Parametric, non-parametric, robust, and Bayesian correlation test.

## Usage

corr_test(
data,
x,
y,
type = "parametric",
digits = 2L,
conf.level = 0.95,
tr = 0.2,
bf.prior = 0.707,
...
)

## 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 column in data containing the explanatory variable to be plotted on the x-axis.

y

The column in data containing the response (outcome) variable to be plotted on the y-axis.

type

A character specifying the type of statistical approach:

• "parametric"

• "nonparametric"

• "robust"

• "bayes"

You can specify just the initial letter.

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.

tr

Trim level for the mean when carrying out robust tests. In case of an error, try reducing the value of tr, which is by default set to 0.2. Lowering the value might help.

bf.prior

A number between 0.5 and 2 (default 0.707), the prior width to use in calculating Bayes factors and posterior estimates. In addition to numeric arguments, several named values are also recognized: "medium", "wide", and "ultrawide", corresponding to r scale values of 1/2, sqrt(2)/2, and 1, respectively. In case of an ANOVA, this value corresponds to scale for fixed effects.

...

## Value

The returned tibble data frame can contain some or all of the following columns (the exact columns will depend on the statistical test):

• 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

• estimate: estimated value of the effect size

• conf.low: lower bound for the effect size estimate

• conf.high: upper bound for the effect size estimate

• conf.level: width of the confidence interval

• conf.method: method used to compute confidence interval

• conf.distribution: statistical distribution for the effect

• effectsize: the name of the effect size

• n.obs: number of observations

• expression: pre-formatted expression containing statistical details

For examples, see data frame output vignette.

## Correlation 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

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()

## Examples

# for reproducibility
set.seed(123)

# ----------------------- parametric -----------------------

corr_test(mtcars, wt, mpg, type = "parametric")
#> # A tibble: 1 × 14
#>   parameter1 parameter2 effectsize          estimate conf.level conf.low
#>   <chr>      <chr>      <chr>                  <dbl>      <dbl>    <dbl>
#> 1 wt         mpg        Pearson correlation   -0.868       0.95   -0.934
#>   conf.high statistic df.error  p.value method              n.obs conf.method
#>       <dbl>     <dbl>    <int>    <dbl> <chr>               <int> <chr>
#> 1    -0.744     -9.56       30 1.29e-10 Pearson correlation    32 normal
#>   expression
#>   <list>
#> 1 <language>

# ----------------------- non-parametric -------------------

corr_test(mtcars, wt, mpg, type = "nonparametric")
#> # A tibble: 1 × 13
#>   parameter1 parameter2 effectsize           estimate conf.level conf.low
#>   <chr>      <chr>      <chr>                   <dbl>      <dbl>    <dbl>
#> 1 wt         mpg        Spearman correlation   -0.886       0.95   -0.945
#>   conf.high statistic  p.value method               n.obs conf.method expression
#>       <dbl>     <dbl>    <dbl> <chr>                <int> <chr>       <list>
#> 1    -0.774    10292. 1.49e-11 Spearman correlation    32 normal      <language>

# ----------------------- robust ---------------------------

corr_test(mtcars, wt, mpg, type = "robust")
#> # A tibble: 1 × 14
#>   parameter1 parameter2 effectsize                     estimate conf.level
#>   <chr>      <chr>      <chr>                             <dbl>      <dbl>
#> 1 wt         mpg        Winsorized Pearson correlation   -0.864       0.95
#>   conf.low conf.high statistic df.error  p.value method
#>      <dbl>     <dbl>     <dbl>    <int>    <dbl> <chr>
#> 1   -0.932    -0.738     -9.41       30 1.84e-10 Winsorized Pearson correlation
#>   n.obs conf.method expression
#>   <int> <chr>       <list>
#> 1    32 normal      <language>

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

corr_test(mtcars, wt, mpg, type = "bayes")
#> # A tibble: 1 × 17
#>   parameter1 parameter2 effectsize                   estimate conf.level
#>   <chr>      <chr>      <chr>                           <dbl>      <dbl>
#> 1 wt         mpg        Bayesian Pearson correlation   -0.843       0.95
#>   conf.low conf.high    pd rope.percentage prior.distribution prior.location
#>      <dbl>     <dbl> <dbl>           <dbl> <chr>                       <dbl>
#> 1   -0.934    -0.734     1               0 beta                         1.41
#>   prior.scale      bf10 method                       n.obs conf.method
#>         <dbl>     <dbl> <chr>                        <int> <chr>
#> 1        1.41 56223033. Bayesian Pearson correlation    32 HDI
#>   expression
#>   <list>
#> 1 <language>