The library `ANOFA`

provides easy-to-use tools to analyze frequency data. It does so using the *Analysis of Frequency datA* (ANOFA) framework (the full reference Laurencelle & Cousineau, 2023). With this set of tools, you can examined if classification factors are non-equal (*have an effect*) and if their interactions (in case you have more than 1 factor) are significant. You can also examine simple effects (a.k.a. *expected marginal* analyses). Finally, you can assess differences based on orthogonal contrasts. ANOFA also comes with tools to make a plot of the frequencies along with 95% confidence intervals (these intervals are adjusted for pair- wise comparisons Cousineau, Goulet, & Harding, 2021); with tools to compute statistical power given some *a priori* expected frequencies or sample size to reach a certain statistical power. In sum, eveything you need to analyse frequencies!

The main function is `anofa()`

which provide an omnibus analysis of the frequencies for the factors given. For example, Light & Margolin (1971) explore frequencies for attending a certain type of higher education as a function of gender:

```
## G df Gcorrected pvalue etasq
## Total 266.889 9 NA NA NA
## vocation 215.016 4 214.668 0.0000 0.258428
## gender 1.986 1 1.985 0.1589 0.003209
## vocation:gender 49.887 4 49.555 0.0000 0.301949
```

A plot of the frequencies can be obtained easily with

Owing to the interaction, simple effects can be analyzed from the *expected marginal frequencies* with

```
## G df Gcorrected pvalue etasq
## gender | Secondary 0.00813 1 0.008124 1.0000 0.000066
## gender | Vocational 2.90893 1 2.906575 0.5736 0.010659
## gender | Teacher 3.38684 1 3.384098 0.4957 0.048118
## gender | Gymnasium 3.22145 1 3.218840 0.5219 0.057299
## gender | University 42.34782 1 42.313530 0.0000 0.289364
```

Follow-up functions includes contrasts examinations with `contrastFrequencies()’.

Power planning can be performed on frequencies using `anofaPower2N()`

or `anofaN2Power`

if you can determine theoretical frequencies.

Finally, `toRaw()`

, `toCompiled()`

, `toTabulated()`

, `toLong()`

and `toWide()`

can be used to present the frequency data in other formats.

Note that the package is named using UPPERCASE letters whereas the main function is in lowercase letters.

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

The development version 0.1.3 can be accessed through GitHub:

The library is loaded with

As seen, the library `ANOFA`

makes it easy to analyze frequency data. Its general philosophy is that of ANOFAs.

The complete documentation is available on this site.

A general introduction to the `ANOFA`

framework underlying this library can be found at *the Quantitative Methods for Psychology* 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 frequency tables: The ANOFA framework. *The Quantitative Methods for Psychology*, *19*, 173–193. https://doi.org/10.20982/tqmp.19.2.p173

Light, R. J., & Margolin, B. H. (1971). An analysis of variance for categorical data. *Journal of the American Statistical Association*, *66*, 534–544. https://doi.org/10.1080/01621459.1971.10482297