*Ecological Archives* E095-106-A4

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Appendix D. Statistical procedure for Dunnett’s test post hoc comparisons.

Following the two-way ANOVA procedure described in the methods, a Dunnett’s post hoc comparison was used to determine whether the C and N isotopic signature of individual species changed over time. The test statistic and standard error were calculated using a modified form of the equations from Zar (1999).

where is the mean δ^{13}C_{NL} or δ^{15}N_{c} of the species being compared from 2010–2012, is the mean of that species from 2002–2003, is the mean δ^{13}C_{NL} or δ^{15}N_{c} of dreissenid mussels from 2010–2012 and is the mean of dreissenid mussels from 2002–2003. The standard error term for our post hoc pairwise comparisons is dependent upon the sample sizes of both the dreissenid baseline for two time periods and a focal species for two time periods. Therefore the standard error term incorporated all four sample sizes and assumes homogeneity of variance. The standard error term was calculated as follows:

where MS_{error} is the mean squares error term from the two-way ANOVA, is the sample size of the species being compared from 2002–2003, is the sample size of that species from 2010–2012, is the sample size of dreissenid mussels from 2002–2003 and is the sample size of dreissenid mussels from 2010–2012.

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