You can cite this package/vignette as:


Patil, I. (2018). Visualizations with statistical details: The
'ggstatsplot' approach. PsyArxiv. doi:10.31234/osf.io/p7mku

A BibTeX entry for LaTeX users is

@Article{,
title = {Visualizations with statistical details: The 'ggstatsplot' approach},
author = {Indrajeet Patil},
year = {2021},
journal = {PsyArxiv},
url = {https://psyarxiv.com/p7mku/},
doi = {10.31234/osf.io/p7mku},
}

Lifecycle:

The function ggbetweenstats is designed to facilitate data exploration, and for making highly customizable publication-ready plots, with relevant statistical details included in the plot itself if desired. We will see examples of how to use this function in this vignette.

To begin with, here are some instances where you would want to use ggbetweenstats-

• to check if a continuous variable differs across multiple groups/conditions

• to compare distributions visually and check for outliers

Note: This vignette uses the pipe operator (%>%), if you are not familiar with this operator, here is a good explanation: http://r4ds.had.co.nz/pipes.html

# Comparisons between groups with ggbetweenstats

To illustrate how this function can be used, we will use the gapminder dataset throughout this vignette. This dataset provides values for life expectancy, GDP per capita, and population, at 5 year intervals, from 1952 to 2007, for each of 142 countries (courtesy Gapminder Foundation). Let’s have a look at the data-

library(gapminder)

dplyr::glimpse(x = gapminder::gapminder)
#> Rows: 1,704
#> Columns: 6
#> $country <fct> "Afghanistan", "Afghanistan", "Afghanistan", "Afghanistan", ~ #>$ continent <fct> Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, ~
#> $year <int> 1952, 1957, 1962, 1967, 1972, 1977, 1982, 1987, 1992, 1997, ~ #>$ lifeExp   <dbl> 28.801, 30.332, 31.997, 34.020, 36.088, 38.438, 39.854, 40.8~
#> $pop <int> 8425333, 9240934, 10267083, 11537966, 13079460, 14880372, 12~ #>$ gdpPercap <dbl> 779.4453, 820.8530, 853.1007, 836.1971, 739.9811, 786.1134, ~

Note: For the remainder of the vignette, we’re going to exclude Oceania from the analysis simply because there are so few observations (countries).

Suppose the first thing we want to inspect is the distribution of life expectancy for the countries of a continent in 2007. We also want to know if the mean differences in life expectancy between the continents is statistically significant.

The simplest form of the function call is-

# since the confidence intervals for the effect sizes are computed using
# bootstrapping, important to set a seed for reproducibility
set.seed(123)

# function call
ggstatsplot::ggbetweenstats(
data = dplyr::filter(gapminder::gapminder, year == 2007, continent != "Oceania"),
x = continent,
y = lifeExp
)

Note:

• The function automatically decides whether an independent samples t-test is preferred (for 2 groups) or a Oneway ANOVA (3 or more groups). based on the number of levels in the grouping variable.

• The output of the function is a ggplot object which means that it can be further modified with ggplot2 functions.

As can be seen from the plot, the function by default returns Bayes Factor for the test. If the null hypothesis can’t be rejected with the null hypothesis significance testing (NHST) approach, the Bayesian approach can help index evidence in favor of the null hypothesis (i.e., $$BF_{01}$$).

By default, natural logarithms are shown because Bayes Factor values can sometimes be pretty large. Having values on logarithmic scale also makes it easy to compare evidence in favor alternative ($$BF_{10}$$) versus null ($$BF_{01}$$) hypotheses (since $$log_{e}(BF_{01}) = - log_{e}(BF_{10})$$).

We can make the output much more aesthetically pleasing as well as informative by making use of the many optional parameters in ggbetweenstats. We’ll add a title and caption, better x and y axis labels, and tag and label the outliers in the data. We can and will change the overall theme as well as the color palette in use.

# for reproducibility
set.seed(123)
library(ggstatsplot)
library(gapminder)

# plot
ggstatsplot::ggbetweenstats(
data = dplyr::filter(.data = gapminder, year == 2007, continent != "Oceania"),
x = continent, # grouping/independent variable
y = lifeExp, # dependent variables
type = "robust", # type of statistics
xlab = "Continent", # label for the x-axis
ylab = "Life expectancy", # label for the y-axis
plot.type = "boxviolin", # type of plot
outlier.tagging = TRUE, # whether outliers should be flagged
outlier.coef = 1.5, # coefficient for Tukey's rule
outlier.label = country, # label to attach to outlier values
outlier.label.args = list(color = "red"), # outlier point label color
# turn off messages
ggtheme = ggplot2::theme_gray(), # a different theme
package = "yarrr", # package from which color palette is to be taken
palette = "info2", # choosing a different color palette
title = "Comparison of life expectancy across continents (Year: 2007)",
caption = "Source: Gapminder Foundation"
) + # modifying the plot further
ggplot2::scale_y_continuous(
limits = c(35, 85),
breaks = seq(from = 35, to = 85, by = 5)
)

As can be appreciated from the effect size (partial eta squared) of 0.635, there are large differences in the mean life expectancy across continents. Importantly, this plot also helps us appreciate the distributions within any given continent. For example, although Asian countries are doing much better than African countries, on average, Afghanistan has a particularly grim average for the Asian continent, possibly reflecting the war and the political turmoil.

So far we have only used a classic parametric test and a boxviolin plot, but we can also use other available options:

• The type (of test) argument also accepts the following abbreviations: "p" (for parametric), "np" (for nonparametric), "r" (for robust), "bf" (for Bayes Factor).

• The type of plot to be displayed can also be modified ("box", "violin", or "boxviolin").

• The color palettes can be modified.

Let’s use the combine_plots function to make one plot from four separate plots that demonstrates all of these options. Let’s compare life expectancy for all countries for the first and last year of available data 1957 and 2007. We will generate the plots one by one and then use combine_plots to merge them into one plot with some common labeling. It is possible, but not necessarily recommended, to make each plot have different colors or themes.

For example,

# for reproducibility
set.seed(123)
library(ggstatsplot)
library(gapminder)

# selecting subset of the data
df_year <- dplyr::filter(.data = gapminder::gapminder, year == 2007 | year == 1957)

# parametric t-test and box plot
p1 <-
ggstatsplot::ggbetweenstats(
data = df_year,
x = year,
y = lifeExp,
xlab = "Year",
ylab = "Life expectancy",
plot.type = "box",
type = "p",
conf.level = 0.99,
title = "Parametric test",
package = "ggsci",
palette = "nrc_npg"
)

# Mann-Whitney U test (nonparametric t) and violin plot
p2 <-
ggstatsplot::ggbetweenstats(
data = df_year,
x = year,
y = lifeExp,
xlab = "Year",
ylab = "Life expectancy",
plot.type = "violin",
type = "np",
conf.level = 0.99,
title = "Non-parametric Test (violin plot)",
package = "ggsci",
palette = "uniform_startrek"
)

# robust t-test and boxviolin plot
p3 <-
ggstatsplot::ggbetweenstats(
data = df_year,
x = year,
y = lifeExp,
xlab = "Year",
ylab = "Life expectancy",
plot.type = "boxviolin",
type = "r",
conf.level = 0.99,
title = "Robust Test (box & violin plot)",
tr = 0.005,
package = "wesanderson",
palette = "Royal2",
k = 3
)

# Bayes Factor for parametric t-test and boxviolin plot
p4 <-
ggstatsplot::ggbetweenstats(
data = df_year,
x = year,
y = lifeExp,
xlab = "Year",
ylab = "Life expectancy",
type = "bayes",
plot.type = "box",
title = "Bayesian Test (box plot)",
package = "ggsci",
palette = "nrc_npg"
)

# combining the individual plots into a single plot
ggstatsplot::combine_plots(
list(p1, p2, p3, p4),
plotgrid.args = list(nrow = 2),
annotation.args = list(
title = "Comparison of life expectancy between 1957 and 2007",
caption = "Source: Gapminder Foundation"
)
)

# Grouped analysis with grouped_ggbetweenstats

What if we want to analyze both by continent and between 1957 and 2007? A combination of our two previous efforts.

ggstatsplot provides a special helper function for such instances: grouped_ggbetweenstats. This is merely a wrapper function around ggstatsplot::combine_plots. It applies ggbetweenstats across all levels of a specified grouping variable and then combines list of individual plots into a single plot. Note that the grouping variable can be anything: conditions in a given study, groups in a study sample, different studies, etc.

Let’s focus on the same 4 continents for the following years: 1967, 1987, 2007. Also, let’s carry out pairwise comparisons to see if there differences between every pair of continents.

# for reproducibility
set.seed(123)

# select part of the dataset and use it for plotting
gapminder::gapminder %>%
dplyr::filter(year %in% c(1967, 1987, 2007), continent != "Oceania") %>%
ggstatsplot::grouped_ggbetweenstats(
# arguments relevant for ggstatsplot::ggbetweenstats
data = .,
x = continent,
y = lifeExp,
grouping.var = year,
xlab = "Continent",
ylab = "Life expectancy",
pairwise.display = "significant", # display only significant pairwise comparisons
p.adjust.method = "fdr", # adjust p-values for multiple tests using this method
ggtheme = ggthemes::theme_tufte(),
package = "ggsci",
palette = "default_jco",
outlier.tagging = TRUE,
ggstatsplot.layer = FALSE,
outlier.label = country,
# arguments relevant for ggstatsplot::combine_plots
annotation.args = list(title = "Changes in life expectancy across continents (1967-2007)"),
plotgrid.args = list(nrow = 3)
)

As seen from the plot, although the life expectancy has been improving steadily across all continents as we go from 1967 to 2007, this improvement has not been happening at the same rate for all continents. Additionally, irrespective of which year we look at, we still find significant differences in life expectancy across continents which have been surprisingly consistent across five decades (based on the observed effect sizes).

# Grouped analysis with ggbetweenstats + purrr

Although this grouping function provides a quick way to explore the data, it leaves much to be desired. For example, the same type of plot and test is applied for all years, but maybe we want to change this for different years, or maybe we want to gave different effect sizes for different years. This type of customization for different levels of a grouping variable is not possible with grouped_ggbetweenstats, but this can be easily achieved using the purrr package.

See the associated vignette here: https://indrajeetpatil.github.io/ggstatsplot/articles/web_only/purrr_examples.html

# Within-subjects designs

For repeated measures designs, ggwithinstats function can be used: https://indrajeetpatil.github.io/ggstatsplot/articles/web_only/ggwithinstats.html

# Summary of tests

The central tendency measure displayed will depend on the statistics:

Type Measure Function used
Parametric mean parameters::describe_distribution
Non-parametric median parameters::describe_distribution
Robust trimmed mean parameters::describe_distribution
Bayesian MAP estimate parameters::describe_distribution

MAP: maximum a posteriori probability

Following (between-subjects) tests are carried out for each type of analyses-

Type No. of groups Test Function used
Parametric > 2 Fisher’s or Welch’s one-way ANOVA stats::oneway.test
Non-parametric > 2 Kruskal–Wallis one-way ANOVA stats::kruskal.test
Robust > 2 Heteroscedastic one-way ANOVA for trimmed means WRS2::t1way
Bayes Factor > 2 Fisher’s ANOVA BayesFactor::anovaBF
Parametric 2 Student’s or Welch’s t-test stats::t.test
Non-parametric 2 Mann–Whitney U test stats::wilcox.test
Robust 2 Yuen’s test for trimmed means WRS2::yuen
Bayesian 2 Student’s t-test BayesFactor::ttestBF

Following effect sizes (and confidence intervals/CI) are available for each type of test-

Type No. of groups Effect size CI? Function used
Parametric > 2 $$\eta_{p}^2$$, $$\omega_{p}^2$$ effectsize::omega_squared, effectsize::eta_squared
Non-parametric > 2 $$\epsilon_{ordinal}^2$$ effectsize::rank_epsilon_squared
Robust > 2 $$\xi$$ (Explanatory measure of effect size) WRS2::t1way
Bayes Factor > 2 $$R_{posterior}^2$$ performance::r2_bayes
Parametric 2 Cohen’s d, Hedge’s g effectsize::cohens_d, effectsize::hedges_g
Non-parametric 2 r (rank-biserial correlation) effectsize::rank_biserial
Robust 2 $$\xi$$ (Explanatory measure of effect size) WRS2::yuen.effect.ci
Bayesian 2 $$\delta_{posterior}$$ bayestestR::describe_posterior

Here is a summary of multiple pairwise comparison tests supported in ggbetweenstats-

Type Equal variance? Test p-value adjustment? Function used
Parametric No Games-Howell test Yes stats::pairwise.t.test
Parametric Yes Student’s t-test Yes PMCMRplus::gamesHowellTest
Non-parametric No Dunn test Yes PMCMRplus::kwAllPairsDunnTest
Robust No Yuen’s trimmed means test Yes WRS2::lincon
Bayes Factor NA Student’s t-test NA BayesFactor::ttestBF

# Reporting

If you wish to include statistical analysis results in a publication/report, the ideal reporting practice will be a hybrid of two approaches:

• the ggstatsplot approach, where the plot contains both the visual and numerical summaries about a statistical model, and

• the standard narrative approach, which provides interpretive context for the reported statistics.

For example, let’s see the following example:

The ggstatsplot reporting -

ggbetweenstats(ToothGrowth, supp, len)

The narrative context (assuming type = "parametric") can complement this plot either as a figure caption or in the main text-

Welch’s t-test revealed that, across 60 guinea pigs, although the tooth length was higher when the animal received vitamin C via orange juice as compared to via ascorbic acid, this effect was not statistically significant. The effect size $$(g = 0.49)$$ was medium, as per Cohen’s (1988) conventions. The Bayes Factor for the same analysis revealed that the data were 1.2 times more probable under the alternative hypothesis as compared to the null hypothesis. This can be considered weak evidence (Jeffreys, 1961) in favor of the alternative hypothesis.

Similar reporting style can be followed when the function performs one-way ANOVA instead of a t-test.

# Effect size interpretation

To see how the effect sizes displayed in these tests can be interpreted, see: https://indrajeetpatil.github.io/ggstatsplot/articles/web_only/effsize_interpretation.html

# Suggestions

If you find any bugs or have any suggestions/remarks, please file an issue on GitHub: https://github.com/IndrajeetPatil/ggstatsplot/issues