COMPUTER PROGRAM FOR ANALYSIS OF THE 

 HOMOGENEITY AND GOODNESS OF FIT OF 

 FREQUENCY DISTRIBUTIONS, FORTRAN IV 



Routinely, in the study of the dynamics of a fish 

 population, one of the initial steps is the examina- 

 tion of length measurements, viz, the frequency 

 distribution of lengths, average length at age, and 

 differential length distribution by gender. Often, 

 length measurements are the only information 

 available from which to estimate the age structure 

 of the population. Standard statistical techniques 

 such as chi-square tests are often used to analyze 

 length-frequency distributions before pooling 

 data, e.g., to estimate the age structure of the 

 population (Yong and Skillman 1975). 



I have developed a computer program which 

 forms frequency distributions from length mea- 

 surements and then calculates a chi-square statis- 

 tic which is used to test the homogeneity of the 

 frequencies for the purpose of pooling. Theoretical 

 frequencies from a normal distribution based upon 

 the sample mean and variance of each length- 

 frequency distribution are used in calculating 

 chi-square tests of goodness of fit (Li 1959). The 

 program does not partition the chi-square test of 

 homogeneity but does pool adjacent class frequen- 

 cies when expected frequencies are small in the 

 case of the test of goodness of fit. Observed adja- 

 cent class frequencies are pooled if their expected 

 frequencies are too small and then the test of 

 goodness of fit is calculated. The usual caution 

 against using small samples and expected fre- 

 quencies less than five in chi-square tests of good- 

 ness of fit should be followed (Sokal and Rohlf 

 1969). 



Data required are either individual length mea- 

 surements in millimeters (from 1 to 1,000 mm) or 

 pairs of length class midpoint and frequency for 

 each of up to five length-frequency distributions 

 per data set; maximum frequency must be less 

 than 1 million. Program storage could be in- 

 creased to accommodate more than five length- 

 frequency distributions, depending on the capac- 

 ity of the computer being used. Class interval 

 width must be specified; lengths are then tallied 

 by up to 100 classes which are identified by mid- 

 point on the output. Multiple data sets are pro- 

 cessed sequentially without limit. 



Output includes listings of arithmetic mean, 

 variance, standard deviation, standard error of 

 the mean, total sample size, and chi-square statis- 

 tic of goodness of fit for individual groups and for 



the pooled frequency distribution. The chi-square 

 value for the test of homogeneity is printed with 

 its degrees of freedom; appropriate tables should 

 be consulted for critical values used in testing 

 hypotheses. The goodness of fit test for the pooled 

 data would not apply to the situation where the 

 distribution is clearly multinomial. Histograms of 

 all frequency distributions are produced as full- 

 page printer charts, scaled if necessary to 50 units 

 by up to 100 class intervals. The pooled frequen- 

 cies and class midpoints are punched on cards to 

 facilitate additional analyses. 



The program was developed on an IBM 360/65 

 OS System' and required 56,811 bytes of storage. 

 A copy of the FORTRAN IV source program list- 

 ing, example input and output, and an instruction 

 manual are available from the author. 



Literature Cited 



LI, J. C. R. 



1959. Introduction to statistical inference. Edward 

 Bros., Ann Arbor, Mich., 553 p. 



Sokal. r. r., and F. J. Rohlf 



1969. Biometry: the principles and practice of statistics in 

 biological research. W. H. Freeman and Co., San Franc, 

 776 p. 



YoNG, M. Y. Y., AND R. A. Skillman 



1975. A computer program for analysis of polymodal fre- 

 quency distributions (ENORMSEP), FORTRAN 

 rV. Fish. Bull., U.S. 73:681. 



MICHAEL L. DAHLBERG 



Northwest and Alaska Fisheries Center Auke Bay Laboratory 

 National Marine Fisheries Service, NOAA 

 P.O. Box 155, Auke Bay, AK 99821 



'Reference to trade name does not imply endorsement by the 

 National Marine Fisheries Service, NOAA. 



PORTABLE TRIPOD DROP NET FOR 

 ESTUARINE FISH STUDIES' 



Since the introduction of a portable drop net sys- 

 tem by Jones et al. (1963) several designs have 

 been utilized for freshwater and estuarine fish 

 studies (Moseley and Copeland 1969; Kjelson and 

 Johnson 1973; Kushlan 1974; Adams 1976). The 

 value of these sampling systems in estimating the 

 density and biomass of certain fish species has 

 been well documented by these authors (Table 1). 



1 Contribution No. 83 from the Harbor Branch Foundation, 

 Inc. 



285 



