Section author: Ravi Selker, Jonathon Love, Damian Dropmann

ANOVA (`ANOVA`)

Description

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

Usage

ANOVA(
  data,
  dep,
  factors = NULL,
  effectSize = NULL,
  modelTest = FALSE,
  modelTerms = NULL,
  ss = "3",
  homo = FALSE,
  norm = FALSE,
  qq = FALSE,
  contrasts = NULL,
  postHoc = NULL,
  postHocCorr = list("tukey"),
  postHocES = list(),
  postHocEsCi = FALSE,
  postHocEsCiWidth = 95,
  emMeans = list(list()),
  emmPlots = TRUE,
  emmPlotData = FALSE,
  emmPlotError = "ci",
  emmTables = FALSE,
  emmWeights = TRUE,
  ciWidthEmm = 95,
  formula
)

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 eta², partial eta², and omega² effect sizes, respectively
`modelTest`	`TRUE` or `FALSE` (default); perform an overall model test
`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
`norm`	`TRUE` or `FALSE` (default), perform Shapiro-Wilk tests of normality
`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
`postHocES`	a possible value of `'d'`; provide Cohen’s d measure of effect size for the post-hoc tests
`postHocEsCi`	`TRUE` or `FALSE` (default), provide confidence intervals for the post-hoc effect sizes
`postHocEsCiWidth`	a number between 50 and 99.9 (default: 95), the width of confidence intervals for the post-hoc effect sizes
`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
`formula`	(optional) the formula to use, see the examples

Details

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.

Output

A results object containing:

`results$main`	a table of ANOVA results
`results$model`	the underlying `aov` object
`results$assump$homo`	a table of homogeneity tests
`results$assump$norm`	a table of normality tests
`results$assump$qq`	a q-q plot
`results$contrasts`	an array of contrasts tables
`results$postHoc`	an array of post-hoc tables
`results$emm`	an array of the estimated marginal means plots + tables

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

results$main$asDF

as.data.frame(results$main)

Examples

data('ToothGrowth')

ANOVA(formula = len ~ dose * supp, data = ToothGrowth)

#
#  ANOVA
#
#  ANOVA
#  -----------------------------------------------------------------------
#                 Sum of Squares    df    Mean Square    F        p
#  -----------------------------------------------------------------------
#    dose                   2426     2         1213.2    92.00    < .001
#    supp                    205     1          205.4    15.57    < .001
#    dose:supp               108     2           54.2     4.11     0.022
#    Residuals               712    54           13.2
#  -----------------------------------------------------------------------
#

ANOVA(
    formula = len ~ dose * supp,
    data = ToothGrowth,
    emMeans = ~ supp + dose:supp, # est. marginal means for supp and dose:supp
    emmPlots = TRUE,              # produce plots of those marginal means
    emmTables = TRUE)             # produce tables of those marginal means

ANOVA (ANOVA)