この節の作者: Ravi Selker, Jonathon Love, Damian Dropmann

ANCOVA (ancova)

Description

The Analysis of Covariance (ANCOVA) is used to explore the relationship between a continuous dependent variable, one or more categorical explanatory variables, and one or more continuous explanatory variables (or covariates). It is essentially the same analysis as ANOVA, but with the addition of covariates.

Usage

ancova(
  data,
  dep,
  factors = NULL,
  covs = 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)
covs	the explanatory covariates (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

Output

A results object containing:

results$main	a table of ANCOVA results
results$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')

ancova(formula = len ~ supp + dose, data = ToothGrowth)

#
#  ANCOVA
#
#  ANCOVA
#  -----------------------------------------------------------------------
#                 Sum of Squares    df    Mean Square    F        p
#  -----------------------------------------------------------------------
#    supp                    205     1          205.4     11.4     0.001
#    dose                   2224     1         2224.3    124.0    < .001
#    Residuals              1023    57           17.9
#  -----------------------------------------------------------------------
#

ancova(
    formula = len ~ supp + dose,
    data = ToothGrowth,
    postHoc = ~ supp,
    emMeans = ~ supp)