{statsExpressions}: Tidy dataframes and expressions with statistical details

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The {statsExpressions} package has two key aims:

Statistical packages exhibit substantial diversity in terms of their syntax and expected input type. This can make it difficult to switch from one statistical approach to another. For example, some functions expect vectors as inputs, while others expect dataframes. Depending on whether it is a repeated measures design or not, different functions might expect data to be in wide or long format. Some functions can internally omit missing values, while other functions error in their presence. Furthermore, if someone wishes to utilize the objects returned by these packages downstream in their workflow, this is not straightforward either because even functions from the same package can return a list, a matrix, an array, a dataframe, etc., depending on the function.

This is where {statsExpressions} comes in: It can be thought of as a unified portal through which most of the functionality in these underlying packages can be accessed, with a simpler interface and no requirement to change data format.


Type Source Command
Release CRAN install.packages("statsExpressions")
Development GitHub remotes::install_github("IndrajeetPatil/statsExpressions")


The package can be cited as:


  Patil, I., (2021). statsExpressions: R Package for Tidy Dataframes
  and Expressions with Statistical Details. Journal of Open Source
  Software, 6(61), 3236, https://doi.org/10.21105/joss.03236

A BibTeX entry for LaTeX users is

    doi = {10.21105/joss.03236},
    url = {https://doi.org/10.21105/joss.03236},
    year = {2021},
    publisher = {{The Open Journal}},
    volume = {6},
    number = {61},
    pages = {3236},
    author = {Indrajeet Patil},
    title = {{statsExpressions: {R} Package for Tidy Dataframes and Expressions with Statistical Details}},
    journal = {{Journal of Open Source Software}},

General Workflow

Summary of types of statistical analyses

Here is a tabular summary of available tests:

Test Function Lifecycle
one-sample t-test one_sample_test lifecycle
two-sample t-test two_sample_test lifecycle
one-way ANOVA oneway_anova lifecycle
correlation analysis corr_test lifecycle
contingency table analysis contingency_table lifecycle
meta-analysis meta_analysis lifecycle

The table below summarizes all the different types of analyses currently supported in this package-

Description Parametric Non-parametric Robust Bayesian
Between group/condition comparisons
Within group/condition comparisons
Distribution of a numeric variable
Correlation between two variables
Association between categorical variables
Equal proportions for categorical variable levels
Random-effects meta-analysis

Summary of Bayesian analysis

Analysis Hypothesis testing Estimation
(one/two-sample) t-test
one-way ANOVA
(one/two-way) contingency table
random-effects meta-analysis

Tidy dataframes from statistical analysis

To illustrate the simplicity of this syntax, let’s say we want to run a one-way ANOVA. If we first run a non-parametric ANOVA and then decide to run a robust ANOVA instead, the syntax remains the same and the statistical approach can be modified by changing a single argument:


mtcars %>% oneway_anova(cyl, wt, type = "nonparametric")
#> # A tibble: 1 x 15
#>   parameter1 parameter2 statistic df.error   p.value
#>   <chr>      <chr>          <dbl>    <int>     <dbl>
#> 1 wt         cyl             22.8        2 0.0000112
#>   method                       effectsize      estimate conf.level conf.low
#>   <chr>                        <chr>              <dbl>      <dbl>    <dbl>
#> 1 Kruskal-Wallis rank sum test Epsilon2 (rank)    0.736       0.95    0.624
#>   conf.high conf.method          conf.iterations n.obs expression  
#>       <dbl> <chr>                          <int> <int> <list>      
#> 1         1 percentile bootstrap             100    32 <expression>

mtcars %>% oneway_anova(cyl, wt, type = "robust")
#> # A tibble: 1 x 12
#>   statistic    df df.error p.value
#>       <dbl> <dbl>    <dbl>   <dbl>
#> 1      12.7     2     12.2 0.00102
#>   method                                           
#>   <chr>                                            
#> 1 A heteroscedastic one-way ANOVA for trimmed means
#>   effectsize                         estimate conf.level conf.low conf.high
#>   <chr>                                 <dbl>      <dbl>    <dbl>     <dbl>
#> 1 Explanatory measure of effect size     1.05       0.95    0.843      1.50
#>   n.obs expression  
#>   <int> <list>      
#> 1    32 <expression>

All possible output dataframes from functions are tabulated here: https://indrajeetpatil.github.io/statsExpressions/articles/web_only/dataframe_outputs.html

Needless to say this will also work with the kable function to generate a table:

# setup

# one-sample robust t-test
# we will leave `expression` column out; it's not needed for using only the dataframe
mtcars %>%
  one_sample_test(wt, test.value = 3, type = "robust") %>%
  dplyr::select(-expression) %>%
statistic p.value n.obs method effectsize estimate conf.level conf.low conf.high
1.179181 0.275 32 Bootstrap-t method for one-sample test Trimmed mean 3.197 0.95 2.854246 3.539754

These functions are also compatible with other popular data manipulation packages.

For example, let’s say we want to run a one-sample t-test for all levels of a certain grouping variable. We can use dplyr to do so:

# for reproducibility

# grouped operation
# running one-sample test for all levels of grouping variable `cyl`
mtcars %>%
  group_by(cyl) %>%
  group_modify(~ one_sample_test(.x, wt, test.value = 3), .keep = TRUE) %>%
#> # A tibble: 3 x 16
#>     cyl    mu statistic df.error  p.value method            alternative
#>   <dbl> <dbl>     <dbl>    <dbl>    <dbl> <chr>             <chr>      
#> 1     4     3    -4.16        10 0.00195  One Sample t-test two.sided  
#> 2     6     3     0.870        6 0.418    One Sample t-test two.sided  
#> 3     8     3     4.92        13 0.000278 One Sample t-test two.sided  
#>   effectsize estimate conf.level conf.low conf.high conf.method
#>   <chr>         <dbl>      <dbl>    <dbl>     <dbl> <chr>      
#> 1 Hedges' g    -1.16        0.95   -1.97     -0.422 ncp        
#> 2 Hedges' g     0.286       0.95   -0.419     1.01  ncp        
#> 3 Hedges' g     1.24        0.95    0.565     1.98  ncp        
#>   conf.distribution n.obs expression  
#>   <chr>             <int> <list>      
#> 1 t                    11 <expression>
#> 2 t                     7 <expression>
#> 3 t                    14 <expression>

Using expressions in custom plots

Note that expression here means a pre-formatted in-text statistical result. In addition to other details contained in the dataframe, there is also a column titled expression, which contains expression with statistical details and can be displayed in a plot.

For all statistical test expressions, the default template attempt to follow the gold standard for statistical reporting.

For example, here are results from Welch’s t-test:

Expressions for centrality measure


# displaying mean for each level of `cyl`
centrality_description(mtcars, cyl, wt) |>
  ggplot(aes(cyl, wt)) +
  geom_point() +
  geom_label(aes(label = expression), parse = TRUE)

Here are a few examples for supported analyses.

Expressions for one-way ANOVAs

Between-subjects design

Let’s say we want to check differences in weight of the vehicle based on number of cylinders in the engine and wish to carry out robust trimmed-means ANOVA:

# setup

# create a ridgeplot
ggplot(iris, aes(x = Sepal.Length, y = Species)) +
    jittered_points = TRUE, quantile_lines = TRUE,
    scale = 0.9, vline_size = 1, vline_color = "red",
    position = position_raincloud(adjust_vlines = TRUE)
  ) + # use the expression in the dataframe to display results in the subtitle
    title = "A heteroscedastic one-way ANOVA for trimmed means",
    subtitle = oneway_anova(iris, Species, Sepal.Length, type = "robust")$expression[[1]]

Within-subjects design

Let’s now see an example of a repeated measures one-way ANOVA.

# setup

ggplot2::ggplot(WineTasting, aes(Wine, Taste, color = Wine)) +
  geom_quasirandom() +
    title = "Friedman's rank sum test",
    subtitle = oneway_anova(
      paired = TRUE,
      subject.id = Taster,
      type = "np"

Expressions for two-sample tests

Between-subjects design

# setup

# create a plot
ggplot(ToothGrowth, aes(supp, len)) +
  geom_half_boxplot() +
  geom_beeswarm() +
  theme_ipsum_rc() +
  # adding a subtitle with
    title = "Two-Sample Welch's t-test",
    subtitle = two_sample_test(ToothGrowth, supp, len)$expression[[1]]

Within-subjects design

We can also have a look at a repeated measures design and the related expressions.

# setup

# get data in tidy format
df <- pivot_longer(PrisonStress, starts_with("PSS"), "PSS", values_to = "stress")

# plot
paired.plotProfiles(PrisonStress, "PSSbefore", "PSSafter", subjects = "Subject") +
    title = "Two-sample Wilcoxon paired test",
    subtitle = two_sample_test(
      data = df,
      x = PSS,
      y = stress,
      paired = TRUE,
      subject.id = Subject,
      type = "np"

Expressions for one-sample tests

# setup

# dataframe with results
df_results <- one_sample_test(mtcars, wt, test.value = 3, type = "bayes",
                              top.text = "Bayesian one-sample t-test")

# creating a histogram plot
ggplot(mtcars, aes(wt)) +
  geom_histogram(alpha = 0.5) +
  geom_vline(xintercept = mean(mtcars$wt), color = "red") +
    subtitle = df_results$expression[[1]]

Expressions for correlation analysis

Let’s look at another example where we want to run correlation analysis:

# setup

# create a scatter plot
ggplot(mtcars, aes(mpg, wt)) +
  geom_point() +
  geom_smooth(method = "lm", formula = y ~ x) +
    title = "Spearman's rank correlation coefficient",
    subtitle = corr_test(mtcars, mpg, wt, type = "nonparametric")$expression[[1]]

Expressions for contingency table analysis

For categorical/nominal data - one-sample:

# setup

df_results <- contingency_table(as.data.frame(table(mpg$class)),
  counts = Freq,
  type = "bayes",
  top.text = "One-sample goodness-of-fit test"

# basic pie chart
ggplot(as.data.frame(table(mpg$class)), aes(x = "", y = Freq, fill = factor(Var1))) +
  geom_bar(width = 1, stat = "identity") +
  theme(axis.line = element_blank()) +
  # cleaning up the chart and adding results from one-sample proportion test
  coord_polar(theta = "y", start = 0) +
    fill = "Class",
    x = NULL,
    y = NULL,
    title = "Pie Chart of class (type of car)",
    caption = df_results$expression[[1]]

You can also use these function to get the expression in return without having to display them in plots:

# setup

# Pearson's chi-squared test of independence
contingency_table(mtcars, am, cyl)$expression[[1]]
#> expression(list(chi["Pearson"]^2 * "(" * 2 * ")" == "8.74", italic(p) == 
#>     "0.01", widehat(italic("V"))["Cramer"] == "0.46", CI["95%"] ~ 
#>     "[" * "0.00", "1.00" * "]", italic("n")["obs"] == "32"))

Expressions for meta-analysis

# setup

# meta-analysis forest plot with results random-effects meta-analysis
  x = mozart[, c("d", "se")],
  study_labels = mozart[, "study_name"],
  xlab = "Cohen's d",
  variant = "thick",
  type = "cumulative"
) + # use `{statsExpressions}` to create expression containing results
    title = "Meta-analysis of Pietschnig, Voracek, and Formann (2010) on the Mozart effect",
    subtitle = meta_analysis(dplyr::rename(mozart, estimate = d, std.error = se))$expression[[1]]
  ) +
  theme(text = element_text(size = 12))

Customizing details to your liking

Sometimes you may not wish include so many details in the subtitle. In that case, you can extract the expression and copy-paste only the part you wish to include. For example, here only statistic and p-values are included:

# setup

# extracting detailed expression
(res_expr <- oneway_anova(iris, Species, Sepal.Length, var.equal = TRUE)$expression[[1]])
#> expression(list(italic("F")["Fisher"](2, 147) == "119.26", italic(p) == 
#>     "1.67e-31", widehat(omega["p"]^2) == "0.61", CI["95%"] ~ 
#>     "[" * "0.53", "1.00" * "]", italic("n")["obs"] == "150"))

# adapting the details to your liking
ggplot(iris, aes(x = Species, y = Sepal.Length)) +
  geom_boxplot() +
  labs(subtitle = ggplot2::expr(paste(
    NULL, italic("F"), "(", "2",
    ",", "147", ") = ", "119.26", ", ",
    italic("p"), " = ", "1.67e-31"

Summary of tests and effect sizes

Here a go-to summary about statistical test carried out and the returned effect size for each function is provided. This should be useful if one needs to find out more information about how an argument is resolved in the underlying package or if one wishes to browse the source code. So, for example, if you want to know more about how one-way (between-subjects) ANOVA, you can run ?stats::oneway.test in your R console.


Type Measure Function used
Parametric mean parameters::describe_distribution
Non-parametric median parameters::describe_distribution
Robust trimmed mean parameters::describe_distribution
Bayesian MAP (maximum a posteriori probability) estimate parameters::describe_distribution

two_sample_test + oneway_anova

No. of groups: 2 => two_sample_test
No. of groups: > 2 => oneway_anova


Hypothesis testing

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

Effect size estimation

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_{Bayesian}^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 \delta_{R}^{AKP} (Algina-Keselman-Penfield robust standardized difference) WRS2::akp.effect
Bayesian 2 \delta_{posterior} bayestestR::describe_posterior


Hypothesis testing

Type No. of groups Test Function used
Parametric > 2 One-way repeated measures ANOVA afex::aov_ez
Non-parametric > 2 Friedman rank sum test stats::friedman.test
Robust > 2 Heteroscedastic one-way repeated measures ANOVA for trimmed means WRS2::rmanova
Bayes Factor > 2 One-way repeated measures ANOVA BayesFactor::anovaBF
Parametric 2 Student’s t-test stats::t.test
Non-parametric 2 Wilcoxon signed-rank test stats::wilcox.test
Robust 2 Yuen’s test on trimmed means for dependent samples WRS2::yuend
Bayesian 2 Student’s t-test BayesFactor::ttestBF

Effect size estimation

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 W_{Kendall} (Kendall’s coefficient of concordance) effectsize::kendalls_w
Robust > 2 \delta_{R-avg}^{AKP} (Algina-Keselman-Penfield robust standardized difference average) WRS2::wmcpAKP
Bayes Factor > 2 R_{Bayesian}^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 \delta_{R}^{AKP} (Algina-Keselman-Penfield robust standardized difference) WRS2::wmcpAKP
Bayesian 2 \delta_{posterior} bayestestR::describe_posterior


Hypothesis testing

Type Test Function used
Parametric One-sample Student’s t-test stats::t.test
Non-parametric One-sample Wilcoxon test stats::wilcox.test
Robust Bootstrap-t method for one-sample test WRS2::trimcibt
Bayesian One-sample Student’s t-test BayesFactor::ttestBF

Effect size estimation

Type Effect size CI? Function used
Parametric Cohen’s d, Hedge’s g effectsize::cohens_d, effectsize::hedges_g
Non-parametric r (rank-biserial correlation) effectsize::rank_biserial
Robust trimmed mean trimcibt (custom)
Bayes Factor \delta_{posterior} bayestestR::describe_posterior


Hypothesis testing and Effect size estimation

Type Test CI? Function used
Parametric Pearson’s correlation coefficient correlation::correlation
Non-parametric Spearman’s rank correlation coefficient correlation::correlation
Robust Winsorized Pearson correlation coefficient correlation::correlation
Bayesian Pearson’s correlation coefficient correlation::correlation


two-way table

Hypothesis testing

Type Design Test Function used
Parametric/Non-parametric Unpaired Pearson’s \chi^2 test stats::chisq.test
Bayesian Unpaired Bayesian Pearson’s \chi^2 test BayesFactor::contingencyTableBF
Parametric/Non-parametric Paired McNemar’s \chi^2 test stats::mcnemar.test
Bayesian Paired

Effect size estimation

Type Design Effect size CI? Function used
Parametric/Non-parametric Unpaired Cramer’s V effectsize::cramers_v
Bayesian Unpaired Cramer’s V effectsize::cramers_v
Parametric/Non-parametric Paired Cohen’s g effectsize::cohens_g
Bayesian Paired

one-way table

Hypothesis testing

Type Test Function used
Parametric/Non-parametric Goodness of fit \chi^2 test stats::chisq.test
Bayesian Bayesian Goodness of fit \chi^2 test (custom)

Effect size estimation

Type Effect size CI? Function used
Parametric/Non-parametric Pearson’s C effectsize::pearsons_c


Hypothesis testing and Effect size estimation

Type Test Effect size CI? Function used
Parametric Meta-analysis via random-effects models \beta metafor::metafor
Robust Meta-analysis via robust random-effects models \beta metaplus::metaplus
Bayes Meta-analysis via Bayesian random-effects models \beta metaBMA::meta_random

Usage in ggstatsplot

Note that these functions were initially written to display results from statistical tests on ready-made ggplot2 plots implemented in ggstatsplot.

For detailed documentation, see the package website: https://indrajeetpatil.github.io/ggstatsplot/

Here is an example from ggstatsplot of what the plots look like when the expressions are displayed in the subtitle-


The hexsticker and the schematic illustration of general workflow were generously designed by Sarah Otterstetter (Max Planck Institute for Human Development, Berlin).


I’m happy to receive bug reports, suggestions, questions, and (most of all) contributions to fix problems and add features. I personally prefer using the GitHub issues system over trying to reach out to me in other ways (personal e-mail, Twitter, etc.). Pull Requests for contributions are encouraged.

Here are some simple ways in which you can contribute (in the increasing order of commitment):

Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.