## ANOVA

The Analysis of Variance (ANOVA) is used to explore the relationship between a continuous dependent variable, and one or more categorical explanatory variables.

ANOVA assumes that the residuals are normally distributed, and that the variances of all groups are equal. If one is unwilling to assume that the variances are equal, then a Welch’s test can be used instead (However, the Welch’s test does not support more than one explanatory factor). Alternatively, if one is unwilling to assume that the data is normally distributed, a non-parametric approach (such as Kruskal-Wallis) can be used.

### Arguments

 data the data as a data frame dep the dependent variable from data, variable must be numeric (not necessary when providing a formula, see examples) factors the explanatory factors in data (not necessary when providing a formula, see examples) effectSize one or more of 'eta', 'partEta', or 'omega'; use η², partial η², and ω² effect sizes, respectively modelTerms a formula describing the terms to go into the model (not necessary when providing a formula, see examples) ss '1', '2' or '3' (default), the sum of squares to use homo TRUE or FALSE (default), perform homogeneity tests qq TRUE or FALSE (default), provide a Q-Q plot of residuals contrasts a list of lists specifying the factor and type of contrast to use, one of 'deviation', 'simple', 'difference', 'helmert', 'repeated' or 'polynomial' postHoc a formula containing the terms to perform post-hoc tests on (see the examples) postHocCorr one or more of 'none', 'tukey', 'scheffe', 'bonf', or 'holm'; provide no, Tukey, Scheffe, Bonferroni, and Holm Post Hoc corrections respectively emMeans a formula containing the terms to estimate marginal means for (see the examples) emmPlots TRUE (default) or FALSE, provide estimated marginal means plots 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 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

### Returns

A results object containing:

 results\$main a table results\$model results\$assump\$homo a table results\$assump\$qq results\$contrasts an array of tables results\$postHoc an array of tables results\$emm an array of groups

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

results\$main\$asDF

as.data.frame(results\$main)

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

results\$contrasts[] # accesses the first element