aov.b: Between-Subject Analysis of Variance

Description

This function performs an one-way between-subject analysis of variance (ANOVA) including Tukey HSD post hoc test for multiple comparison and provides descriptive statistics, effect size measures, and a plot showing error bars for difference-adjusted confidence intervals with jittered data points.

Usage

aov.b(formula, data, posthoc = FALSE, conf.level = 0.95, hypo = TRUE,
      descript = TRUE, effsize = FALSE, weighted = FALSE, correct = FALSE,
      plot = FALSE, point.size = 4, adjust = TRUE, errorbar.width = 0.1,
      xlab = NULL, ylab = NULL, ylim = NULL, breaks = ggplot2::waiver(),
      jitter = TRUE, jitter.size = 1.25, jitter.width = 0.05,
      jitter.height = 0, jitter.alpha = 0.1, title = "",
      subtitle = "Confidence Interval", digits = 2, p.digits = 3,
      as.na = NULL, write = NULL, append = TRUE, check = TRUE,
      output = TRUE, ...)

Value

Returns an object of class misty.object, which is a list with following entries:

call: function call
type: type of analysis
data: data frame with variables used in the current analysis
formula: formula of the current analysis
args: specification of function arguments
plot: ggplot2 object for plotting the results
result: list with result tables, i.e., descript for descriptive statistics, test for the ANOVA table, posthoc for post hoc tests, and aov for the return object of the aov function

Arguments

formula: a formula of the form y ~ group where y is a numeric variable giving the data values and group a numeric variable, character variable or factor with more than two values or factor levels giving the corresponding groups.
data: a matrix or data frame containing the variables in the formula formula.
posthoc: logical: if TRUE, Tukey HSD post hoc test for multiple comparison is conducted.
conf.level: a numeric value between 0 and 1 indicating the confidence level of the interval.
hypo: logical: if TRUE (default), null and alternative hypothesis are shown on the console.
descript: logical: if TRUE (default), descriptive statistics are shown on the console.
effsize: logical: if TRUE, effect size measures $\eta^2$ and $\omega^2$ for the ANOVA and Cohen's d for the post hoc tests are shown on the console.
weighted: logical: if TRUE, the weighted pooled standard deviation is used to compute Cohen's d.
correct: logical: if TRUE, correction factor to remove positive bias in small samples is used.
plot: logical: if TRUE, a plot showing error bars for confidence intervals is drawn.
point.size: a numeric value indicating the size aesthetic for the point representing the mean value.
adjust: logical: if TRUE (default), difference-adjustment for the confidence intervals is applied.
errorbar.width: a numeric value indicating the horizontal bar width of the error bar.
xlab: a character string specifying the labels for the x-axis.
ylab: a character string specifying the labels for the y-axis.
ylim: a numeric vector of length two specifying limits of the limits of the y-axis.
breaks: a numeric vector specifying the points at which tick-marks are drawn at the y-axis.
jitter: logical: if TRUE (default), jittered data points are drawn.
jitter.size: a numeric value indicating the size aesthetic for the jittered data points.
jitter.width: a numeric value indicating the amount of horizontal jitter.
jitter.height: a numeric value indicating the amount of vertical jitter.
jitter.alpha: a numeric value indicating the opacity of the jittered data points.
title: a character string specifying the text for the title of the plot.
subtitle: a character string specifying the text for the subtitle of the plot.
digits: an integer value indicating the number of decimal places to be used for displaying descriptive statistics and confidence interval.
p.digits: an integer value indicating the number of decimal places to be used for displaying the p-value.
as.na: a numeric vector indicating user-defined missing values, i.e. these values are converted to NA before conducting the analysis.
write: a character string naming a text file with file extension ".txt" (e.g., "Output.txt") for writing the output into a text file.
append: logical: if TRUE (default), output will be appended to an existing text file with extension .txt specified in write, if FALSE existing text file will be overwritten.
check: logical: if TRUE (default), argument specification is checked.
output: logical: if TRUE (default), output is shown on the console.
...: further arguments to be passed to or from methods.

Author

Takuya Yanagida takuya.yanagida@univie.ac.at

Details

Post Hoc Test

Tukey HSD post hoc test reports Cohen's d based on the non-weighted standard deviation (i.e., weighted = FALSE) when requesting an effect size measure (i.e., effsize = TRUE) following the recommendation by Delacre et al. (2021).

Confidence Intervals

Cumming and Finch (2005) pointed out that when 95% confidence intervals (CI) for two separately plotted means overlap, it is still possible that the CI for the difference would not include zero. Baguley (2012) proposed to adjust the width of the CIs by the factor of $\sqrt{2}$ to reflect the correct width of the CI for a mean difference:

$$\hat{\mu}_{j} \pm t_{n - 1, 1 - \alpha/2} \frac{\sqrt{2}}{2} \hat{\sigma}_{{\hat{\mu}}_j}$$

These difference-adjusted CIs around the individual means can be interpreted as if it were a CI for their difference. Note that the width of these intervals is sensitive to differences in the variance and sample size of each sample, i.e., unequal population variances and unequal n alter the interpretation of difference-adjusted CIs.

References

Baguley, T. S. (2012a). Serious stats: A guide to advanced statistics for the behavioral sciences. Palgrave Macmillan.

Cumming, G., and Finch, S. (2005) Inference by eye: Confidence intervals, and how to read pictures of data. American Psychologist, 60, 170–80.

Delacre, M., Lakens, D., Ley, C., Liu, L., & Leys, C. (2021). Why Hedges' g*s based on the non-pooled standard deviation should be reported with Welch's t-test. https://doi.org/10.31234/osf.io/tu6mp

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. John Wiley & Sons.

Examples

Run this code

dat <- data.frame(group = c(1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3),
                  y = c(3, 1, 4, 2, 5, 3, 2, 3, 6, 6, 3, NA))

# Example 1: Between-subject ANOVA
aov.b(y ~ group, data = dat)

# Example 2: Between-subject ANOVA
# print effect size measures
aov.b(y ~ group, data = dat, effsize = TRUE)

# Example 3: Between-subject ANOVA
# do not print hypotheses and descriptive statistics,
aov.b(y ~ group, data = dat, descript = FALSE, hypo = FALSE)

if (FALSE) {
# Example 4: Write results into a text file
aov.b(y ~ group, data = dat, write = "ANOVA.txt")}

# Example 5: Between-subject ANOVA
# plot results
aov.b(y ~ group, data = dat, plot = TRUE)

# Load ggplot2 package
library(ggplot2)

if (FALSE) {
# Example 6: Save plot, ggsave() from the ggplot2 package
ggsave("Between-Subject_ANOVA.png", dpi = 600, width = 4.5, height = 6)}

# Example 7: Between-subject ANOVA
# extract plot
p <- aov.b(y ~ group, data = dat, output = FALSE)$plot
p

# Extract data
plotdat <- aov.b(y ~ group, data = dat, output = FALSE)$data

# Draw plot in line with the default setting of aov.b()
ggplot(plotdat, aes(group, y)) +
  geom_jitter(alpha = 0.1, width = 0.05, height = 0, size = 1.25) +
  geom_point(stat = "summary", fun = "mean", size = 4) +
  stat_summary(fun.data = "mean_cl_normal", geom = "errorbar", width = 0.20) +
  scale_x_discrete(name = NULL) +
  labs(subtitle = "Two-Sided Confidence Interval") +
  theme_bw() + theme(plot.subtitle = element_text(hjust = 0.5))

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