ANOVA {jmv}

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.

Value

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$emm					an array of the estimated marginal means plots + tables
results$residsOV					an output

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