posthocProportions {ANOPA}

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 Laurencelle and Cousineau (2023) 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 $F$s of the simple effects are equal to the interaction and main effect $F$s, as this is an additive decomposition of the effects.

Value

a model fit of the simple effect.

References

Laurencelle L, Cousineau D (2023). “Analysis of frequency tables: The ANOFA framework.” The Quantitative Methods for Psychology, 19, 173–193. doi:10.20982/tqmp.19.2.p173.

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))