{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/.

You can install the development version from GitHub with:

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

{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.

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")`

.

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")`

.

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.

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

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

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}
}
```

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.