{PRDA} allows performing a prospective or retrospective design analysis to evaluate inferential risks (i.e., power, Type M error, and Type S error) in a study considering Pearson’s correlation between two variables or mean comparisons (one-sample, paired, two-sample, and Welch’s t-test).

For an introduction to design analysis and a general overview of the package see vignette("PRDA"). Examples for retrospective design analysis and prospective design analysis are provided in vignette("retrospective") and vignette("prospective") respectively.

All the documentation is available at https://claudiozandonella.github.io/PRDA/.

Installation

You can install the released version of PRDA from CRAN with:

install.packages("PRDA")

And the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("ClaudioZandonella/PRDA",
                         build_vignettes = TRUE)

The Package

{PRDA} package can be used for Pearson’s correlation between two variables or mean comparisons (i.e., one-sample, paired, two-sample, and Welch’s t-test) considering an hypothetical value of ρ or Cohen’s d respectively. See vignette("retrospective") and vignette("prospective") to know how to set function arguments for the different effect types.

Functions

In {PRDA} there are two main functions retrospective() and prospective().

• retrospective()

Given the hypothetical population effect size and the study sample size, the function retrospective() performs a retrospective design analysis. According to the defined alternative hypothesis and the significance level, the inferential risks (i.e., Power level, Type M error, and Type S error) are computed together with the critical effect value (i.e., the minimum absolute effect size value that would result significant).

Consider a study that evaluated the correlation between two variables with a sample of 30 subjects. Suppose that according to the literature the hypothesized effect is ρ = .25. To evaluate the inferential risks related to the study we use the function retrospective().

set.seed(2020) # set seed to make results reproducible
retrospective(effect_size = .25, sample_n1 = 30,
              test_method = "pearson")
#> 
#>  Design Analysis
#> 
#> Hypothesized effect:  rho = 0.25 
#> 
#> Study characteristics:
#>    test_method   sample_n1   sample_n2   alternative   sig_level   df
#>    pearson       30          NULL        two_sided     0.05        28
#> 
#> Inferential risks:
#>    power   typeM   typeS
#>    0.27    1.826   0.003
#> 
#> Critical value(s): rho  =  ± 0.361

In this case, the statistical power is almost 30% and the associated Type M error and Type S error are respectively around 1.80 and 0.003. That means, statistical significant results are on average an overestimation of 80% of the hypothesized population effect and there is a .3% probability of obtaining a statistically significant result in the opposite direction.

To know more about function arguments and further examples see the function documentation ?retrospective and vignette("retrospective").

• prospective()

Given the hypothetical population effect size and the required power level, the function prospective() performs a prospective design analysis. According to the defined alternative hypothesis and the significance level, the required sample size is computed together with the associated Type M error, Type S error, and the critical effect value (i.e., the minimum absolute effect size value that would result significant).

Consider a study that will evaluate the correlation between two variables. Knowing from the literature that we expect an effect size of ρ = .25, the function prospective() can be used to compute the required sample size to obtain a power of 80%.

prospective(effect_size = .25, power = .80, test_method = "pearson",
            display_message = FALSE)
#> 
#>  Design Analysis
#> 
#> Hypothesized effect:  rho = 0.25 
#> 
#> Study characteristics:
#>    test_method   sample_n1   sample_n2   alternative   sig_level   df 
#>    pearson       122         NULL        two_sided     0.05        120
#> 
#> Inferential risks:
#>    power   typeM   typeS
#>    0.797   1.119   0    
#> 
#> Critical value(s): rho  =  ± 0.178

The required sample size is