emFrequencies {ANOFA}

emFrequencies: simple effect analysis of frequency data.

Description

The function emFrequencies() performs a simple effect analyses of frequencies after an omnibus analysis has been obtained with anofa() according to the ANOFA framework. See Laurencelle and Cousineau (2023) for more.

Usage

emFrequencies(w, formula)

Arguments

w

An ANOFA object obtained from anofa();

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

emFrequencies computes expected marginal frequencies and analyze the hypothesis of equal frequencies. The sum of the Gs of the simple effects are equal to the interaction and main effect Gs, 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

# Basic example using a two-factors design with the data in compiled format. 
# Ficticious data present frequency of observation classified according
# to Intensity (three levels) and Pitch (two levels) for 6 possible cells.
minimalExample

# performs the omnibus analysis first (mandatory):
w <- anofa(Frequency ~ Intensity * Pitch, minimalExample) 
summary(w)

# execute the simple effect of Pitch for every levels of Intensity
e <- emFrequencies(w, ~ Pitch | Intensity)
summary(e)

# As a check, you can verify that the Gs are decomposed additively
sum(e$results[,1])
w$results[3,1]+w$results[4,1] 

# Real-data example using a two-factor design with the data in compiled format:
LandisBarrettGalvin2013

w <- anofa( obsfreq ~ provider * program, LandisBarrettGalvin2013)
anofaPlot(w)
summary(w)

# there is an interaction, so look for simple effects
e <- emFrequencies(w, ~ program | provider )
summary(e)

# Example from Gillet1993 : 3 factors for appletrees 
Gillet1993

w <- anofa( Freq ~ species * location * florished, Gillet1993)
e <- emFrequencies(w, ~ florished | location )

# Again, as a check, you can verify that the Gs are decomposed additively
w$results[4,1]+w$results[7,1] # B + B:C
sum(e$results[,1])

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