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# Analytical and statistical methods

Pilot studies indicated that after an initial acclimation period spent in the holding tanks, and in the absence of a predator, no shrimp died during exposure to the conditions of the experiments. Therefore, the distribution of the mean number of shrimp surviving in each condition of macrophytic cover in the presence of the predator was compared (using a Chi-square test) to the expected distribution based upon the *a priori* assumption that no deaths (thus 100% survival) would occur in each cover condition. A significant Chi-square value was taken to indicate a significant influence of the predator upon the number of survivors in the four macrophytic cover conditions. In the Chi-square analysis, the null hypothesis was that there is no difference between the observed distribution of survivors and the distribution expected by assuming that the predator would consume no prey in any cover condition. The alternative hypothesis was that the predator would consume enough prey in at least one of the cover conditions to cause the distribution of surviving shrimp among the cover types to be significantly different from that based upon 100 percent survival in all cover conditions.

Since in this study all deaths were assumed to be due to predation, predation pressure was measured by calculating the percentage of the starting population of each prey species that was missing after 24 hours of exposure to the predator.

The number of shrimp surviving in each condition of macrophytic cover in the presence of the predator was converted to percent of the starting population of shrimp of that species. The percent values were normalized using the angular transformation (Sokal and Rohlf, 1995).

A test for homogeneity of variances between the data for each species was conducted by calculating separately the total variance within the arcsine transformed data for each species (*P*. *pugio* and *P*. *vulgaris*). Following Sokal and Rohlf (1995), these variances were compared using an F- test and found to be not significantly different (F = 1.15; df = 15, 15; .10 < P < .25). Therefore, the arcsine transformed survivorship data for both species were combined into a single data set and analyzed using a three- factor analysis of variance (ANOVA). In this analysis, the main effects were “species” (predator’s effect on the survivorship of each prey species: *P*. *pugio* and *P*. *vulgaris*); “cover” (predator’s effect on the prey’s survivorship in each type of cover: none, *Ulva*, *Codium*, and “*Ambulia*”); “exposure” (predator’s effect on the prey’s survivorship when the prey were exposed to the predator alone or in the presence of the second prey species).

In the ANOVA, estimates of the variation contributed by the main effects (the independent sources of variation) and by the interactions between and among them were compared with random (error) variation using F-tests. The working hypothesis was that one or more of the designed sources of variation and/or interactions between and among them contributes more variation than that due to error and thereby is identified as a significant contributor to the differences in observed shrimp survivorship among the different macrophytic covers. When interactions were determined to be significant, further testing of the entangled main effects was precluded. Multiple-means analyses using Tukey’s honestly significant difference (T-method of Sokal and Rohlf, 1995) were performed on sources of variation showing significant F values (α = .05).

In each F-test, the null hypothesis was that there is no difference between the variance contributed by the main effect (or by the interaction between or among main effects) and the variance due to chance (error). If the null hypothesis for any source of variation was rejected, then the null hypothesis for the T-method multiple-means comparisons was that all means of all levels for the significant source of variation were not significantly different from each other.