ANOPA is a library to perform proportion analyses.
It is based on the F statistics (first developed by Fisher).
This statistics is fully additive and can be decomposed in
main effects and interaction effects, in simple effects in the
decomposition of a significant interaction, in contrasts, etc.
The present library performs these analyses and also can be used
to plan statistical power for the analysis of proportions, obtain
plots of the various effects, etc. It aims at replicating the most
commonly-used ANOVA commands so that using this package should be
easy.
The data supplied to an ANOPA can be in three formats: (i) long format, (ii) wide format, (iii) compiled format, or (iv) raw format. Check the 'anopa' commands for more precision (in what follow, we assume the compiled format where the proportions are given in a column name 'Freq')
The main function is
w <- anopa(formula, data)
where formula is a formula giving the factors, e.g., "Freq ~ A * B".
For more details on the underlying math, see Laurencelle and Cousineau (2023) .
An omnibus analysis may be followed by simple effects or contrasts analyses:
emProportions(w, formula)
contrast(w, listOfContrasts)
As usual, the output can be obtained with
print(w) #implicite
summary(w) # or summarize(w) for the G statistics table
explain(w) # for human-readable output
Data format can be converted to other format with
The package includes additional, helper, functions:
anopaPower2N() to compute sample size given effect size;
anopaN2Power() to compute statistical power given a sample size;
anopaProp2fsq() to compute the effect size;
anopaPlot() to obtain a plot of the proportions with error bars;
GRP() to generate random proportions from a given design.
and example datasets, some described in the article:
ArringtonEtAl2002 illustrates a 3 x 2 x 4 design;
ArticleExample1 illustrates a 4-way design;
ArticleExample2 illustrates a 2 x 3 design;
ArticleExample3 illustrates a (4) within-subject design;
The functions uses the following options:
ANOPA.feedback 'design', 'warnings', 'summary', 'all' or 'none';
ANOPA.zeros how are handled the zero trials to avoid 0 divided by 0 error;
ANOPA.digits for the number of digits displayed in the summary table.
ANOPA library for analyses of proportions using Anscombe transform
Laurencelle L, Cousineau D (2023). “Analysis of proportions using arcsine transform with any experimental design.” Frontiers in Psychology, 13, 1045436. doi:10.3389/fpsyg.2022.1045436 .
Useful links: