`{statsExpressions}`: Tidy dataframes and expressions with statistical details

Status	Usage	Miscellaneous

Introduction

The {statsExpressions} package has two key aims:

to provide a consistent syntax to do statistical analysis with tidy data (in pipe-friendly manner),
to provide statistical expressions (pre-formatted in-text statistical results) for plotting functions.

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.

This package forms the statistical processing backend for ggstatsplot package.

For more documentation, see the dedicated website.

Installation

Type	Command
Release	`install.packages("statsExpressions")`
Development	`pak::pak("IndrajeetPatil/statsExpressions")`

On Linux, {statsExpressions} installation may require additional system dependencies, which can be checked using:

pak::pkg_sysreqs("statsExpressions")

Citation

The package can be cited as:

citation("statsExpressions")
To cite package 'statsExpressions' in publications use:

  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

  @Article{,
    doi = {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 functionality

Summary of available analyses

Test	Function
one-sample t-test	`one_sample_test()`
two-sample t-test	`two_sample_test()`
one-way ANOVA	`oneway_anova()`
correlation analysis	`corr_test()`
contingency table analysis	`contingency_table()`
meta-analysis	`meta_analysis()`
pairwise comparisons	`pairwise_comparisons()`

Summary of details available for analyses

Analysis	Hypothesis testing	Effect size estimation
(one/two-sample) t-test	✅	✅
one-way ANOVA	✅	✅
correlation	✅	✅
(one/two-way) contingency table	✅	✅
random-effects meta-analysis	✅	✅

Summary of supported statistical approaches

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	✅	❌	✅	✅

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 × 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 <language>

mtcars %>% oneway_anova(cyl, wt, type = "robust")
#> # A tibble: 1 × 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 <language>

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:

set.seed(123)

# 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) %>%
  knitr::kable()

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
set.seed(123)
library(dplyr)

# 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) %>%
  ungroup()
#> # A tibble: 3 × 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   -1.88     -0.402 ncp        
#> 2 Hedges' g     0.286       0.95   -0.388     0.937 ncp        
#> 3 Hedges' g     1.24        0.95    0.544     1.91  ncp        
#>   conf.distribution n.obs expression
#>   <chr>             <int> <list>    
#> 1 t                    11 <language>
#> 2 t                     7 <language>
#> 3 t                    14 <language>

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:

Let’s load the needed library for visualization:

library(ggplot2)

Expressions for centrality measure

Note that when used in a geometric layer, the expression need to be parsed.

# 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

The returned data frame will always have a column called expression.

Assuming there is only a single result you need to display in a plot, to use it in a plot, you have two options:

extract the expression from the list column (results_data$expression[[1]]) without parsing
use the list column as is, in which case you will need to parse it (parse(text = results_data$expression))

If you want to display more than one expression in a plot, you will have to parse them.

Between-subjects design

set.seed(123)
library(ggridges)

results_data <- oneway_anova(iris, Species, Sepal.Length, type = "robust")

# create a ridgeplot
ggplot(iris, aes(x = Sepal.Length, y = Species)) +
  geom_density_ridges() +
  labs(
    title = "A heteroscedastic one-way ANOVA for trimmed means",
    subtitle = results_data$expression[[1]]
  )

Within-subjects design

set.seed(123)
library(WRS2)
library(ggbeeswarm)

results_data <- oneway_anova(
  WineTasting,
  Wine,
  Taste,
  paired = TRUE,
  subject.id = Taster,
  type = "np"
)

ggplot2::ggplot(WineTasting, aes(Wine, Taste, color = Wine)) +
  geom_quasirandom() +
  labs(
    title = "Friedman's rank sum test",
    subtitle = parse(text = results_data$expression)
  )

Expressions for two-sample tests

Between-subjects design

set.seed(123)
library(gghalves)

results_data <- two_sample_test(ToothGrowth, supp, len)

ggplot(ToothGrowth, aes(supp, len)) +
  geom_half_dotplot() +
  labs(
    title = "Two-Sample Welch's t-test",
    subtitle = parse(text = results_data$expression)
  )

Within-subjects design

set.seed(123)
library(tidyr)
library(PairedData)
data(PrisonStress)

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

results_data <- two_sample_test(
  data = df,
  x = PSS,
  y = stress,
  paired = TRUE,
  subject.id = Subject,
  type = "np"
)

# plot
paired.plotProfiles(PrisonStress, "PSSbefore", "PSSafter", subjects = "Subject") +
  labs(
    title = "Two-sample Wilcoxon paired test",
    subtitle = parse(text = results_data$expression)
  )

Expressions for one-sample tests

set.seed(123)

# dataframe with results
results_data <- one_sample_test(mtcars, wt, test.value = 3, type = "bayes")

# creating a histogram plot
ggplot(mtcars, aes(wt)) +
  geom_histogram(alpha = 0.5) +
  geom_vline(xintercept = mean(mtcars$wt), color = "red") +
  labs(subtitle = parse(text = results_data$expression))

Expressions for correlation analysis

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

set.seed(123)

# dataframe with results
results_data <- corr_test(mtcars, mpg, wt, type = "nonparametric")

# create a scatter plot
ggplot(mtcars, aes(mpg, wt)) +
  geom_point() +
  geom_smooth(method = "lm", formula = y ~ x) +
  labs(
    title = "Spearman's rank correlation coefficient",
    subtitle = parse(text = results_data$expression)
  )

Expressions for contingency table analysis

For categorical/nominal data - one-sample:

set.seed(123)

# dataframe with results
results_data <- contingency_table(
  as.data.frame(table(mpg$class)),
  Var1,
  counts = Freq,
  type = "bayes"
)

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

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

set.seed(123)

# Pearson's chi-squared test of independence
contingency_table(mtcars, am, vs)$expression[[1]]
#> list(chi["Pearson"]^2 * "(" * 1 * ")" == "0.91", italic(p) == 
#>     "0.34", widehat(italic("V"))["Cramer"] == "0.00", CI["95%"] ~ 
#>     "[" * "0.00", "0.49" * "]", italic("n")["obs"] == "32")

Expressions for meta-analysis

set.seed(123)
library(metaviz)
library(metaplus)

# dataframe with results
results_data <- meta_analysis(dplyr::rename(mozart, estimate = d, std.error = se))

# meta-analysis forest plot with results random-effects meta-analysis
viz_forest(
  x = mozart[, c("d", "se")],
  study_labels = mozart[, "study_name"],
  xlab = "Cohen's d",
  variant = "thick",
  type = "cumulative"
) +
  labs(
    title = "Meta-analysis of Pietschnig, Voracek, and Formann (2010) on the Mozart effect",
    subtitle = parse(text = results_data$expression)
  ) +
  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:

set.seed(123)

# extracting detailed expression
(res_expr <- oneway_anova(iris, Species, Sepal.Length, var.equal = TRUE)$expression[[1]])
#> 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.

`centrality_description`

Type	Measure	Function used
Parametric	mean	`datawizard::describe_distribution()`
Non-parametric	median	`datawizard::describe_distribution()`
Robust	trimmed mean	`datawizard::describe_distribution()`
Bayesian	MAP	`datawizard::describe_distribution()`

`oneway_anova`

between-subjects

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()`

Effect size estimation

Type	No. of groups	Effect size	CI available?	Function used
Parametric	> 2	partial eta-squared, partial omega-squared	Yes	`effectsize::omega_squared()`, `effectsize::eta_squared()`
Non-parametric	> 2	rank epsilon squared	Yes	`effectsize::rank_epsilon_squared()`
Robust	> 2	Explanatory measure of effect size	Yes	`WRS2::t1way()`
Bayes Factor	> 2	Bayesian R-squared	Yes	`performance::r2_bayes()`

within-subjects

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()`

Effect size estimation

Type	No. of groups	Effect size	CI available?	Function used
Parametric	> 2	partial eta-squared, partial omega-squared	Yes	`effectsize::omega_squared()`, `effectsize::eta_squared()`
Non-parametric	> 2	Kendall’s coefficient of concordance	Yes	`effectsize::kendalls_w()`
Robust	> 2	Algina-Keselman-Penfield robust standardized difference average	Yes	`WRS2::wmcpAKP()`
Bayes Factor	> 2	Bayesian R-squared	Yes	`performance::r2_bayes()`

`two_sample_test`

between-subjects

Hypothesis testing

Type	No. of groups	Test	Function used
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 available?	Function used
Parametric	2	Cohen’s d, Hedge’s g	Yes	`effectsize::cohens_d()`, `effectsize::hedges_g()`
Non-parametric	2	r (rank-biserial correlation)	Yes	`effectsize::rank_biserial()`
Robust	2	Algina-Keselman-Penfield robust standardized difference	Yes	`WRS2::akp.effect()`
Bayesian	2	difference	Yes	`bayestestR::describe_posterior()`

within-subjects

Hypothesis testing

Type	No. of groups	Test	Function used
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 available?	Function used
Parametric	2	Cohen’s d, Hedge’s g	Yes	`effectsize::cohens_d()`, `effectsize::hedges_g()`
Non-parametric	2	r (rank-biserial correlation)	Yes	`effectsize::rank_biserial()`
Robust	2	Algina-Keselman-Penfield robust standardized difference	Yes	`WRS2::wmcpAKP()`
Bayesian	2	difference	Yes	`bayestestR::describe_posterior()`

`one_sample_test`

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 available?	Function used
Parametric	Cohen’s d, Hedge’s g	Yes	`effectsize::cohens_d()`, `effectsize::hedges_g()`
Non-parametric	r (rank-biserial correlation)	Yes	`effectsize::rank_biserial()`
Robust	trimmed mean	Yes	`WRS2::trimcibt()`
Bayes Factor	difference	Yes	`bayestestR::describe_posterior()`

`corr_test`

Hypothesis testing and Effect size estimation

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

`contingency_table`

two-way table

Hypothesis testing

Type	Design	Test	Function used
Parametric/Non-parametric	Unpaired	Pearson’s chi-squared test	`stats::chisq.test()`
Bayesian	Unpaired	Bayesian Pearson’s chi-squared test	`BayesFactor::contingencyTableBF()`
Parametric/Non-parametric	Paired	McNemar’s chi-squared test	`stats::mcnemar.test()`
Bayesian	Paired	No	No

Effect size estimation

Type	Design	Effect size	CI available?	Function used
Parametric/Non-parametric	Unpaired	Cramer’s V	Yes	`effectsize::cramers_v()`
Bayesian	Unpaired	Cramer’s V	Yes	`effectsize::cramers_v()`
Parametric/Non-parametric	Paired	Cohen’s g	Yes	`effectsize::cohens_g()`
Bayesian	Paired	No	No	No

one-way table

Hypothesis testing

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

Effect size estimation

Type	Effect size	CI available?	Function used
Parametric/Non-parametric	Pearson’s C	Yes	`effectsize::pearsons_c()`
Bayesian	No	No	No

`meta_analysis`

Hypothesis testing and Effect size estimation

Type	Test	Effect size	CI available?	Function used
Parametric	Meta-analysis via random-effects models	beta	Yes	`metafor::metafor()`
Robust	Meta-analysis via robust random-effects models	beta	Yes	`metaplus::metaplus()`
Bayes	Meta-analysis via Bayesian random-effects models	beta	Yes	`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-

Acknowledgments

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

Contributing

Bug reports, suggestions, questions, and (most of all) contributions are welcome.

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.

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README.md

File metadata and controls

{statsExpressions}: Tidy dataframes and expressions with statistical details

Introduction

Installation

Citation

General Workflow

Summary of functionality

Tidy dataframes from statistical analysis

Using expressions in custom plots

Expressions for centrality measure

Expressions for one-way ANOVAs

Between-subjects design

Within-subjects design

Expressions for two-sample tests

Between-subjects design

Within-subjects design

Expressions for one-sample tests

Expressions for correlation analysis

Expressions for contingency table analysis

Expressions for meta-analysis

Customizing details to your liking

Summary of tests and effect sizes

centrality_description

oneway_anova

between-subjects

within-subjects

two_sample_test

between-subjects

within-subjects

one_sample_test

corr_test

contingency_table

two-way table

one-way table

meta_analysis

Usage in {ggstatsplot}

Acknowledgments

Contributing

`{statsExpressions}`: Tidy dataframes and expressions with statistical details

`centrality_description`

`oneway_anova`

`two_sample_test`

`one_sample_test`

`corr_test`

`contingency_table`

`meta_analysis`

Usage in `{ggstatsplot}`