## Repeated Measures ANOVA

The Repeated Measures ANOVA is used to explore the relationship between a continuous dependent variable and one or more categorical explanatory variables, where one or more of the explanatory variables are ‘within subjects’ (where multiple measurements are from the same subject). Additionally, this analysis allows the inclusion of covariates, allowing for repeated measures ANCOVAs as well.

This analysis requires that the data be in ‘wide format’, where each row represents a subject (as opposed to long format, where each measurement of the dependent variable is represented as a row).

A non-parametric equivalent of the repeated measures ANOVA also exists; the Friedman test. However, it has the limitation of only being able to test a single factor.

### Arguments

 data the data as a data frame rm a list of lists, where each list describes the label (as a string) and the levels (as vector of strings) of a particular repeated measures factor rmCells a list of lists, where each list decribes a repeated measure (as a string) from data defined as measure and the particular combination of levels from rm that it belongs to (as a vector of strings) defined as cell bs a vector of strings naming the between subjects factors from data cov a vector of strings naming the covariates from data. Variables must be numeric effectSize one or more of 'eta', 'partEta', or 'omega'; use η², partial η², and ω² effect sizes, respectively depLabel a string (default: 'Dependent') describing the label used for the dependent variable throughout the analysis rmTerms a list of character vectors describing the repeated measures terms to go into the model bsTerms a list of character vectors describing the between subjects terms to go into the model ss '2' or '3' (default), the sum of squares to use spherTests TRUE or FALSE (default), perform sphericity tests spherCorr one or more of 'none' (default), 'GG', or HF; use no p-value correction, the Greenhouse-Geisser p-value correction, and the Huynh-Feldt p-value correction for shericity, respectively leveneTest TRUE or FALSE (default), test for homogeneity of variances (i.e., Levene's test) qq TRUE or FALSE (default), provide a Q-Q plot of residuals contrasts in development postHoc a list of character vectors describing the post-hoc tests that need to be computed postHocCorr one or more of 'none', 'tukey' (default), 'scheffe', 'bonf', or 'holm'; use no, Tukey, Scheffe, Bonferroni and Holm posthoc corrections, respectively emMeans a list of lists specifying the variables for which the estimated marginal means need to be calculate. Supports up to three variables per term. emmPlots TRUE (default) or FALSE, provide estimated marginal means plots emmTables TRUE or FALSE (default), provide estimated marginal means tables emmWeights TRUE (default) or FALSE, weigh each cell equally or weigh them according to the cell frequency ciWidthEmm a number between 50 and 99.9 (default: 95) specifying the confidence interval width for the estimated marginal means emmPlotData TRUE or FALSE (default), plot the data on top of the marginal means emmPlotError 'none', 'ci' (default), or 'se'. Use no error bars, use confidence intervals, or use standard errors on the marginal mean plots, respectively groupSumm TRUE or FALSE (default), report a summary of the different groups

### Returns

A results object containing:

 results\$rmTable a table results\$bsTable a table results\$assump\$spherTable a table results\$assump\$leveneTable a table results\$assump\$qq results\$contrasts an array of tables results\$postHoc an array of tables results\$emm an array of groups results\$groupSummary a table

Tables can be converted to data frames with asDF or as.data.frame(). For example:

results\$rmTable\$asDF

as.data.frame(results\$rmTable)

Elements in arrays can be accessed with [[n]]. For example:

results\$contrasts[] # accesses the first element