Statistical Problems in Studies of Temperature Preference of Fishes

Abstract

When the laboratory determined acute temperature preference vs. acclimation relationship of fishes is analyzed, the correct assessment of degrees of freedom is central to analyses of covariance, analysis of variance, and regression analysis. Many investigators have assumed that recordings of fish positions in a horizontal temperature gradient trough made at 1 -min intervals in a test of 20-min duration represent 20 degrees of freedom. Such an assumption can arbitrarily allow an investigator to increase or decrease the number of degrees of freedom by simply shortening or lengthening the time intervals for observation of the position of fish in the trough. We contend that each temperature preference test provides only one data point (single degree of freedom) even though an investigator may have used more than one fish in a test. Failure to recognize this distinction may lead to erroneous conclusions from data. For illustrative purposes, we reanalyzed three sets of published data using the correct number of degrees of freedom. The reanalysis showed that the significant values were overstated.Key words: statistics, analysis, sample size, temperature, preference, fishes