Sunfish cognition and pseudoreplication

In a recent study Dugatkin & Wilson (1992) tested for cognitive abilities in bluegill sunfish. They found that when a focal fish was allowed to forage with different companions, it was able to remember with which ones it had had greatest success and to use this information in future interactions. Moreover, fish seemed to prefer to associate with familiar conspecifics over unfamiliar ones. A number of subsidiary analyses were also reported. Lamprecht & Hofer (1994) claimed that results presented by Dugatkin and Wilson did not provide unambiguous support for their conclusions. They criticized the authors’ way of quantifying preference, their experimental protocol and their statistical analyses. They noted that some of these analyses constituted pseudoreplication (sensu Hurlbert 1984) and, for one data set, suggested an alternative type of analysis. Dugatkin & Wilson (1994) responded to these criticisms by, among other things, commenting on the nature of pseudoreplication and statistical independence, re-analysing one data set in the manner suggested by Lamprecht & Hofer (1994), and implying that the latter had suggested only ‘refinements’ in their analyses. They concluded that ‘the statistical significance of our results . . . remain[s] unchanged’ (page 1461). We are offering comment on this exchange because it seems likely to leave readers confused as to the nature of pseudoreplication and the seriousness and extent of statistical error in Dugatkin & Wilson (1992). The original critique by Lamprecht & Hofer (1994) was perhaps too gentle. Its effectiveness was also diminished by the editor’s liberality in allowing Dugatkin & Wilson (1994) to claim in response that correct re-analysis of their data would not affect the statistical significance of their many results. Our comments will be restricted to strictly statistical matters. Because Dugatkin & Wilson (1992) used a variety of designs and protocols in their study, these cannot be summarized here even briefly; thus the reader should refer to the original article to follow our commentary. Dugatkin & Wilson (1992) carried out 11 different types of statistical analyses, eight of which were carried out separately for each of the two tanks of fish used. We give the results of these analyses and of a twelfth analysis undertaken at the behest of Lamprecht & Hofer (1994) (Table I) Ten of these analyses represent clear cases of sacrificial pseudoreplication (sensu Hurlbert 1984; Hurlbert & White 1993; see below), and one (analysis 1) appears to represent some simpler miscalculation of error degrees of freedom. As is usually the case, pseudoreplication is most clearly evidenced by an error degrees of freedom (or specified sample size, N, in the case of a chisquared test) that exceeds the number of independent observations made. In the right-hand column of Table I, we indicate the tests and error degrees of freedom that we regard as appropriate to the hypotheses Dugatkin & Wilson (1992) wished to test. Sacrificial pseudoreplication may be characterized as follows. An experiment is conducted with a satisfactory design involving multiple experimental units per treatment and multiple samples or measurements per experimental unit. The data Correspondence: C. M. Lombardi, Museo Argentino de Ciencias Naturales, Avenida Angel Gallardo 470, 1405 Buenos Aires, Argentina. S. H. Hurlbert is at Department of Biology, San Diego State University, San Diego, CA92182, U.S.A.