{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.

## 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 n = 122, the associated Type M error is around 1.10 and the Type S error is approximately 0.

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

### Hypothetical effect size

The hypothetical population effect size can be defined as a single value according to previous results in the literature or experts indications. Alternatively, {PRDA} allows users to specify a distribution of plausible values to account for their uncertainty about the hypothetical population effect size. To know how to specify the hypothetical effect size according to a distribution and an example of application see vignette("retrospective").

## Contributing to PRDA

The PRDA package is still in the early stages of its life. Thus, surely there are many bugs to fix and features to propose. Anyone is welcome to contribute to the PRDA package.

Please note that this project is released under a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.

#### Bugs and New Features

To propose a new feature or to report a bug, please open an issue on GitHub. See Community guidelines.

#### Future Plans

• Improve compute time by parallelizing the code
• Implement design analysis in the case of linear regression models

## Citation

To cite {PRDA} in publications use:

Zandonella Callegher, C., Pastore, M., Andreella, A., Vesely, A., Toffalini, E., Bertoldo, G., & Altoè G. (2020). PRDA: Prospective and Retrospective Design Analysis (Version 1.0.0). Zenodo. https://doi.org/10.5281/zenodo.4044214

A BibTeX entry for LaTeX users is

@Misc{,
author       = {Zandonella Callegher, Claudio and Pastore, Massimiliano and Andreella, Angela and
Vesely, Anna and Toffalini, Enrico and Bertoldo, Giulia and Altoè, Gianmarco},
title        = {PRDA: Prospective and Retrospective Design
Analysis},
year         = 2020,
publisher    = {Zenodo},
version      = {1.0.0},
doi          = {10.5281/zenodo.4044214},
url          = {https://doi.org/10.5281/zenodo.4044214}
}

## References

Altoè, Gianmarco, Giulia Bertoldo, Claudio Zandonella Callegher, Enrico Toffalini, Antonio Calcagnì, Livio Finos, and Massimiliano Pastore. 2020. “Enhancing Statistical Inference in Psychological Research via Prospective and Retrospective Design Analysis.” Frontiers in Psychology 10. https://doi.org/10.3389/fpsyg.2019.02893.

Bertoldo, Giulia, Claudio Zandonella Callegher, and Gianmarco Altoè. 2020. “Designing Studies and Evaluating Research Results: Type M and Type S Errors for Pearson Correlation Coefficient.” Preprint. PsyArXiv. https://doi.org/10.31234/osf.io/q9f86.

Gelman, Andrew, and John Carlin. 2014. “Beyond Power Calculations: Assessing Type S (Sign) and Type M (Magnitude) Errors.” Perspectives on Psychological Science 9 (6): 641–51. https://doi.org/10.1177/1745691614551642.