GROUP.DIFFS {DFA.CANCOR}

Group Mean Differences on a Continuous Outcome Variable

Description

Produces a variety of statistics for all possible pairwise independent groups comparisons of means on a continuous outcome variable.

Usage

GROUP.DIFFS(data, GROUPS=NULL, DV=NULL, var.equal=FALSE, p.adjust.method="holm", 
	            Ncomps=NULL, verbose=TRUE)

Arguments

data

A dataframe where the rows are cases & the columns are the variables. If GROUPS and DV are not specified, then the GROUPS variable should be in the first column and the DV should be in the second column of data.

GROUPS

The name of the groups variable in the dataframe, e.g., groups = 'Group'.

DV

The name of the dependent (outcome) variable in the dataframe, e.g., DV = 'esteem'.

var.equal

(from stats::t.test) A logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.

p.adjust.method

The method to be used to adjust the p values for the number of comparisons. The options are "holm" (the default), "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", "none".

Ncomps

The number of pairwise comparisons for the adjusted p values. If unspecified, it will be the number of all possible comparisons (i.e., the family-wise number of number of comparisons). Ncomps could alternatively be set to, e.g., the experiment-wise number of number of comparisons.

verbose

Should detailed results be displayed in console?
The options are: TRUE (default) or FALSE.

Details

The function conducts all possible pairwise comparisons of the levels of the GROUPS variable on the continuous outcome variable. It supplements independent groups t-test results with effect size statistics and with the Bayes factor for each pairwise comparison.

The d values are the Cohen d effect sizes, i.e., the mean difference expressed in standard deviation units.

The g values are the Hedges g value corrections to the Cohen d effect sizes.

The r values are the effect sizes for the group mean difference expressed in the metric of Pearson's r.

The BESD values are the binomial effect size values for the group mean differences. The BESD casts the effect size in terms of the success rate for the implementation of a hypothetical procedure (e.g., the percentage of cases that were cured, or who died.) For example, an r = .32 is equivalent to increasing the success rate from 34% to 66% (or, possibly, reducing an illness or death rate from 66% to 34%).

The Bayes factor values are obtained from the ttest.tstat function in the BayesFactor package.

For example, a Bayes_Factor_alt_vs_null = 3 indicates that the data are 3 times more likely under the alternative hypothesis than under the null hypothesis. A Bayes_Factor_alt_vs_null = .2 indicates that the data are five times less likely under the alternative hypothesis than under the null hypothesis (1 / .2).

Conversely, a Bayes_Factor_null_vs_alt = 3 indicates that the data are 3 times more likely under the null hypothesis than under the alternative hypothesis. A Bayes_Factor_null_vs_alt = .2 indicates that the data are five times less likely under the null hypothesis than under the alternative hypothesis (1 / .2).

Value

If verbose = TRUE, the displayed output includes the means, standard deviations, and Ns for the groups, the t-test results for each pairwise comparison, the mean difference and its 95% confidence interval, four indices of effect size for each pairwise comparison (r, d, g, and BESD), and the Bayes factor. The returned output is a matrix with these values.

Author(s)

Brian P. O'Connor

References

Funder, D. C., & Ozer, D. J. (2019). Evaluating effect size in psychological research: Sense and nonsense. Advances in Methods and Practices in Psychological Science, 2(2), 156168.

Jarosz, A. F., & Wiley, J. (2014). What are the odds? A practical guide to computing and reporting Bayes factors. Journal of Problem Solving, 7, 29.

Randolph, J. & Edmondson, R.S. (2005). Using the binomial effect size display (BESD) to present the magnitude of effect sizes to the evaluation audience. Practical Assessment Research & Evaluation, 10, 14.

Rosenthal, R., Rosnow, R.L., & Rubin, D.R. (2000). Contrasts and effect sizes in behavioral research: A correlational approach. Cambridge UK: Cambridge University Press.

Rosenthal, R., & Rubin, D. B. (1982). A simple general purpose display of magnitude and experimental effect. Journal of Educational Psychology, 74, 166-169.

Rouder, J. N., Haaf, J. M., & Vandekerckhove, J. (2018). Bayesian inference for psychology, part IV: parameter estimation and Bayes factors. Psychonomic Bulletin & Review, 25(1), 102113.

Examples

GROUP.DIFFS(data_DFA$Field_2012, var.equal=FALSE, p.adjust.method="fdr")


GROUP.DIFFS(data = data_DFA$Sherry_2006, var.equal=FALSE, p.adjust.method="bonferroni")