ANCOVA
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.
Example usage
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)
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 η², partial η², and ω² 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 |
| 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 |
Returns
A results object containing:
| results$main | a table |
| results$model | |
| results$assump$homo | a table |
| results$assump$norm | 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[[1]] # accesses the first element