84-2 Erma NorFl HLKlts DIVISION L I B R A R Y INSTI"TTE FOR FISHERIES RESEARCH University Museums Annex r Anr" Arbor, Michigan 4'1QA TECHNICA -, 1111111 IN =owl~ A Statistical Comparison of Catch Per Hour Rates Between Complete and Incomplete Fishing Trips in Michigan I h TNI M I ý C; "7z) Number 84-2 anuary 24, 1984 m E~~rs~8aa~sa~s~%%~i~ Michigan Departmnent of u/i '1 - MICHIGAN DEPARTMENT OF NATURAL RESOURCES FISHERIES DIVISION Fisheries Technical Report No. 84-2 January 24, 1984 A STATISTICAL COMPARISON OF CATCH PER HOUR RATES BETWEEN COMPLETE AND INCOMPLETE FISHING TRIPS IN MICHIGAN Roger N. Lockwood 2 Abstract Creel census data collected from Michigan anglers are frequently composed of complete and incomplete fishing trip interviews. The purpose of this study was to compare catch rates, by species, of complete and incomplete fishing trips. In each comparison, variances of catch rates were first tested to determine equivalency. The appropriate t test was then applied and statistical differences were determined, at the 5% level of significance. Data collected indicated that the catch per hour rates of incomplete trips were different from complete fishing trips more than 20% of the time. Introduction The creel census is an important tool for monitoring fisheries. Managers can use a census to estimate the amount of fishing effort occurring and to help determine the effects of fishing on the fish stocks. Both biological and sociological information can be obtained from census and these data are vital for making management decisions such as evaluating the need for regulations or stocking. In most censuses, anglers are either interviewed while they are fishing (incomplete interview) or after they complete their fishing trip (complete interview). Basic information recorded during an interview includes: fishing location, date, type of fishing (boat, shore, or pier), whether the trip is complete or incomplete, number of anglers in the party, length of the fishing trip, and the number of fish (by species) caught and kept by the fishing party. Surveys being run over large bodies of water, or on areas having many access points, frequently include large numbers of incomplete interviews (Geis and Gustafson 1977). Thus, catch estimates may be based almost entirely on incomplete interviews. Few studies have been conducted to compare catch rates of complete versus incomplete fishing trips, but I did find two studies (Malvestuto, Davies, and Shelton 1978; and Fierstine, Geis, and Gustafson 1978) and they both concluded that no 3 significant differences existed between these catch rates. However, I made the same comparison, using data from four Michigan censuses, and found that significant differences did exist. Study Areas and Methods The original purposes of the four surveys used to compare complete and incomplete catch rates were to estimate the number of angler fishing trips, hours fished, and the numbers of fish caught (by species). The species of fish available at each site varied, and only those species which were most abundant in the anglers' creels were used for this analysis. Also, only interviews from shore anglers were examined. In the spring, 1980, a creel census was conducted on the Grand River, which flows 478 miles through southwestern Michigan before emptying into Lake Michigan at Grand Haven. Anglers were counted and interviewed at the 6th Street Dam in Grand Rapids during March and April. The species of fish of major concern during this census was the rainbow trout (Salmo gairdneri). From May through October, in 1978, anglers fishing from Chesterfield Pier, located on Lake St. Clair (Wayne County, Chesterfield Township) were interviewed. The main species of fish taken by these anglers were rock bass (Ambloplites rupestris), yellow perch (Perca flavescens), and freshwater drum (Aplodinotus grunniens). From June to August in 1976 and from April to October in 1977, Belleville Lake, a 1,270-acre impoundment on the Huron River, was censused. Anglers were interviewed at various points along the shore line. Here the fish examined were bluegill (Lepomis macrochirus), sunfish sp. (Lepomis sp.), and black crappie (Pomoxis nigromaculatus). Angling parties interviewed at each location fished a minimum of 0.5 hour and each fishing trip was recorded to the nearest 0.5 hour. Catch per hour (C/H) rates were calculated by party, thus, if two anglers fished 5 hours and caught one rainbow trout, the C/H would be 0.1. Since catch rates are -4 - typically calculated by species and time period (i.e., month), no catch rates by season or with species combined were determined (Tait 1953). Data were not used for months in which one interview type (complete or incomplete) represented less than 10% of the opposing interview type in sample size. For each month variances of mean catch rates for complete 2 2 (S ) and incomplete (SI ) interviews were tested to determine equivalence. Equivalence of variances were tested first to determine the correct test to compare means. The method used for this test (Dixon and Massey 1951) is as follows: 2 2 a. H: a1 2 -= 2 ' b. Choose significance level of test (a), 2 2 c. Use the statistics F (S /S ) to test the hypothesis, d. If the observations are random samples from normal populations, and if the hypothesis is true, then the sampling distribution of this statistic is F (NI-l, N2-1), e. Reject if F>F_ 1l(N1-1, N2-l) or, if F<F~ l(N1-,2 N2-1), f. Compute the F from sample, and reject or accept the hypothesis. 2 2 When differences between S and S were noted, the mean catch I C rates were compared using the t' test found in Snedecor and Cochran (1971), where, -A - 2 + S2 t< = (X1X2)/ Sl/N /N (t1 + 2 1 IN-1 2 N the significance level of t (df) is, (wI tI + w2 t) (w, + w2) when, 2 WI - SI / NI, and W - 2 W2 - 2/N2 5 If tV > t'(, the difference is significant at that - \.(df) 2 given level. The standard t test, using a pooled S,was 2 2 used when S = S and is also found in Snedecor and Cochran I C (1971), where, t = (X - X1 ) / S2 (N + N2) N1 N2 and, 2 2 2 2 S2 {X - (X ) /N1} + {X2 - (X2) /N2} N1 + N2 - 2 if, t > t, then, X = X2. -(df )-1) 1 2 2 2 2 The t test with a pooled S should not be used when S A S X I C because, when the larger sample has the smaller SX, it results in a significant difference being found too often. Conversely, 2 when the larger sample has the larger SX, significant differences may go undetected (Snedecor and Cochran 1971). This same problem would also result if an analysis of variance were used to test means. Tests using confidence limits about the means also proved unreliable. A significant difference was noted in only 1 case out of 44 when confidence limits were used, while the t test indicated a difference in 9 additional cases. Since the confidence limits do not extract between sample variation, significant differences appear to go undetected. Statistical differences were tested at the 5% level of significance. Results There was a significant difference between catch rates of rainbow trout for complete versus incomplete interviews for March and April of 1980, on the Grand River. In both instances 6 mean catch rates were greater for incomplete than for complete fishing trips (Table 1). The 1973 data from Lake St. Clair, Chesterfield Pier, showed significant differences between catch rates for complete versus incomplete interviews for yellow perch and drum in June, drum in July, and yellow perch in August. Here mean catch rates were greater for complete fishing trips than for incomplete fishing trips (Table 2). On Belleville Lake in 1977, significant differences occurred for bluegill in May, for sunfish sp. in June, for black crappie in July, and for bluegill in October. The catch rates for incomplete angler trips were greater than those for complete angler trips (Table 3). No significant differences were detected for catch rates on Belleville Lake in 1976 (Table 4). The t test, using a pooled variance was used on Lake St. Clair for 1978 during May for yellow perch and June for rock bass (Table 2), and on Belleville Lake for 1977 during September for bluegill and black crappie and October for sunfish sp. and black crappie (Table 3). In each of these instances, no significant differences were found. All of the remaining comparisons 2 2 were made utilizing the t test where S SC. Of the total 44 comparisons made, statistical differences, at the 5% level, were detected in 10 instances. This is equivalent to a 23% difference rate for the data tested. Discussion Differences in catch rates between complete and incomplete interviews were detected more than 20% of the time in the data I used. This suggests that future data collected should be tested prior to having complete and incomplete interviews combined. Incomplete interviews had significantly higher catch rates than complete interviews from Belleville Lake (1977) and on the Grand River. This seemed to indicate that anglers continued to fish until their success rates remained low for a given period of time. Anglers on Chesterfield Pier, however, 7 appeared to continue fishing until their trip was successful. In each of these cases, the relationship between significantly different catch rates remained constant for that particular survey. This would seem to indicate the presence of factors which may enable a fisheries manager to predict the type of interviews necessary for an accurate survey. These factors may include such things as, the group of key species of fish being sampled, type of water, and time of year. The major drawback in predicting the necessity for a high percentage of complete interviews is the manpower requirement for a survey of this type. One alternative to increasing manpower would be to extend the length of the census clerk's day. For example, if most anglers fish until 9 pm and the census clerk quits at 8 pm, many complete interviews would be missed. By moving the clerk's work day from 11 am-8 pm to 1 pm- 10 pm, this problem would be solved. A second solution would be to adjust incomplete catch rates on data which have already been collected. Since the data tested seem to indicate that this bias is consistant for a particular survey, an adjustment factor should be relatively easy to calculate. Increasing the minimum time limit on incomplete interviews from 0.5 hour may also improve the accuracy of their catch rates. Data previously collected may be analyzed to determine the minimum acceptable trip length. Interviews containing trips less than this minimum may be discarded and the remaining data processed with the complete interviews. While the sample size, and therefore precision, is decreased, the improved accuracy of the estimates may be improved. Realizing the minimum trip length requirement, fisheries managers would thus be able to caution creel census clerks against collecting incomplete interviews, in the future, from anglers fishing less than the alloted time. Additional analysis will be necessary to determine if appropriate minimum trip lengths vary between surveys. -8 -Acknowledgments Creel census data for this project were provided by Percy W. Laarman, Merle G. Galbraith, Jr., and District 9 fisheries personnel. Jim Ryckman provided statistical advice and encouragement. This manuscript was reviewed, at various stages, by William C. Latta, Richard D. Clark, Jr., and William E. Fennel. Barbara A. Lowell typed the manuscript,. A contribution, in part, from Dingell-Johnsoyn F-35-R, Michigan. 9 Table 1.. Catch rates of rainbow trout for complete and incomplete angler trips with t and F statistics for the Grand River in 1980. Month Complete Incomplete F Lower Upper Student t No. C/H No. C/H limit limit t0.05 March 54 0.0682 52 0.1726 0.4180 0.5650 1.77 2.7641 2.0086* April 79 0.1579 84 0.2648 0.3333 0.6452 1.55 2.1611 1.9901* * Significant at oc = 0.05. Table 2. Catch rates for complete F statistics on Lake St. 10 and incomplete angler trips with t and Clair, Chesterfield Pier, in 1978. Month Complete Incomplete F Lower Upper Student t0. and No. C/H No. C/H limit limit t species May Rock bass 107 Yellow perch 107 Drum 107 June Rock bass 151 Yellow perch 151 Drum 151 July Rock bass 128 Yellow perch 128 Drum 128 August Rock bass 93 Yellow perch 93 Drum 93 September Rock bass 58 Yellow perch 58 Drum 58 October Rock bass 22 Yellow perch 22 0.0752 0.0081 0.0169 0.0286 0.0064 0.1694 0.0031 0.0226 0.0253 0.0008 0.0111 0.0039 0.0 0.0172 0.0031 0.0 0.0835 65 65 65 26 26 26 59 59 59 42 42 42 18 18 18 4 4 0.1540 0.0069 0.0 0.0251 0.0 0.0 0.0 0.0040 0.0025 0.0 0.0019 0.0 0.0 0.0017 0.0017 0.0 0.0100 0.3004 1.0707 0.0 0.8783 0.0 0.0 0.0 103.1235 61.8099 0.0 9.1229 0.0 120.4897 10.8364 66.9451 0.6426 0.6426 0.6426 0.6141 0.6141 0.6141 0.6623 0.6623 0.6623 0.5952 0.5952 0.5952 0.4970 0.4970 1.7390 1.7390 1.7390 1.9100 1.9100 1.9100 1.5600 1.5600 1.5600 1.7600 1.7600 1.7600 2.3800 2.3800 1.1337 0.1638 1.5374 0.1608 2.6469 4.3099 1.7051 0.8854 2.4152 0.9956 2.1164 1.6820 1.4602 0.4032 2. 0239 2.0239 1.9978 1.9749 1.9840 2.0485 1.9749* 1.9749* 1.9799 1.9803 1.9806* 1.9867 1.9933* 1.9867 2.0031 2.0256 2.1623 0.2618 14.2000 Drum 22 0.0 4 0.0 * Significant at oc = 0.05. 11 Table 3. Catch rates for complete and incomplete angler trips with t and F statistics on Belleville Lake in 1977. Month Complete Incomplete F Lower Upper Student t0.05 and No. C/H No. C/H limit limit t species April A- il Bluegill 159 Sunfish 159 Crappie 159 May Bluegill 186 Sunfish 186 Crappie 186 June Bluegill 47 Sunfish 47 Crappie 47 July Bluegill 39 Sunfish 39 Crappie 39 September Bluegill 26 Sunfish 26 Crappie 26 October Bluegill 21 Sunfish 21 Crappie 21 0.0749 0.0478 0.5074 0.0235 0.0114 0.2345 0.0091 0.0033 0.0127 0.0028 0.1230 0.0051 0.3197 0.1868 1.2021 0.0079 0.0992 1.5193 241 241 241 165 165 165 281 281 281 252 252 252 91 91 91 73 73 73 0.0865 0.0167 0.3178 0.0903 0.0313 0.3138 0.0190 0.0951 0.0043 0.0045 0.2148 0.0484 0.6922 0.1218 0.6676 0.1544 0.1404 0.9131 0.9180 18.9400 3.7758 0.1089 0.3088 0.7470 0.1651 0.0008 3.7440 0.2035 0.5624 0.0105 0.7562 5.7643 0.7981 0.0129 0.7500 1.7091 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.6944 0.6944 0.6944 0.6757 0.6757 0.6757 0.5495 0.5495 0.5495 0.5092 0.5092 0.5092 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.5600 1.5600 1.5600 1.6400 1.6400 1.6400 2.0000 2.0000 2.0000 2.2300 2.2300 2.2300 0.3038 0.9410 1.4835 2.2357 1.5339 1.2353 0.8141 2.3902 0.7537 0.4286 0.8748 2.1254 1.0169 0.3435 1.0316 3.8215 0.4530 0.8605 1.9693 1.9744 1.9727 1.9748* 1.9746 1.9743 1.9867 1.9603* 2.0118 1.9940 2.0079 1.9638* 1.9799 2.0561 1.9799 1.9984* 1.9867 1.9867 * Significant at o = 0.05. 12 Table 4. Catch rates for complete and incomplete angler trips with t and F statistics on Belleville Lake in 1976. Month Complete Incomplete F Lower Upper Student t0 and No. C/H No. C/H limit limit t 0.05 species June Bluegill 85 0.0121 18 0.0278 0.2943 0.5155 2.2900 0.5481 2.1029 Sunfish 85 0.0374 18 0.0 0.0 0.5155 2.2900 1.5309 1.9901 Crappie 85 0.0471 18 0.0 0.0 0.5155 2.2900 0.9991 1.9901 August Bluegill 49 0.0074 7 0.0 0.0 0.3922 4.2800 1.0029 2.0086 Sunfish 49 0.0121 7 0.0 0.0 0.3922 4.2800 1.1708 2.0086 Crappie 49 0.1307 7 0.0 0.0 0.3922 4.2800 1.1046 2.0086 13 Literature Cited Dixon, Wilfred J., and Frank J. Massey, Jr. 1951. Introduction to statistical analysis. The McGraw-Hill Book Company, Inc., New York, New York, 370 pp. Fierstine, Harlan L., Joseph L. Geis, and Scott P. Gustafson. 1978. A statistical comparison of incomplete and complete angler trip catch rates. Minnesota Department of Natural Resources, Division of Fish and Wildlife, Section of Ecological Services, Investigational Report No. 360, 8 pp. Geis, J. L., and S. P. Gustafson. 1977. Progress report on the Prairie Island creel survey, March 6-November 21, 1976. Pages 2.5.3-1 - 2.5.3-60 in Prairie Island Nuclear Generating Plant Environmental Monitoring Program 1976 Annual Report, Volume II. Northern States Power Company, Minneapolis, Minnesota. Malvestuto, S. P., W. D. Davies, and W. L. Shelton. 1978. An evaluation of the roving creel survey with nonuniform probability sampling. Transactions of the American Fisheries Society 107(2):255-262. Snedecor, George W., and William G. Cochran. 1971. Statistical methods. The Iowa State University Press, Ames, Iowa, 593 pp. Tait, Howard D. 1953. Sampling problems in the Michigan creel census. The University of Michigan, Ph.D. thesis, 131 pp. ( * it I, * II 0 *0 4