posthocProportions: posthocProportions: post-hoc analysis of proportions.

In ANOPA: Analyses of Proportions using Anscombe Transform

posthocProportions: post-hoc analysis of proportions.

Description

The function posthocProportions() performs post-hoc analyses of proportions after an omnibus analysis has been obtained with 'anopa()' according to the ANOPA framework. It is based on the tukey HSD test. See \insertCitelc23b;textualANOPA for more.

Usage

posthocProportions(w, formula)

Arguments

w	An ANOPA object obtained from anopa();
formula	A formula which indicates what post-hocs to analyze. only one simple effect formula at a time can be analyzed. The formula is given using a vertical bar, e.g., " ~ factorA | factorB " to obtain the effect of Factor A within every level of the Factor B.

Details

posthocProportions() computes expected marginal proportions and analyzes the hypothesis of equal proportion. The sum of the F of the simple effects are equal to the interaction and main effect F, as this is an additive decomposition of the effects.

Value

a model fit of the simple effect.

References

\insertAllCited

Examples

# -- FIRST EXAMPLE --
# This is a basic example using a two-factors design with the factors between 
# subjects. Ficticious data present the number of success according
# to Class (three levels) and Difficulty (two levels) for 6 possible cells
# and 72 observations in total (equal cell sizes of 12 participants in each group).
twoWayExample

# As seen the data are provided in a compiled format (one line per group).
# Performs the omnibus analysis first (mandatory):
w <- anopa( {success;total} ~ Class * Difficulty, twoWayExample) 
summary(w)

# The results shows an important interaction. You can visualize the data
# using anopaPlot:
anopaPlot(w)
# The interaction is overadditive, with a small differences between Difficulty
# levels in the first class, but important differences between Difficulty for 
# the last class.

# Let's execute the post-hoc tests
e <- posthocProportions(w, ~ Difficulty | Class )
summary(e)


# -- SECOND EXAMPLE --
# Example using the Arrington et al. (2002) data, a 3 x 4 x 2 design involving 
# Location (3 levels), Trophism (4 levels) and Diel (2 levels), all between subject.
ArringtonEtAl2002

# first, we perform the omnibus analysis (mandatory):
w <- anopa( {s;n} ~ Location * Trophism * Diel, ArringtonEtAl2002) 
summary(w)

# There is a near-significant interaction of Trophism * Diel (if we consider
# the unadjusted p value, but you really should consider the adjusted p value...).
# If you generate the plot of the four factors, we don't see much:
# anopaPlot(w)
#... but with a plot specifically of the interaction helps:
anopaPlot(w, ~ Trophism * Diel )
# it seems that the most important difference is for omnivorous fishes
# (keep in mind that there were missing cells that were imputed but there does not
# exist to our knowledge agreed-upon common practices on how to impute proportions...
# Are you looking for a thesis topic?).

# Let's analyse the simple effect of Tropism for every levels of Diel and Location
e <- posthocProportions(w, ~ Tropism | Diel )
summary(e)


# You can ask easier outputs with
summarize(w) # or summary(w) for the ANOPA table only
corrected(w)   # or uncorrected(w) for an abbreviated ANOPA table
explain(w)   # for a human-readable ouptut ((pending))

ANOPA documentation built on Aug. 19, 2025, 1:11 a.m.