README.md
In esvis: Visualization and Estimation of Effect Sizes

esvis

R Package for effect size visualization and estimation.

This package is designed to help you very quickly estimate and visualize distributional differences by categorical factors (e.g., the effect of treatment by gender and income category). Emphasis is placed on evaluating distributional differences across the entirety of the scale, rather than only by measures of central tendency (e.g., means).

Install directly from CRAN with

install.packages("esvis")

Or the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("datalorax/esvis")

There are three primary data visualizations: (a) binned effect size plots, (b) probability-probability plots, and (c) empirical cumulative distribution functions. All plots use the ggplot2 package and are fully manipulable after creation using standard ggplot commands (e.g., changing the theme, labels, etc.). These plots were all produced by first running library(ggplot2); theme_set(theme_minimal()) to produce the plots with the minimal theme, but no theme structure is imposed on any of the plots.

At present, the binned effect size plot can only be produced with Cohen’s d, although future development will allow the user to select the type of effect size. The binned effect size plot splits the distribution into quantiles specified by the user (defaults to lower, middle, and upper thirds), calculates the mean difference between groups within each quantile bin, and produces an effect size for each bin by dividing by the overall pooled standard deviation (i.e., not by quantile). For example

library(esvis)
binned_plot(benchmarks, math ~ ell)
#> Warning: `cols` is now required.
#> Please use `cols = c(data, q)`

Note that in this plot one can clearly see that the magnitude of the differences between the groups depends upon scale location, as evidence by the reversal of the effect (negative to positive) for the Non-ELL (non-English Language Learners) group. We could also change the reference group, change the level of quantile binning, and evaluate the effect within other factors. For example, we can look by season eligibility for free or reduced price lunch, with quantiles binning, and non-ELL students as the reference group with

binned_plot(benchmarks, 
            math ~ ell + frl + season, 
            ref_group = "Non-ELL",
            qtile_groups = 5)
#> Warning: `cols` is now required.
#> Please use `cols = c(data, q)`

The ref_group argument can also supplied as a formula.

Probability-probability plot can be produced with a call to pp_plot and an equivalent argument structure. In this case, we’re visualizing the difference in reading achievement by race/ethnicity by season.

pp_plot(benchmarks, reading ~ ethnicity + season)

Essentially, the empirical cummulative distribution function (ECDF) for the reference group (by default, the highest performing group) is mapped against the ECDF for each corresponding group. The magnitude of the achievement gap is then displayed by the distance from the diagonal reference line, representing, essentially, the ECDF for the reference group.

By default, the area under the curve is shaded, which itself is an effect-size like measure, but this is also manipulable.

Finally, the ecdf_plot function essentially dresses up the base plot.ecdf function, but also adds some nice referencing features through additional, optional arguments. Below, I have included the optional hor_ref = TRUE argument such that horizontal reference lines appear, relative to the cuts provided.

ecdf_plot(benchmarks, math ~ season, 
    cuts = c(190, 200, 215))

These are the curves that go into the PP-Plot, but occasionally can be useful on their own.

Compute effect sizes for all possible pairwise comparisons.

coh_d(benchmarks, math ~ season + frl)
#> `mutate_if()` ignored the following grouping variables:
#> Column `season`
#> # A tibble: 30 x 6
#>    season_ref frl_ref season_foc frl_foc      coh_d     coh_se
#>    <chr>      <chr>   <chr>      <chr>        <dbl>      <dbl>
#>  1 Fall       FRL     Fall       Non-FRL  0.7443868 0.07055679
#>  2 Fall       FRL     Spring     FRL      1.321191  0.04957348
#>  3 Fall       FRL     Spring     Non-FRL  2.008066  0.07873488
#>  4 Fall       FRL     Winter     FRL      0.6246112 0.04716189
#>  5 Fall       FRL     Winter     Non-FRL  1.300031  0.07326622
#>  6 Fall       Non-FRL Fall       FRL     -0.7443868 0.07055679
#>  7 Fall       Non-FRL Spring     FRL      0.5498306 0.06939873
#>  8 Fall       Non-FRL Spring     Non-FRL  1.140492  0.09189070
#>  9 Fall       Non-FRL Winter     FRL     -0.1269229 0.06934576
#> 10 Fall       Non-FRL Winter     Non-FRL  0.5009081 0.08716735
#> # … with 20 more rows

Or specify a reference group. In this case, I’ve used the formula-based interface, but a string vector specifying the specific reference group could also be supplied.

coh_d(benchmarks, 
      math ~ season + frl, 
      ref_group = ~Fall + `Non-FRL`)
#> `mutate_if()` ignored the following grouping variables:
#> Column `season`
#> # A tibble: 5 x 6
#>   season_ref frl_ref season_foc frl_foc      coh_d     coh_se
#>   <chr>      <chr>   <chr>      <chr>        <dbl>      <dbl>
#> 1 Fall       Non-FRL Fall       FRL     -0.7443868 0.07055679
#> 2 Fall       Non-FRL Spring     FRL      0.5498306 0.06939873
#> 3 Fall       Non-FRL Spring     Non-FRL  1.140492  0.09189070
#> 4 Fall       Non-FRL Winter     FRL     -0.1269229 0.06934576
#> 5 Fall       Non-FRL Winter     Non-FRL  0.5009081 0.08716735

Notice that the reference to Non-FRL is wrapped in back-ticks, which should be used anytime there are spaces or other non-standard characters.

Other effect sizes are estimated equivalently. For example, compute V (Ho, 2009) can be estimated with

v(benchmarks, 
  math ~ season + frl, 
  ref_group = ~Fall + `Non-FRL`)
#> # A tibble: 5 x 5
#> # Groups:   frl, season [1]
#>   frl_ref season_ref frl_foc season_foc          v
#>   <chr>   <chr>      <chr>   <chr>           <dbl>
#> 1 Non-FRL Fall       Non-FRL Winter      0.5070737
#> 2 Non-FRL Fall       FRL     Spring      0.5454666
#> 3 Non-FRL Fall       FRL     Winter     -0.1117226
#> 4 Non-FRL Fall       Non-FRL Spring      1.139235 
#> 5 Non-FRL Fall       FRL     Fall       -0.7051069

or AUC with

auc(benchmarks, 
    math ~ season + frl, 
    ref_group = ~Fall + `Non-FRL`)
#> # A tibble: 5 x 5
#> # Groups:   frl, season [1]
#>   frl_ref season_ref frl_foc season_foc       auc
#>   <chr>   <chr>      <chr>   <chr>          <dbl>
#> 1 Non-FRL Fall       Non-FRL Winter     0.6400361
#> 2 Non-FRL Fall       FRL     Spring     0.6501417
#> 3 Non-FRL Fall       FRL     Winter     0.4685164
#> 4 Non-FRL Fall       Non-FRL Spring     0.7897519
#> 5 Non-FRL Fall       FRL     Fall       0.3090356