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Subject: Re: Statistical problem text/plain (100 lines)
 ```This seems a simple problem, but in fact it is not a simple problem if you want to give it some thoughts. What you really want to do is compare two samples for which you use the allometric model W=a.L power b. This relationship is not linear, you use a transformation to linearize and tentatively achieve homoscedascity. You already know that your two samples do not come from the same population, you wish to check whether the model you are using fits the two differents populations equally well with the same parameters. Your goal is to use only one model and the same parameters for simplification. There are measurement errors on both variables, and the relationship between the two variables is probably specific to each individual. Given this you may of course agree to use accepted procedures and for instance simplify by assuming that no error is made on measurements of length in order to have a predictive rather than a functional regression. You may also accept that comparing the tramsformed data rather than the original is acceptable. Using standard packages without giving some thoughts to the nature of the problem may be misleading. Actually the true problem seems to be "may I use the same relationship over and over again, knowing that the populations keep on changing", this is not the standard statistics problem of comparing sample regressions to check if they come from the same population regression. If you were taking large enough samples, you would probably gain enough power to detect that your samples come from different populations even if the differences between populations were very small. May be what you want to do is check whether you can use the same preset relationship over and over again for the purpose of consistency and accept the risk of a given error on your predictions of weight from a known size, eventually estimate the range of variation of your estimates from the actual value in 95% of cases, and this will involve both precision and bias calculations. On the other hand, if you wish to do what "everybody else does" just assume that the linear transformation is alright, that the regressions are predictive regressions (no errors on L), that all animals in a sample obey to the same law but with an added random variability component which obeys to the same probability distribution for all individuals. Allow that the "law" may vary between samples i.e. that not all samples may obey to the same "law". If you accept that logic, then pick up the latest edition of a most respected book of statistics such as Snedecor and Cochran, Statistical Methods, Iowa State University Press, Ames Iowa, USA. check chapter 14.6 Comparison of regression lines. You will find that all you require are the following statistics for each sample: sumX, sumXX,sumXY,sumYY,sumY, and N. Everything else is quite straightforward and can be calculated by hand, no need for a package as long as you have a table of one tailed and two tailed F and eventually a chi square table. This is a comparison of regression lines by ANOVA, it is not an ANOVA, which would be less powerfull, and would indeed require the same Ln L values for each sample, it is not an ANCOVA sticto sensu, which would allow you to compare the Ln of weights, once you have removed the linear trend associated with different ln L. Best wishes. At 12:41 PM 9/18/96 +0200, you wrote: >Dear Fish-folks, > >I want to compare linear regressions (for example ln length - ln weigth) >with respect >to differences in slope and intercept. We have found several >complicate formulae in statistical textbooks. However, I know that one could use >also the ANOVA-approach - but how? I have intensively studied the manual of our >statistical software (Statistika), and have found that linear regression and >ANOVA are basically identical. Thus, it may be simple if we have similar >x-values >each year. But in practice, the fish lengths (x-values) are measured >independently each year, >that means the range of fish lengths and weights may vary. My idea was to group >the weigths of fish as dependent variables, and to use the lengths as >covariables, >and then to run an ANCOVA-procedure. But I could not identify whether this is >correct. Has anyone some experience with this topic? > >Many thanks >Yours sincerely >Thomas >####################################### > >Dr. Thomas Mehner >Institute of Hydrobiology >University of Technology >D-01062 Dresden >Germany > >Tel.: (++49)(351) 463 2018 >Fax: (++49)(351) 463 7108 >internet: [log in to unmask] > ------------------------------------------------------------------------------ Gerard Y. Conan, M.S., Ph.D. Research Scientist, Department of Fisheries and Oceans Canada North Atlantic Fisheries Center, St John's, Newfoundland Phone 1 709 772 3898, FAX 1 709 772 4105 Home Fax and Phone 1 709 739 4639 Adjunct Professor, Department of Mathematics and Statistics, Université de Moncton. E.mail [log in to unmask] Have a nice day ! ```