship which actually exists among the various items correlated than does any other figure. 1 The first question which our coefficients enable us to answer concerns the relationship of the total cost per pupil to the prin- cipal items of the budget. Does an increased cost per pupil mean a proportionate increase in the amount spent for teaching and supervision, for janitors' salaries, for text-books and sup- plies, for fuel, and for repairs; or is the relationship between the total cost per pupil and the various items of the budget closer for some than for others ? Examining our coefficients we find that the relationship between the total cost per pupil and the cost for teaching and supervision is expressed by a coefficient of + 100 % (see explanation under Table XXVII), i. e., the amount spent for teaching and supervision is determined by the total amount spent per pupil. If a small total amount per 1 The true relationship between any two items in the budget for these cities is the relationship which would be found if we had perfect measures of the cities' tendencies to spend money for school; such, for instance, as their budgets for forty or fifty years. The effect of chance deviations of any single year from the cities' general tendencies is to bring the calcu- lated correlation from its true value toward zero. By the Spearman formulae we estimate the true relationship ( 1 ) from the obtained relation- ship and the amount of deviation of one year's budget from another year's, or (2) from the difference between the relationship obtained from one year's budget and that from two or more years' budgets. For the theory of the correction see, in general, Thorndike, Mental and Social Measurements, pp. 128 and 129, and in detail C. Spearman, on "The Proof and Measurement of Association between Two Things," American Journal of Psychology, January, 1904. 84 City School Expenditures pupil is spent, we may expect a correspondingly small amount per pupil for teaching and supervision; if a large total amount per pupil is spent, we may expect a correspondingly large amount per pupil for teaching and supervision ; if the cities were ranked in order on the basis of total amount spent per pupil, and then in order on the basis of the amount spent per pupil for teaching and supervision, we would expect to find that the rank of the cities would be the same for each item. The next closest rela- tionship is that for text-books and supplies, which gives a co- efficient of + .955. The others are, in order, janitors' salaries, + .716; fuel, +.522; and repairs, + .246. In general, these re- lationships show that the amount spent per pupil for teaching and supervision, and for text -books and supplies, corresponds very closely to the total amount spent per pupil ; if the cost per pupil is above the average, we may expect that the amount spent per pupil will be high for these items, and any diminution in the total amount spent per pupil is likely to be accompanied by a smaller expenditure per pupil for these purposes. The coefficients found for janitors' salaries and fuel show a less close correspondence. From the relationship here we may infer that the rank of any city above or below the median in total cost per pupil might be compatible with various ranks for janitors' salaries or fuel, which would tend to be approxi- mately three fourths of the rank in total cost per pupil. The item of repairs is least closely related with the total cost per pupil. This is as we might have expected. The fact that a school system is expensive does not increase the cost of re- pairing the buildings, except in so far as the labor necessary to do the work may cost more in those cities which are able to spend the large amount per pupil. We might expect the ex- pensive city to keep its buildings in better repair than the poorer cities, which, with the difference in the cost of labor mentioned above, would seem to account for the coefficient of +.246. The fact that we find a direct relationship between the total cost per pupil and the cost per pupil for each of the principal items of expenditure makes it clear that, in general, an expen- sive school system is expensive because it spends more money for everything, and that an inexpensive school system is one that retrenches all along the line. However, the fact that cer- tain of the items are less closely related to the total cost per City School Expenditures 85 pupil than others does indicate that these items will probably not be found to increase or decrease in a proportion equal to that of the items showing a closer relationship, nor in propor- tion to the increase in the total cost per pupil. Table XXXVIII shows just how an increased or a decreased total cost per pupil affects the principal items of the budget. The figures given refer to dollars, and are calculated from the average amount spent for each item for two years. The data are from thirty cities reporting for the school years 1 902-1 903 and 1 903-1 904. TABLE XXXVIII 2% H Average for the five cities nearest the median $29.00 First group of five cities above the me- dian group 31.00 Second group of five cities 34.10 The two cities having the greatest expense per pupil , ... 51.70 Average for the five cities nearest the me- dian 29.00 First group of five cities below the me- dian 27.70 Second group of five cities 25.50 The three cities having the smallest expense per pupil 20.80 $17.80 $2.20 19.20 3.20 21.80 2.30 .00 $1.90 $1.80 $1.90 $1.60 22.40 1.80 1.30 24.10 2.20 1.80 1.90 1.30 2.20 1.30 30.80 5.40 36.20 2.80 4.80 2.20 2.00 17.80 2.20 20.00 1.90 1.80 1.90 1.60 18.20 1.30 15.70 2.40 19.50 1.90 1.60 18.10 1.50 1.60 1.50 1.30 1.40 .90 13.60 1.60 15.20 1.10 1.10 1.50 .60 EXPLANATION OF TABLE XXXVIII The first line of the table gives the average total cost per pupil and the average amount spent for each of the principal items of the budget, for the five cities which have a total cost per pupil nearest the median total cost per pupil. The next line gives the same information for the group of five cities having the next highest total cost per pupil. The next two 86 City School Expenditures lines are explained in like manner. The fifth line repeats the first line. The sixth line gives the average total cost per pupil and the average ex- penditure for the several items of expenditure for the five cities which have the next lowest total cost per pupil below the median group. The next two lines are explained in like manner. From this table (XXXVIII) the relationships already shown by the coefficients of correlation given in Table XXXVII are made clear. In general, the table shows that an increased cost per pupil means an increased expenditure for each item, and that a decreased total cost per pupil is accompanied by a de- crease in the amount spent per pupil for everything. An in- crease of two dollars in the total cost per pupil (see line 2) is accompanied by an increase of $2.40 per pupil in amount spent for teaching and supervision, and a decrease in janitors' sal- aries, text-books and supplies, and repairs, while fuel remains the same. In the next group, however, with an increase in total cost per pupil above the median group of $5.10, teaching and supervision show an increase of $4.10, janitors' salaries and fuel show an increase of thirty cents each, text-books and sup- plies remain the same, and repairs decrease thirty cents per pupil. The next group, with an increased total cost per pupil of $22.70, gives an increase for teaching and supervision of $16.20, an increase for janitors' salaries of ninety cents, an in- crease for text-books and supplies of $3, an increase for fuel of thirty cents, and an increase for repairs of forty cents per pupil. By examining the part of the table giving the expenditures for groups of cities spending less than the median group, we find the decrease in all items more constant than was the in- crease for the cities spending more than was spent by the median group. The very fact that the city spends less than the average probably means that it would be very difficult to keep the ex- penditure in any one item up to the average without eliminating other necessary expenditures. On the other hand, a city spend- ing more than the average can put the additional money in any place where the demand, of one kind or another, may be strongest. Let us return again to a consideration of the relationships given in Table XXXVII. The relationship (+ .746) between teaching and supervision and janitors' salaries tends to confirm City School Expenditures 87 the observation made above with reference to -the relation be- tween these items and the total cost per pupil. We may not expect janitors' salaries to correspond so closely to the total cost per pupil as do teachers' salaries. Apparently there are causes other than those (the cost per pupil of teaching and supervision) which influence the amount per pupil spent for janitors' salaries. The coefficients for teaching and for supervision with text- books and supplies (+.737 and +.869, respectively), indicate a closer relationship between the cost per pupil for supervision and for text-books and supplies than exists between the cost per pupil for teaching and for text-books and supplies. That the relationship between supervision and repairs is negative (-.128) might seem to imply that high-priced super- vision means better care of buildings. The coefficient of super- vision correlated with teachers' salaries is + .366. This is rather smaller than one might have expected. It is rather natural to suppose that high-priced supervisors would want high-priced teachers, and that a city spending a large amount per pupil for teachers would spend a correspondingly large amount for super- vision. The small coefficient found for supervision correlated with fuel (+.11), seems to indicate that while greater expense for supervisors increases the amount spent for text -books and supplies (see coefficient for supervision with text-books and supplies), it has little in common with the expense for fuel. The relationship between janitors' salaries and fuel, and janitors' salaries and repairs, is expressed by coefficients of + .531 and +.219, respectively. It will be remembered that fuel is more closely correlated with the total cost per pupil than is janitors' salaries. This being true, it would seem that the correspondence between janitors' salaries and fuel might be accounted for by the fact that they are both determined largely by the total amount spent per pupil. It was found also that supervision and repairs show a negative relationship, and here we find a positive relationship between janitors' salaries and repairs nearly equal to the relationship between repairs and the total cost per pupil. Apparently costly supervision means more for economy in repairs than does a large amount per pupil spent for janitors' salaries. The next table (No. XXXIX) gives the coefficients which were calculated on the "per cent, of total" basis. 88 City School Expenditures These coefficients show what effect the spending of a certain proportion of the money available for one item has on the pro- portion spent for other items. TABLE XXXIX Pearson Coefficients of Correlation calculated on the per cent. of total basis. ° 3 oScS ^o2- >-^ m ")£ > ? £ >«h.«-5 s£ £ "C 2 ° m u « >-3 o ° -a-d ° -3 >-3<» -SeS l| •«;§ . 2^-2 «~ .§§- J&Sg Teaching and Supervision correlated with Janitors' Salaries - . 356 - . 30 - . 25 - . 43 - . 48 Teaching correlated with Text- Books and Supplies - . 746 - . 46 - . 09 - . 59 - . 12 Janitors' Salaries correlated with Fuel -.024 -.03 +.12 -.33 +.26 Janitors' Salaries correlated with Repairs +.155 +.17 +.12 +.48 +.13 Supervision correlated with Text-Books and Supplies ... + . 203 + . 17 + . 17 + . 27 + . 01 Supervision correlated with Repairs . -.409 -.28 -.06 -.38 +.03 Supervision correlated with Teaching -.983 -.68 -.54 -.69 -.67 Supervision correlated with Fuel.... -.333 -.20 -.17 -.03 -.02 Repairs correlated with Fuel . . + . 195 - . 03 + . 003 + . 12 + . 23 In this table (XXXIX) the significant thing is not so much the size of the positive or negative coefficients as the order, the relative closeness of relationship or opposition among the various items. Rearranging the table on this basis and calling the median relationship zero, and transmuting the others on this basis, the following table is derived: Transmuted Coefficients. Supervision correlated with Teaching — . 983 — . 650 Teaching " " Text-Books and Supplies . . -.746 -.413 Supervision " Repairs — .409 — . 076 Teaching and Supervision correlated with Janitors' Salaries -.356 -.023 Supervision correlated with Fuel — . 333 Janitors' Salaries correlated with Fuel — . 024 + . 309 " Repairs +.155 +.488 Repairs correlated with Fuel + . 195 + . 528 Supervision correlated with Text-Books and Supplies . • + . 203 + . 536 City School Expenditures 89 I believe that the transmuted coefficients more nearly ex- press the true relationship than do those originally found, for we must have expected a negative relationship between any two items, because a larger proportion than usual spent for one item leaves a smaller proportion of the total to be divided among the other items of the budget. So far as the coefficients obtained enable us to judge, this negative relationship, due simply to the fact that a larger proportion of money than usual spent for any one item leaves a smaller proportion for other items, is approximately the relationship half-way between the extremes, — the relationship between supervision and fuel, — .333. If we call this relationship zero, the transmuted rela- tionships give us, as nearly as we can obtain them, the relation- ships between the other items freed from this constant error. Let us consider the transmuted coefficients. Suppose a city spends more than the usual proportion for supervision, what other items may we expect to find receiving an unusual propor- tion of the money spent? The coefficient of + .536 between supervision and text-books and supplies indicates that the probability is that a city which spends a large proportion for one of these items will spend a large proportion for the other, — that we may expect to find some cities unusual both in respect to the proportion spent for supervision and that spent for text-books and supplies. The positive coefficients between janitors' salaries, fuel, and repairs, no matter which two are taken together, shows that in cities where one of these items is proportionately large, the others will probably receive more than the usual proportion. Comparing these coefficients with those found for teaching and supervision with janitors' salaries and supervision with fuel, it is suggested that some boards of education are interested particularly in the physical side — the buildings, their care, etc., — and that this over-emphasis on this side means less money for the purely educational activities. The very large negative coefficient for supervision correlated with teachers' salaries would doubtless be reduced if more accurate reports of the amounts spent for each of these items were available. It is in this relationship between the two items that any mistakes in reporting in either an amount which really belonged to the other would be most apparent. Any amount reported as teaching which should have been given as supervi- 90 City School Expenditures sion would make the amount for teaching too large and the amount for supervision too small, and the opposite would be true if an amount which should have been reported as teaching were given as supervision. In either case, such mistakes would make this particular coefficient show a more pronounced negative relationship than actually exists. Such mistakes would not, however, have a like effect on other coefficients, where the in- crease or decrease in the item of supervision or teaching has no effect on the other item correlated. The fact that the amounts given for teaching or supervision may in one case be slightly too large and in another slightly too small, means that, except when the two items themselves are correlated, the mistake in one direction would be offset by the mistake in the other. The relationship between teachers' salaries and text -books and supplies ( — .413) is particularly interesting when con- trasted with the relationship between supervision and text- books and supplies (+ .536). If a city spends an undue proportion for supervision we may expect that an unusually large proportion will be spent for text-books and supplies ; while the opposite condition holds for the proportion spent for teaching. Possibly the relationship between supervision and text -books and supplies is simply that the highly paid supervisors are able to get appropriations for books and supplies, and that poorly paid supervisors do not have the ability or influence, rather than that the supervisors have much to do with the actual use or waste of supplies furnished. On the other hand, if there is anything that a good teacher wants, it is plenty of books and supplies of the right quality, consequently it seems strange that there should be this opposition in the relative proportions spent for these two items. However, expensive teachers may effect economy by the proper use of materials, and poorly paid teach- ers may be the most careless. There is nothing that hurts a book so little as using it properly, and it is conceivable that the best teachers may actually use fewer supplies than those with less ability. Table XL gives the correlation of the first and second years' figures on both the cost per pupil and per cent, of total bases. These coefficients give us some idea of the relative stability of the various items of the budget. They are used also in making the Spearman correction. City School Expenditures 9i TABLE XL First and second year's figures correlated, the school years 1902-03 and 1903-04. Thirty cities reporting for l I — Cost per Pupil Basis Total cost per pupil correlated with total cost per pupil + Supervision and teaching correlated with supervision and teaching -j- Supervision Teachers' salaries Janitors' Text-books and supplies Fuel Repairs supervision . -\- teachers' salaries -j- janitors' " + text-books and supplies.. + fueL + repairs + II — Per Cent, of Total Basis Supervision Teachers' salaries Janitors' " Text-books and supplies Fuel _ Repairs 92 89 69 79 90 89 17 34 Supervision and teaching correlated with supervision and teaching + . 56 supervision + . 58 teachers' salaries -j- . 51 janitors' " + -80 text-books and supplies . -j- . 65 fuel +.34 repairs + • 54 The total cost per pupil gives a coefficient of + .92, showing that the amount per child spent does not vary much from year to year, — the expensive city remains so, and the city spending little does not suddenly devote a much larger proportion of its revenues for schools. Almost as constant as the total cost per pupil are the amounts spent for janitors' salaries, text -books and supplies, teaching and supervision, giving, as they do, coeffi- cients of +.90, + .89, + .89, respectively. The items of teach- ing and supervision, when taken alone, show greater variation (coefficients of + .79 and + .69, respectively) , due largely to the fact that, in reporting, amounts properly belonging to one item were reported under the other, rather than in a change of policy as to the relative amount to be allowed for teaching and for supervision. As one might expect, the amount spent for repairs varies more than any of the items mentioned above (a coefficient of + .34 was found). A large amount spent for repairs one year means a smaller amount the next year, rather than an equally large amount. That the coefficient for fuel is as low as + .17, might seem to indicate that fuel in excess of that which is used is often bought and paid for out of a single year's budget, rather 92 City School Expenditures than that there is any very great difference in the value of the fuel actually consumed each year. When we come to consider the proportion of the total which is spent for any one item for two successive years, we find the variability rather greater than for the amount spent per pupil. This is due to the fact that, while the amount per pupil spent for any one purpose remains fairly constant, any additional ex- penditure for some new item which increases the gross amount spent, or any diminution in any item of expenditure, affects the proportion which this item is of the total amount spent. It is interesting to note that in the relative constancy with which a given proportion is spent for any item, janitors' salaries lead, followed by text-books and supplies, supervision, teaching and supervision, repairs, teaching, and fuel (see part II of Table XL). Table XLI gives the coefficients for the total cost per pupil correlated with the per cent, which each item is of the total. These coefficients tell us what effect a larger or smaller expendi- ture per pupil may be expected to have on the proportion which is spent for any one item of the budget. TABLE XLI Pearson Coefficients of Correlation The total cost per pupil correlated with the per cent, which each item is of the total. The average cost per pupil and per cent, of total for two years is used as the basis of calculation. Total cost per pupil correlated with per cent, of total spent for: Teaching and Supervision — . 05 Janitors' Salaries — . 06 Text-Books and Supplies + .35 Fuel.. -.22 Repairs + . 13 Apparently the total cost per pupil may not be expected to affect the proportion spent for teaching and supervision and for janitors' salaries. Cities spending a large amount per pupil do not necessarily spend any greater proportion of their money for these purposes than do cities spending a smaller amount per child. (The coefficients of —.05 and —.06 are so small as to be practically negligible.) On the other hand, the positive co- City School Expenditures 93 efficient of + .35 for text-books and supplies indicates that there is a direct relationship between the total amount spent per pupil and the proportion which is spent for this purpose. We may expect an expensive city to spend a larger proportion of its money for text-books and supplies than does the poorer city, even though we may infer from this coefficient that the increase in the proportion spent for this purpose will not be proportion- ate to the increased cost per pupil. The negative coefficient for fuel shows that the proportion spent for fuel decreases as the total cost per pupil increases. The most expensive city will probably spend a smaller proportion of its money for fuel than a poor city. That the proportion spent for repairs should give a positive coefficient of + .13 when correlated with the total cost per pupil seems to indicate that there is some tendency for the more expensive cities to spend a larger proportion for re- pairs than the less expensive city — possibly the cities spending the greater amount per pupil do keep their buildings in better repair. Table XLII gives the average salary received by elementary and by high school teachers, and the average daily wage re- ceived by carpenters, bricklayers, and day laborers. This in- formation was calculated from two years' data for the thirty cities reporting for the school years 1 902-1 903 and 1 903-1 904. The figure given for elementary and high school teachers' sal- aries was derived by finding first the average salary paid to each class of teachers for each year separately by dividing the gross amount spent for each item by the number of teachers (see form sent to superintendents), and then the average for the two years was taken. In a similar manner, from the report given by city superintendents on the blank filled out by them, the average wage of carpenters, bricklayers, and day laborers was calculated. The information concerning the daily wage of carpenters, bricklayers, and day laborers is probably less exact than we might wish, but sufficiently accurate, I think, to show whether or not any relationship exists between the amounts paid to this class of laborers and to teachers. It is for the pur- pose last mentioned that these data are given. Coefficients will be given to show what relationship exists between the wages paid carpenters, bricklayers, and day laborers and the salaries paid teachers. 94 City School Expenditures TABLE XLII 5 6 8 13 14 15 16 20 27 28 29 30 31 32 34 35 36 37 39 40 4i 42 43 45 48 52 54 55 56 57 5 cS $■£ »" £12 3HJ2 pa m-3 Jo g>u g nj g,cj gu-, ^ ^ |° <^ 1 1* . -. --n Xtr, O Q u ,8s £ u- 0,fl a) bo t.W wS en S3 ■go ™>£ . - to DO J? s *** m (2 CD bo . el-gsa (< y > " g >< JB £ CSTT3 bo 3 a* J3 . °s 5 Z, H 2; % H . o o £ z; Per Cent, of the Total Number of Pupils who are Enrolled in Elementary Schools ; Average for Two Years. "3 H CO i +» a V u< V Amount Spent for Salaries ; that is, Spent for Element- ary Teachers' Sala- ries ; Average for Two Years. Per Cent, of the Total Number of Pupils who are Enrolled in High Schools; Aver- age for Two Years. "c8 O H *o a 6 u C4 Amount Spent for Salaries ; that is, Spent for High School Teachers' Salaries ; Average for Two Years. »3 . m JS r3 O 0,u O 3 O.C O,"*-' <-ij3 ™ ft,VM O <- w JJ »° <*.G 55 5- 88.5 75.2 11.5 24.8 43 22 6. 86.9 72.0 13.1 28.0 50 25 8. 87.7 77.9 12.3 22.1 47 27 13. 93. 85.3 7. 14.7 38 30 14. 91.8 80.9 8.2 19.1 35 23 15. 90.1 82.3 9.9 17.7 48 31 16. 93.1 77.6 6.9 22.3 35 17 20. 89.6 78.3 10.4 21.7 49 28 27. 84.4 72.6 15.6 27.4 47 31 28. 96.1 83.7 3.9 16.3 44 18 30. 91.4 78.2 8.6 21.8 38 26 31. 94.1 82.2 5.9 17.8 38 24 32. 90.9 85.4 9.1 14.6 47 36 34- 90.1 78.8 9.9 21.2 39 23 35- 85.4 81.2 14.6 18.8 38 34 36. 82.8 74.2 17.2 25.8 42 27 37- 88.5 76.3 11.5 23.7 54 34 39- 82.9 72.8 17.1 27.2 37 30 40. 70.6 56.2. 29.4 43.8 49 34 41. 88.8 79.1 11.2 20.9 47 30 42. 90.2 77.0 9.8 23.0 56 29 43. 85.3 78.3 14.7 21.7 40 36 45- 93.4 80.6 6.6 19.4 43 19 48. 94.7 86.1 5.3 13.9 48 21 52. 94.0 86.9 6. 13.1 50 35 54- 92.5 82.6 7.5 17.4 35 20 55- 90.2 83.6 9.8 16.4 54 43 56. 95.4 91.1 4.6 8.9 46 24 57- 87.7 74.7 12.3 25.3 38 22 Li If 99 ioo City School Expenditures the item of salaries is a good index, first, because the item of salaries forms from 60 % to 80 % of the entire budget; and, second, because other expenditures for books, supplies, and ap- paratus are enough larger, in proportion to the number of pupils enrolled, in the high school to offset an expenditure of the same amount per pupil for janitors' salaries, fuel, repairs, etc. CONCLUSION This section will give a brief general summary of the results which have already been obtained, and some practical sugges- tions which grow out of these facts. First, with regard to vari- ability, it will be remembered that the cost per pupil for the maintenance and operation of schools in the cities considered varies from $9 to $55. That this variation in the total cost per pupil is not due entirely to the relative wealth or poverty of the different communities is shown conclusively when we know that the cost of schools in cities in the United States varies from 6 % to 46 % of the total city expenditure. 1 An equally striking variability is found in the cost per pupil for each of the prin- cipal items of expense. Even when cities spending about the same amount per pupil are considered, it is found that the dis- tribution of the money among the several items seems not to show anything like the degree of uniformity which might be expected (see page 44). It is found that the percentage of the total cost of maintenance and operation which is spent for teaching and supervision varies from 44 % to 82 %; and what possibly seems more astonishing is the fact that the city spend- ing the smallest proportion for teaching and supervision, spends the smallest total amount per pupil. Janitors' salaries amount to from 3 % to 9 % of the budget ; one city spends 3 % of its money for fuel and another spends 12% for the same purpose ; text-books and supplies cost from 1 % to 13 % of the total cost of maintenance and operation. Fuel costs three times as much per pupil in one city as in another. The expenditure per pupil for the salaries of high school teachers varies from one and one half to four times the cost per pupil for salaries of teachers in the elementary schools. 1 These results are from an unpublished study by Mr. E. 0. Elliott, and were obtained by using the data found in the bulletins of the Com- missioner of Labor. City School Expenditures 101 In our consideration of relationships we found that an ex- pensive school system is one that spends more than the usual amount for all of the principal items of expense. A large posi- tive relationship exists between the proportion spent for super- vision and the proportion spent for text-books and supplies. A lack of relationship between the total cost per pupil and the proportion which is spent for teaching and supervision seems to indicate that additional expenditures may not mean, as they should, a greater proportion for those items which count most for the efficiency of the schools. These and the many other facts which are given above con- cerning the variability and interrelation of the principal items of expense for schools, prove conclusively that the problem of the business administration of city school systems is not only a real and vital one, but also that we may expect that the schools will increase in efficiency when the money devoted to public education is distributed among the various items in the best possible way. As has been stated, our final test can only be found by testing the pupils in the schools in order to rate different systems for efficiency, and then we must conclude that those cities which get the best results for a given expenditure per pupil are the cities which properly distribute their money. How- ever, before any such comparison among the various cities can be made, we must have more detailed information with regard to the way in which the money is used. If we may not ask city superintendents or boards of education to report their expendi- tures according to a certain fixed form, it does seem that we might insist that their reports tell us for just what purposes the money is spent. A report which gave the various items of ex- pense in detail would enable any one to compare cities accord- ing to whatever classification seemed best. Nor would such reports be without their value to the persons making them. If the administrator of schools is to secure additional money, either for purposes for which money is already used, or for any new field of activity, he can have no better argument than to be able to show just what results are obtained in his own and other cities from a given expenditure. Suppose, for example, that a superintendent wishes to introduce manual training or domestic science ; he will be met immediately by the statement that these "fads" are expensive and not at all necessary as a 102 City School Expenditures part of public education. Now, if it were possible for him to show from the reports of other cities that the additional ex- penditure was comparatively small, and that results obtained in the way of retaining pupils in school were considerable, he could make an argument which would have some weight. If the greatest economy is to be had, it is essential that the accounting should show just how much money is spent for each item, and, within a system itself, how various schools compare. It should be possible for the administrative officer to tell just what the cost per pupil is for each school within the system, and to compare the relative cost with the relative efficiency as found by testing the pupils of each school. No great corpora- tion would to-day continue to spend money for purposes for which no results could be shown, and no school system should so report its expenditures that it is impossible to tell how much the educational policies cost which it advocates and carries out. It seems hardly right to expect that a superintendent whose time is already overcrowded, and who has as his assistant a clerk worth $500 a year, should be asked or expected to origi- nate or carry out any such policy of accounting as has been suggested above. But when we recall again the great variability which is found for those items of expense which might be ex- pected to be fairly constant, we feel that it is not out of place to suggest that the salary of a competent business agent or director might be paid out of the savings which would be made by the proper administration of the business affairs of the schools, and that the efficiency of the schools might be increased as the result of the proper distribution of the money spent. When the best judgment is used in the purchase and use of supplies and equipment as well as in the selection of teachers and" supervisiors of instruction, when the money which is spent for schools is properly distributed among the various items of the budget, when expenditures are shown in reports in connec- tion with the results obtained, then our schools will be found to have improved in efficiency, and then they will be able to com- mand the respect and increased support of the community. City School Expenditures 103 ACKNOWLEDGMENT The author wishes to acknowledge his indebtedness to those whose aid has made this study possible. It is only through the efficient cooperation of very many friends that such a study as this can be undertaken. It is, therefore, with a sense of pe- culiar obligation that I express my thanks to all those who helped in the collection of data. Among them are: Messrs. F. W. Atkinson, Emmet Belknap, N. L. Bishop, D. C. Bliss, G. N. Bliss, Eugene Bouton, H. O. Bowers, C. B. Boyer, F. D. Boynton, A. D. Call, J. H. Carfrey, W. E. Chancellor, J. H. Christie, R. J. Condon, F. E. Corbin, J. M. Crane, A. D. Dunbar, J. G. Edgerly, Thomas Emerson, J. A. Estes, W. B. Ferguson, E. H. Forbes, J. B. Gifford, J. C. Gray, I. F. Hall, E. S. Harris, F. J. Heavens, E. J. Hitchner, C. L. Hunt, L. R. Hunt, T. R. Kneil, H. W. Lull, A. B. Mather, F. E. McFee, John Millar, H. T. Morrow, C. H. Morss, W. A. Mowry, F. R. Page, W. D. Par- kinson, F. E. Parian, Freeman Putney, E. S. Redman, R. R. Rogers, A. L. Safford, F. J. Sagendorph, S. R. Shear, E. E. Sher- man, Randall Spaulding, R. A. Taylor, W. H. Truesdale, J. F. Tuthill, J. C. Van Etten, C. F. Walker, Robt. Waters, E. C. Willard, J. I. Wood, and I.E. Young. To these and the many others who rendered valuable assistance in the collection of material, the author acknowledges his indebtedness. Whatever merit the treatment of the data which were col- lected has, is due to the teaching of Professor Edward Lee Thorndike, to whom the author is also indebted for very many most helpful suggestions and for constant criticism. For assistance in the numerical work, without which this study could not have been completed for some months to come, the author is indebted to Miss Jeanette F. Seibert, Assistant in Psychology in Teachers College. io4 City School Expenditures VITA The author of this dissertation, George Drayton Stray er, was born at Wayne, Delaware County, Pennsylvania, on No- vember 29, 1876. He received his early education in the public schools of Pennsylvania, graduating from the Lewistown High School in 1893. He was a student at Bucknell University during the year 1896-1897, and at the Johns Hopkins Univer- sity from 1900 to 1903, from which last-named University he received the degree of Bachelor of Arts in 1903. He was a student at the Columbia University Summer School in 1903; student at Columbia University and Earl Scholar in Teachers College during the year 1 903-1 904; and Fellow in Education in Teachers College, Columbia University, during the year 1904- i9°5- LIBRARY OF CONGRESS 021 324 838 8 I LIBRARY OF CONGRESS 021 324 838 8