{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	Source	Command
Release		install.packages("statsExpressions")
Development		pak::pak("IndrajeetPatil/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},
    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 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, lets 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, lets 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 Welchs t-test:

Lets 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

Lets 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", "1.00" * "]", 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	Fishers or Welchs 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	Fishers 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	Kendalls 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	Students or Welchs t-test	stats::t.test()
Non-parametric	2	Mann-Whitney U test	stats::wilcox.test()
Robust	2	Yuens test for trimmed means	WRS2::yuen()
Bayesian	2	Students t-test	BayesFactor::ttestBF()

Effect size estimation

Type	No.of groups	Effect size	CI available?	Function used
Parametric	2	Cohens d, Hedges 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	Students t-test	stats::t.test()
Non-parametric	2	Wilcoxon signed-rank test	stats::wilcox.test()
Robust	2	Yuens test on trimmed means for dependent samples	WRS2::yuend()
Bayesian	2	Students t-test	BayesFactor::ttestBF()

Effect size estimation

Type	No.of groups	Effect size	CI available?	Function used
Parametric	2	Cohens d, Hedges 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 Students 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 Students t-test	BayesFactor::ttestBF()

Effect size estimation

Type	Effect size	CI available?	Function used
Parametric	Cohens d, Hedges 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	Pearsons correlation coefficient	Yes	correlation::correlation()
Non-parametric	Spearmans rank correlation coefficient	Yes	correlation::correlation()
Robust	Winsorized Pearsons correlation coefficient	Yes	correlation::correlation()
Bayesian	Bayesian Pearsons correlation coefficient	Yes	correlation::correlation()

contingency_table

two-way table

Hypothesis testing

Type	Design	Test	Function used
Parametric/Non-parametric	Unpaired	Pearsons chi-squared test	stats::chisq.test()
Bayesian	Unpaired	Bayesian Pearsons chi-squared test	BayesFactor::contingencyTableBF()
Parametric/Non-parametric	Paired	McNemars 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	Cramers V	Yes	effectsize::cramers_v()
Bayesian	Unpaired	Cramers V	Yes	effectsize::cramers_v()
Parametric/Non-parametric	Paired	Cohens 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	Pearsons 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.