{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.

You can install the development version from GitHub with:

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

{PRDA} package can be used for Pearson’s correlation between two variables or mean comparisons (one-sample, paired, two-sample, and Welch’s t-test) considering a 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()`

.

retrospective(effect_size = .25, sample_n1 = 30, effect_type = "correlation", test_method = "pearson", seed = 2020) #> #> 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% of probability to obtain 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, effect_type = "correlation", test_method = "pearson", display_message = FALSE, seed = 2020) #> #> Design Analysis #> #> Hypothesized effect: rho = 0.25 #> #> Study characteristics: #> test_method sample_n1 sample_n2 alternative sig_level df #> pearson 126 NULL two_sided 0.05 124 #> #> Inferential risks: #> power typeM typeS #> 0.807 1.107 0 #> #> Critical value(s): rho = ± 0.175

The required sample size is *n* = 126, 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")`

.

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

To cite {PRDA} in publications use:

Claudio Zandonella Callegher, Massimiliano Pastore, Angela Andreella, Anna Vesely, Enrico Toffalini, Giulia Bertoldo, & Gianmarco Altoè. (2020). PRDA: Prospective and Retrospective Design Analysis (Version v0.1). Zenodo. http://doi.org/10.5281/zenodo.3630733

A BibTeX entry for LaTeX users is

```
@Misc{,
title = {{PRDA}: Prospective and Retrospective Design Analysis},
author = {Claudio {Zandonella Callegher} and Massimiliano Pastore and Angela Andreella and Anna Vesely and Enrico Toffalini and Giulia Bertoldo and Gianmarco Altoè},
year = {2020},
publisher = {Zenodo},
version = {v0.1},
doi = {10.5281/zenodo.3630733},
url = {https://doi.org/10.5281/zenodo.3630733},
}
```

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.