AObootBetween: Bootstrapped ANOVA for Between-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 between-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

AObootBetween(var.between,
              var.dv,
              var.id,
              levels.b1,
              levels.b2 = 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 2 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.between: Variable(s) reflecting the between-subject level.
var.dv: Dependent variable.
var.id: Unique person specifier.
levels.b1: Levels of the first-named independent variable. Must be identical with the levels in the dataset.
levels.b2: 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.
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 between-subjects ANOVA
# \donttest{
AObootBetween(
  var.between = "treatment",
  var.dv = "pre.1",
  var.id = "pers",
  levels.b1 = c("control", "A", "B"),
  eff.si = "ges",
  data = ao,
  n.sim = 1000,
  alpha = .05,
  seed = 1234,
  n.round = 2)
  # }

# Two-way between-subjects ANOVA
# \donttest{
AObootBetween(
  var.between = c("treatment", "gender"),
  var.dv = "pre.1",
  var.id = "pers",
  levels.b1 = c("control", "A", "B"),
  levels.b2 = c("M", "F"),
  eff.si = "pes",
  data = ao,
  n.sim = 1000,
  alpha = .05,
  seed = 1236,
  n.round = 2)
# }

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