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 (or fitted value), the mean of the replicates of the data (but see below for repeated measures).  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 (or fitted value), the mean of the replicates of the data (but see below for repeated measures).  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.

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 two tests. The Brown-Forsythe test and the Barlett test. Both these tests compute a P value designed to answer this question:If the populations really have the same standard deviations, what is the chance that you'd randomly select samples whose standard deviations are as different from one another (or more different) as they are in your experiment?

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

How residuals are computed

Residuals with  one-way ANOVA and related tests are simple to understand.

•One-way ANOVA. A residual is computed for each value. Each residual is the difference between a entered value and the mean of all values for that group. A residual is positive when the corresponding value is greater than the sample mean, and is negative when the value is less than the sample mean.

•One-way repeated measures ANOVA. This is harder to understand. The residual is calculated as Actual value - Predicted value, where Predicted value = predicted group mean + predicted subject (row) mean - predicted grand mean.

•Kruskal-Wallis test. A residual is computed for each value. Each residual is the difference between a entered value and the median of all values for that group. A residual is positive when the corresponding value is greater than the sample median, and is negative when the value is less than the sample median.

•Friedman matched pairs test. This is harder to understand than the others. The residual is calculated as Actual value - Predicted value, where Predicted value = predicted group median + predicted subject median - predicted grand median.