Statistical Analyses
Chi-square analyses were conducted on all preference data in this study and
tested the observed proportions against a null model assuming random
preferences. Dugatkin & Alfieri (1991) demonstrated that 80% of the guppies
used in their study preferred inspectors that were on average closer to the
predator, a difference of 0.3 probability units from the null model of random
preferences (50:50). Cohen (1988) describes methods for evaluating power in tests
of proportions of this kind, wherein the effect size is equivalent to some
biologically relevant difference between the expected and null proportions.
Instead of choosing arbitrarily, we used an effect size of 0.3, corresponding to the
preference results of Dugatkin & Alfieri (1991), a technique supported by Cohen
(1988). Two-tailed tests of proportions yielded a priori power values that ranged
from 0.89 to 0.99 depending on the sample size used in the chi-square test
(e.g. n ¼ 29, 1)b ¼ 0.95; n ¼ 61, 1)b ¼ 0.99); these calculations were based on
equations in Zar (1996). According to Cohen (1988), 0.3 qualifies as a large effect
size in these types of analyses. Despite choosing our initial effect size based on
existing data for preference formation in guppies, we also conducted more
stringent a priori power analyses with effect sizes of 0.15 (0.31 < 1)b < 0.72)
and 0.25 (0.73 < 1)b < 0.99) to accommodate the conventions described in
Cohen (1988). Overall, these a priori power calculations indicate that our sample
sizes were sufficient to detect whether the observer guppies form preferences based
on watching predator inspection trials.