# Statsexpressions

Tidy data frames and expressions with statistical summaries 📜
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Tidy data frames and expressions with statistical summaries 📜
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# 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[]`) 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[]
)
`````` ### 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[]
#> 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[])
#> 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")

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.

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