AObootWithin: Bootstrapped ANOVA for Within-Subject Designs

Description

In case of violations of the assumption of the normal distribution, researchers usually employ bootstrapping. Based on the R packages afex and emmeans, this function computes bootstrapped confidence intervals for the effect sizes, estimated marginal means, and post hoc tests for one-way and two-way ANOVAs following a within-subject design. Furthermore, the p-values of the F-statistic are adjusted to reflect the probability to obtain equal or higher values than the raw, non-bootstrapped ANOVA (Stine, 1989 <doi:10.1177/0049124189018002003>; see also this tutorial by Nadine Spychala.).

Usage

AObootWithin(var.within,
             var.id,
             levels.w1,
             levels.w2 = NULL,
             eff.si = c("pes", "ges"),
             data,
             silence = FALSE,
             n.sim = 1000,
             alpha = .05,
             seed = 1234,
             n.round = 2)

Value

type.aov: Type of ANOVA conducted.
factor: Name of the groups in the factor (in one-way ANOVA).
factor1: Name of the groups in the first factor (in two-way ANOVA).
factor2: Name of the groups in the second factor (in two-way ANOVA).
anova: Results of the conducted ANOVA (i.e., degrees of freedom, F-test, p-value, effect size with bootstrap confidence interval, and numbers of tests for which convergence was achieved.
em: Estimated marginal means in one-way ANOVA.
em.1: Estimated marginal means for factor 1 in two-way ANOVA.
em.2: Estimated marginal means for factor 2 in two-way ANOVA.
em.3: Estimated marginal means for factor 1 by factor 1 in two-way ANOVA.
em.4: Estimated marginal means for factor 2 by factor 1 in two-way ANOVA.
no.test: Number of post hoc tests in one-way ANOVAs for which convergence was achieved.
no.test1: Number of post hoc tests for factor 1 in two-way ANOVAs for which convergence was achieved.
no.test2: Number of post hoc tests for factor 2 in two-way ANOVAs for which convergence was achieved.
no.test3: Number of post hoc tests for factor 1 by factor 2 in two-way ANOVAs for which convergence was achieved.
no.test4: Number of post hoc tests for factor 2 by factor 1 in two-way ANOVAs for which convergence was achieved.
ph: Post hoc tests in one-way ANOVAs.
ph.1: Post hoc tests for factor 1 in two-way ANOVAs.
ph.2: Post hoc tests for factor 2 in two-way ANOVAs.
ph.3: Post hoc tests for factor 1 by factor 2 in two-way ANOVAs.
ph.4: Post hoc tests for factor 2 by factor 1 in two-way ANOVAs.

Arguments

var.within: Variable(s) reflecting the within-subject level.
var.id: Unique person specifier.
levels.w1: Levels of the first-named independent variable. Must be identical with the levels in the dataset.
levels.w2: For two-way ANOVAs. Levels of the second-named independent variable. Must be identical with the levels in the dataset.
eff.si: Effect size for the F-tests. pes reflects partial eta-squared, ges reflects eta-squared.
data: Name of the dataframe. The dataset must be in a wide-format, with one row per participant. If the original data is available in long format, we advise users to apply the longToWide() function from the lsr package to convert data to wide format.
silence: Logical. If FALSE, progress of the bootstrapping procedure will be displayed.
n.sim: Number of bootstrap samples to be drawn.
alpha: Type I error.
seed: To make the results reproducible, it is recommended to set a random seed parameter.
n.round: Number of digits in the output.

Author

Lisa-Marie Segbert, Christian Blötner c.bloetner@gmail.com

Details

The p-value of the F-test (Pr(>F)) in the output reflects the probability to obtain an F-value as high as or higher than the F-value from the raw, non-bootstrapped ANOVA. Thus, it should not be mistaken as a p-value in the sense of a null hypothesis significance test. More information about this can be found in this tutorial by Nadine Spychala.

References

Stine, R. (1989). An introduction to bootstrap methods: Examples and ideas. Sociological Methods & Research, 18(2-3), 243--291. <https://doi.org/10.1177/0049124189018002003>

Examples

Run this code

library(carData)

# The OBrienKaiser dataset from the carData package

ao <- OBrienKaiser

# Add a unique person identifier to the dataset

ao$pers <- 1:nrow(OBrienKaiser)

# One-way within-subjects ANOVA
# \donttest{
AObootWithin(
    var.within = c("pre.1", "post.1", "fup.1"),
    var.id = "pers",
    levels.w1 = c("pre", "post", "fup"),
    eff.si = "ges",
    data = ao,
    n.sim = 1000,
    alpha = .05,
    seed = 1234,
    n.round = 2)
    # }

# Two-way within-subjects ANOVA
# \donttest{
AObootWithin(
  var.within = c("pre.1", "pre.2", "pre.3", "pre.4", "pre.5",
                 "post.1", "post.2", "post.3", "post.4", "post.5",
                 "fup.1", "fup.2", "fup.3", "fup.4", "fup.5"),
  var.id = "pers",
  levels.w1 = c("pre", "post", "fup"),
  levels.w2 = c("1", "2", "3", "4", "5"),
  eff.si = "pes",
  data = ao,
  n.sim = 1000,
  alpha = .05,
  seed = 1234,
  n.round = 2)
# }

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