In cyplessen/tailRatio: What the Package Does (One Line, Title Case)

knitr::opts_chunk$set(echo = TRUE,
                      collapse = T
                      )

Introduction

Differences in group means, variance differences, or a combination of both, can generate large imbalances in the the distributional tail regions. Such imbalances are relevant for any threshold, susceptibility, diathesis-stress, selection, or similar models.

When the tail regions of the distribution are the focus of interest, mean differences such as Hedges g are quite uninformative. You may wish to calculate a tail ratio (TR): the relative proportion of the two groups in the region above (or below) a certain cutoff.

With the tailRatio package you can easily calculate TRs for different cutoffs (in sds below or above the mean of a reference group) and for groups that differ both in mean and sd.

For a thourough discussion see Voracek, Mohr & Hagmann 2013.

Setup

You can install the tailRatio package with:

devtools::install_github("cyplessen/tailRatio")

And load it with:

library(tailRatio)

plot_tail_ratio

If you are interested in the tails and not only in mean differences, tail ratios are suited to do the job.

Example 1: Different means and sds

Two groups differ in intelligence, group 1 has a higher mean IQ = 115 (sd = 12) and group 2 a lower IQ = 95 (sd = 15). Above a cutoff of two standard deviations from the mean of group 1, there are 7x as many individuals from group 1 than 2!

plot_tail_ratio(area = "above", 
                cutoff = 2, 
                mean_high = 115, 
                sd = 12, 
                mean_low = 95, 
                sd_low = 16, 
                x_lab_name = "IQ", 
                mean_of_interest = 100)

Example 2: Different means and equal sds

Two populations differ in their depression scores. Group 1 has a higher score (mean = 10, sd = 3) and group 2 a lower score (mean = 7, sd = 3). Yet below a cutoff of 1 sd from the mean of group 1, there are 1.68x as many indiviuals from group 2 than group 1.

plot_tail_ratio(area = "below", 
                cutoff = 1, 
                mean_high = 10, 
                sd = 3, 
                mean_low = 7, 
                sd_low = 3, 
                x_lab_name = "Depression", 
                mean_of_interest = 10)

calculate_tail_ratio()

If you simply want to calculate the tail ratios without visualizing them you can use the calculate_tail_ratio() function.

calculate_tail_ratio(area = "below", 
                     cutoff = 2, 
                     mean_high = 100, 
                     sd = 15, 
                     mean_low = 85, 
                     sd_low = 15)