statsExpressions: Tidy Dataframes and Expressions with Statistical Details

Indrajeet Patil

doi:10.21105/joss.03236

Parametric and Bayesian one-way and two-way contingency table analyses.

Usage

contingency_table(
  data,
  x,
  y = NULL,
  paired = FALSE,
  type = "parametric",
  counts = NULL,
  ratio = NULL,
  alternative = "two.sided",
  digits = 2L,
  conf.level = 0.95,
  sampling.plan = "indepMulti",
  fixed.margin = "rows",
  prior.concentration = 1,
  ...
)

Arguments

data

A data frame (or a tibble) from which variables specified are to be taken. Other data types (e.g., matrix,table, array, etc.) will not be accepted. Additionally, grouped data frames from {dplyr} should be ungrouped before they are entered as data.

x

The variable to use as the rows in the contingency table.

y

The variable to use as the columns in the contingency table. Default is NULL. If NULL, one-sample proportion test (a goodness of fit test) will be run for the x variable.

paired

Logical indicating whether data came from a within-subjects or repeated measures design study (Default: FALSE).

type

A character specifying the type of statistical approach:

"parametric"
"nonparametric"
"robust"
"bayes"

You can specify just the initial letter.

counts

The variable in data containing counts, or NULL if each row represents a single observation.

ratio

A vector of proportions: the expected proportions for the proportion test (should sum to 1). Default is NULL, which means the null is equal theoretical proportions across the levels of the nominal variable. E.g., ratio = c(0.5, 0.5) for two levels, ratio = c(0.25, 0.25, 0.25, 0.25) for four levels, etc.

alternative

A character string specifying the alternative hypothesis; Controls the type of CI returned: "two.sided" (default, two-sided CI), "greater" or "less" (one-sided CI). Partial matching is allowed (e.g., "g", "l", "two"...). See section One-Sided CIs in the effectsize_CIs vignette.

digits

Number of digits for rounding or significant figures. May also be "signif" to return significant figures or "scientific" to return scientific notation. Control the number of digits by adding the value as suffix, e.g. digits = "scientific4" to have scientific notation with 4 decimal places, or digits = "signif5" for 5 significant figures (see also signif()).

conf.level

Scalar between 0 and 1 (default: 95% confidence/credible intervals, 0.95). If NULL, no confidence intervals will be computed.

sampling.plan

Character describing the sampling plan. Possible options:

"indepMulti" (independent multinomial; default)
"poisson"
"jointMulti" (joint multinomial)
"hypergeom" (hypergeometric). For more, see BayesFactor::contingencyTableBF().

fixed.margin

For the independent multinomial sampling plan, which margin is fixed ("rows" or "cols"). Defaults to "rows".

prior.concentration

Specifies the prior concentration parameter, set to 1 by default. It indexes the expected deviation from the null hypothesis under the alternative, and corresponds to Gunel and Dickey's (1974) "a" parameter.

...

Additional arguments (currently ignored).

Value

The returned object is a tibble data frame with the additional class "statsExpressions". The exact set of columns depends on the test and, for functions that accept a type argument, on the chosen analysis (parametric, non-parametric, robust, or Bayesian). Any given call therefore returns some (not all) of the columns below.

Hypothesis testing

statistic: the numeric value of a statistic
df: the numeric value of a parameter being modeled (often degrees of freedom for the test)
df.error and df: relevant only if the statistic in question has two degrees of freedom (e.g. anova)
p.value: the two-sided p-value associated with the observed statistic
method: the name of the inferential statistical test

Effect size estimation

effectsize: the name of the effect size
estimate: estimated value of the effect size
conf.level: the coverage level of the confidence/credible interval (e.g. 0.95); the interval itself spans conf.low to conf.high
conf.low: lower bound for the effect size estimate
conf.high: upper bound for the effect size estimate
conf.method: method used to compute the confidence/credible interval
conf.distribution: statistical distribution for the effect

Bayesian analysis (only when type = "bayes")

bf10: Bayes factor for the alternative hypothesis relative to the null
log_e_bf10: natural logarithm of the Bayes factor (present for most, but not all, Bayesian analyses)
prior.distribution, prior.scale, prior.location: prior specification used to compute the Bayes factor and posterior estimates

Pairwise comparisons (for pairwise_comparisons() and pairwise_contingency_table())

group1, group2: the two levels being compared
p.adjust.method: the adjustment method used for multiple comparisons
p.value.adj: the adjusted p-value; returned by pairwise_contingency_table(). Note that pairwise_comparisons() instead folds the adjusted value into p.value (and does not return a separate p.value.adj column)

Common columns

n.obs: number of observations
expression: a list-column of pre-formatted plotmath expressions; each element is a language object (not a character string) containing the statistical details, ready to be used in {ggplot2} (e.g. in labs() or annotate())

For a per-function, column-by-column breakdown of the output (and an explanation of the internal add_expression_col() engine that builds the expression column), see the Return value schema article. For more examples, see the data frame output vignette.

Contingency table analyses

The table below provides summary about:

statistical test carried out for inferential statistics
type of effect size estimate and a measure of uncertainty for this estimate
functions used internally to compute these details

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

Examples

#### -------------------- association test ------------------------ ####

# ------------------------ frequentist ---------------------------------

# unpaired

set.seed(123)
contingency_table(
  data = mtcars,
  x = am,
  y = vs,
  paired = FALSE
)
#> # A tibble: 1 × 13
#>   statistic    df p.value method                     effectsize        estimate
#>       <dbl> <int>   <dbl> <chr>                      <chr>                <dbl>
#> 1     0.907     1   0.341 Pearson's Chi-squared test Cramer's V (adj.)        0
#>   conf.level conf.low conf.high conf.method conf.distribution n.obs expression
#>        <dbl>    <dbl>     <dbl> <chr>       <chr>             <int> <list>    
#> 1       0.95        0     0.490 ncp         chisq                32 <language>

# paired

paired_data <- dplyr::tibble(
  response_before = structure(
    c(1L, 2L, 1L, 2L),
    levels = c("no", "yes"),
    class = "factor"
  ),
  response_after = structure(
    c(1L, 1L, 2L, 2L),
    levels = c("no", "yes"),
    class = "factor"
  ),
  Freq = c(65L, 25L, 5L, 5L)
)

set.seed(123)
contingency_table(
  data = paired_data,
  x = response_before,
  y = response_after,
  paired = TRUE,
  counts = Freq
)
#> # A tibble: 1 × 12
#>   statistic    df  p.value method                     effectsize estimate
#>       <dbl> <dbl>    <dbl> <chr>                      <chr>         <dbl>
#> 1      13.3     1 0.000261 McNemar's Chi-squared test Cohen's g     0.333
#>   conf.level conf.low conf.high conf.method n.obs expression
#>        <dbl>    <dbl>     <dbl> <chr>       <int> <list>    
#> 1       0.95    0.164     0.427 binomial      100 <language>

# ------------------------ Bayesian -------------------------------------

# unpaired

set.seed(123)
contingency_table(
  data = mtcars,
  x = am,
  y = vs,
  paired = FALSE,
  type = "bayes"
)
#> # A tibble: 1 × 15
#>   term  conf.level effectsize estimate conf.low conf.high
#>   <chr>      <dbl> <chr>         <dbl>    <dbl>     <dbl>
#> 1 Ratio       0.95 Cramers_v         0        0     0.421
#>   prior.distribution      prior.location prior.scale  bf10
#>   <chr>                            <dbl>       <dbl> <dbl>
#> 1 independent multinomial              0           1 0.643
#>   method                              conf.method log_e_bf10 n.obs expression
#>   <chr>                               <chr>            <dbl> <int> <list>    
#> 1 Bayesian contingency table analysis ETI             -0.442    32 <language>

# paired

set.seed(123)
contingency_table(
  data = paired_data,
  x = response_before,
  y = response_after,
  paired = TRUE,
  counts = Freq,
  type = "bayes"
)
#> # A tibble: 1 × 15
#>   term  conf.level effectsize estimate conf.low conf.high
#>   <chr>      <dbl> <chr>         <dbl>    <dbl>     <dbl>
#> 1 Ratio       0.95 Cramers_v     0.111        0     0.340
#>   prior.distribution      prior.location prior.scale  bf10
#>   <chr>                            <dbl>       <dbl> <dbl>
#> 1 independent multinomial              0           1 0.461
#>   method                              conf.method log_e_bf10 n.obs expression
#>   <chr>                               <chr>            <dbl> <int> <list>    
#> 1 Bayesian contingency table analysis ETI             -0.775   100 <language>

#### -------------------- goodness-of-fit test -------------------- ####

# ------------------------ frequentist ---------------------------------

set.seed(123)
contingency_table(
  data = as.data.frame(HairEyeColor),
  x = Eye,
  counts = Freq
)
#> # A tibble: 1 × 13
#>   statistic    df  p.value method                                   effectsize 
#>       <dbl> <dbl>    <dbl> <chr>                                    <chr>      
#> 1      133.     3 9.65e-29 Chi-squared test for given probabilities Pearson's C
#>   estimate conf.level conf.low conf.high conf.method conf.distribution n.obs
#>      <dbl>      <dbl>    <dbl>     <dbl> <chr>       <chr>             <int>
#> 1    0.429       0.95    0.364     0.483 ncp         chisq               592
#>   expression
#>   <list>    
#> 1 <language>

# ------------------------ Bayesian -------------------------------------

set.seed(123)
contingency_table(
  data = as.data.frame(HairEyeColor),
  x = Eye,
  counts = Freq,
  ratio = c(0.2, 0.2, 0.3, 0.3),
  type = "bayes"
)
#> # A tibble: 1 × 4
#>      bf10 prior.scale method                                      expression
#>     <dbl>       <dbl> <chr>                                       <list>    
#> 1 4.17e55           1 Bayesian one-way contingency table analysis <language>