Why residuals?

Prism 8 introduced the ability to plot residual plots with ANOVA, provided that you entered raw data and not averaged data as mean, n and SD or SEM.

Many scientists thing of residual as values that are obtained with regression. But ANOVA is really regression in disguise. It fits a model. One of the assumptions of ANOVA is that the residuals from that model are sampled from a Gaussian distribution. A residual plot helps you assess this assumption.

Which graph to create?

Prism can make three kinds of residual plots.

•Residual plot. The X axis is the predicted value.  The Y axis is the residual. This lets you spot residuals that are much larger or smaller than the rest.

•Homoscedasticity plot. The X axis is the predicted value.  The Y axis is the absolute value of the residual.This lets you check whether larger values are associated with bigger residuals (large absolute value).

•QQ plot. The X axis is the actual residual. The Y axis is the predicted residual, computed from the percentile of the residual (among all residuals) and assuming sampling from a Gaussian distribution. ANOVA assumes a Gaussian distribution of residuals, and this graph lets you check that assumption.

For ordinary ANOVA, the predicted values (used for residual and homoscedasticity plots) are simply the means of the replicates in a cell. For repeated measures ANOVA, the predicted value also takes into account the subject mean.

Diagnostics for residuals

•Are the residuals clustered or heteroscedastic? ANOVA assumes each sample was randomly drawn from populations with the same standard deviation. Prism can test this assumption with Spearman’s rank correlation coefficient test. This test uses the Spearman correlation coefficient (ρ) which is similar to the more-commonly encountered Pearson correlation coefficient (r). While the Pearson correlation coefficient compares two sets of values, the Spearman correlation coefficient compares two sets of ranks. Thus, this is a test to see if larger values tend to have larger residuals.

•Are the residuals Gaussian? Prism runs four normality tests on the residuals. The residuals from all groups are pooled and then entered into one set of normality tests.