The library `ANOPA`

provides easy-to-use tools to analyze proportions . With it, you can examine if proportions are significantly different (*show an effect*). In the case where there is more than one factor, you can also test if the interaction(s) are significant. You can also test simple effects (a.k.a. *expected marginal* analysis), as well as post-hoc tests (using Tukey’s *Honestly Significant Difference* test HSD). Finally, you can assess differences based on orthogonal contrasts. You can consult Laurencelle & Cousineau (2023) for details.

ANOPA also comes (a) with tools to make a plot of the proportions along with 95% confidence intervals [these intervals are adjusted for pair- wise comparisons; Cousineau, Goulet, & Harding (2021)]; (b) with tools to compute statistical power given some *a priori* expected proportions or sample size to reach a certain statistical power; (c) to generate random proportions if you wish to perform Monte Carlo simulations on proportions. In sum, eveything you need to analyse proportions!

The main function is `anopa()`

which returns an omnibus analysis of the proportions for the factors given. For example, if you have a data frame `ArticleExample2`

which contains a column called `s`

where the number of successes per group are stored, and a column called `n`

where the group sizes are stored, then the following performs an analysis of proportions as a function of the groups based on the columns `SES`

and `MofDiagnostic`

:

```
## MS df F pvalue correction Fcorr pvalcorr
## SES 0.022242 2 6.394845 0.001670 1.004652 6.365237 0.001720
## MofDiagnostic 0.001742 1 0.500966 0.479076 1.002248 0.499842 0.479569
## SES:MofDiagnostic 0.007443 2 2.140035 0.117651 1.040875 2.055997 0.127965
## Error(between) 0.003478 Inf
```

As the results suggest (consult the first three columns), there is a main effect of the factor SES (F(2, inf) = 6.395, p = .002). A plot of the proportions can be obtained easily with

`anopaPlot(w) `

or just the main effect figure with

`anopaPlot(w, ~ SES)`

If the interaction had been significant, simple effects can be analyzed from the *expected marginal frequencies* with `e <- emProportions(w, ~ SES | MofDiagnostic )`

.

Follow-up analyses include contrasts examinations with `contrastProportions()`

; finally, post-hoc pairwise comparisons can be obtained with `posthocProportions()`

.

Prior to running an experiment, you might consider some statistical power planning on proportions using `anopaPower2N()`

or `anopaN2Power()`

as long as you can anticipate the expected proportions. A convenient effect size, the f-square and eta-square can be obtained with `anopaPropTofsq()`

.

Finally, `toCompiled()`

, `toLong()`

and `toWide()`

can be used to present the proportion in other formats.

The official **CRAN** version can be installed with

```
install.packages("ANOPA")
library(ANOPA)
```

The development version 0.1.3 can be accessed through GitHub:

```
devtools::install_github("dcousin3/ANOPA")
library(ANOPA)
```

Note that the package `ANOPA`

is named using UPPERCASE letters whereas the main function `anopa()`

is written using lowercase letters.

The library is loaded with

As seen, the library `ANOPA`

makes it easy to analyze proportions using the same general vocabulary found in ANOVAs.

The complete documentation is available on this site.

A general introduction to the `ANOPA`

framework underlying this library can be found at Laurencelle & Cousineau (2023).

Cousineau, D., Goulet, M.-A., & Harding, B. (2021). Summary plots with adjusted error bars: The superb framework with an implementation in R. *Advances in Methods and Practices in Psychological Science*, *4*, 1–18. https://doi.org/10.1177/25152459211035109

Laurencelle, L., & Cousineau, D. (2023). Analysis of proportions using arcsine transform with any experimental design. *Frontiers in Psychology*, *13*, 1045436. https://doi.org/10.3389/fpsyg.2022.1045436