{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/PRDAbeta/.

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. .

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.
.

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.
.

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