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.
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, error.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 = 4,
as.na = NULL, write = NULL, append = TRUE, check = TRUE,
output = TRUE, ...)Returns an object of class misty.object, which is a list with following
entries:
callfunction call
typetype of analysis
datadata frame with variables used in the current analysis
formulaformula of the current analysis
plotggplot2 object for plotting the results
argsspecification of function arguments
resultlist 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
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.
a matrix or data frame containing the variables in the
formula formula.
logical: if TRUE, Tukey HSD post hoc test for
multiple comparison is conducted.
a numeric value between 0 and 1 indicating the confidence level of the interval.
logical: if TRUE (default), null and alternative hypothesis
are shown on the console.
logical: if TRUE (default), descriptive statistics are shown
on the console.
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.
logical: if TRUE, the weighted pooled standard
deviation is used to compute Cohen's d.
logical: if TRUE, correction factor to remove
positive bias in small samples is used.
logical: if TRUE, a plot showing error bars for
confidence intervals is drawn.
a numeric value indicating the size aesthetic for
the point representing the mean value.
logical: if TRUE (default), difference-adjustment
for the confidence intervals is applied.
a numeric value indicating the horizontal bar width of the error bar.
a character string specifying the labels for the x-axis.
a character string specifying the labels for the y-axis.
a numeric vector of length two specifying limits of the limits of the y-axis.
a numeric vector specifying the points at which tick-marks are drawn at the y-axis.
logical: if TRUE (default), jittered data points
are drawn.
a numeric value indicating the size aesthetic
for the jittered data points.
a numeric value indicating the amount of horizontal jitter.
a numeric value indicating the amount of vertical jitter.
a numeric value indicating the opacity of the jittered data points.
a character string specifying the text for the title for the plot.
a character string specifying the text for the subtitle for the plot.
an integer value indicating the number of decimal places to be used for displaying descriptive statistics and confidence interval.
an integer value indicating the number of decimal places to be used for displaying the p-value.
a numeric vector indicating user-defined missing values,
i.e. these values are converted to NA before conducting
the analysis.
a character string naming a text file with file extension
".txt" (e.g., "Output.txt") for writing the
output into a text file.
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.
logical: if TRUE (default), argument specification is checked.
logical: if TRUE (default), output is shown on the console.
further arguments to be passed to or from methods.
Takuya Yanagida takuya.yanagida@univie.ac.at
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).
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.
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.
aov.w, test.t, test.z,
test.levene, test.welch, cohens.d,
ci.mean.diff, ci.mean