emProportions {ANOPA}

emProportions: simple effect analysis of proportions.

Description

The function 'emProportions()' performs a simple effect analyses of proportions after an omnibus analysis has been obtained with 'anopa()' according to the ANOPA framework. Alternatively, it is also called an expected marginal analysis of proportions. See Laurencelle and Cousineau (2023) for more.

Usage

emProportions(w, formula)

Arguments

w

An ANOPA object obtained from anopa();

formula

A formula which indicates what simple effect 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

emProportions() 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

An ANOPA table of the various simple main effets and if relevant, of the simple interaction effets.

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} ~ Difficulty * Class, 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 simple effect of Difficulty for every levels of Class
e <- emProportions(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 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 Trophism for every levels of Diel and Location
e <- emProportions(w, ~ Trophism | Diel )
summary(e)


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