posthocProportions: post-hoc analysis of proportions.
Source:R/ANOPA-posthocProportions.R
posthocProportions.RdThe 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 lc23b;textualANOPA for more.
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.
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
#> Class Difficulty success total
#> 1 First Easy 11 12
#> 2 First Moderate 9 12
#> 3 First Difficult 6 12
#> 4 Last Easy 10 12
#> 5 Last Moderate 8 12
#> 6 Last Difficult 3 12
# 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)
#> MS df F pvalue correction Fcorr pvalcorr
#> Class 0.032569 1 1.628455 0.201917 1.013889 1.606147 0.205034
#> Difficulty 0.136787 2 6.839333 0.001071 1.027778 6.654486 0.001288
#> Class:Difficulty 0.003660 2 0.183006 0.832763 1.243056 0.147223 0.863102
#> Error(between) 0.020000 Inf
# 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 )
#> Not yet programmed...
summary(e)
#> Length Class Mode
#> 0 NULL NULL
# -- 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
#> Location Trophism Diel s n
#> 1 Africa Detritivore Diurnal 16 217
#> 2 Africa Invertivore Diurnal 76 498
#> 3 Africa Invertivore Nocturnal 55 430
#> 4 Africa Omnivore Diurnal 2 87
#> 5 Africa Piscivore Diurnal 673 989
#> 6 Africa Piscivore Nocturnal 221 525
#> 7 Central/South America Detritivore Diurnal 68 1589
#> 8 Central/South America Detritivore Nocturnal 9 318
#> 9 Central/South America Invertivore Diurnal 706 7452
#> 10 Central/South America Invertivore Nocturnal 486 2101
#> 11 Central/South America Omnivore Diurnal 293 6496
#> 12 Central/South America Omnivore Nocturnal 82 203
#> 13 Central/South America Piscivore Diurnal 1275 5226
#> 14 Central/South America Piscivore Nocturnal 109 824
#> 15 North America Detritivore Diurnal 142 1741
#> 16 North America Invertivore Diurnal 525 3368
#> 17 North America Invertivore Nocturnal 231 1539
#> 18 North America Omnivore Diurnal 210 1843
#> 19 North America Omnivore Nocturnal 7 38
#> 20 North America Piscivore Diurnal 536 1289
#> 21 North America Piscivore Nocturnal 19 102
# first, we perform the omnibus analysis (mandatory):
w <- anopa( {s;n} ~ Location * Trophism * Diel, ArringtonEtAl2002)
#> ANOPA::fyi(1): Combination of cells missing. Adding:
#> Location Trophism Diel s n
#> Africa Detritivore Nocturnal 0 0
#> Africa Omnivore Nocturnal 0 0
#> North America Detritivore Nocturnal 0 0
#> Warning: ANOPA::warning(1): Some cells have zero over zero data. Imputing...
summary(w)
#> MS df F pvalue correction Fcorr
#> Location 0.027449 2 0.961802 0.382203 1.000112 0.961694
#> Trophism 0.095656 3 3.351781 0.018102 1.000115 3.351396
#> Diel 0.029715 1 1.041227 0.307536 1.000049 1.041176
#> Location:Trophism 0.029485 6 1.033146 0.401285 1.013842 1.019041
#> Location:Diel 0.005277 2 0.184900 0.831187 1.010164 0.183040
#> Trophism:Diel 0.073769 3 2.584868 0.051365 1.012197 2.553721
#> Location:Trophism:Diel 0.011297 6 0.395837 0.882184 1.055660 0.374967
#> Error(between) 0.028539 Inf
#> pvalcorr
#> Location 0.382245
#> Trophism 0.018111
#> Diel 0.307548
#> Location:Trophism 0.410515
#> Location:Diel 0.832735
#> Trophism:Diel 0.053559
#> Location:Trophism:Diel 0.895351
#> Error(between)
# 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 )
#> Not yet programmed...
summary(e)
#> Length Class Mode
#> 0 NULL NULL
# You can ask easier outputs with
summarize(w) # or summary(w) for the ANOPA table only
#> MS df F pvalue correction Fcorr
#> Location 0.027449 2 0.961802 0.382203 1.000112 0.961694
#> Trophism 0.095656 3 3.351781 0.018102 1.000115 3.351396
#> Diel 0.029715 1 1.041227 0.307536 1.000049 1.041176
#> Location:Trophism 0.029485 6 1.033146 0.401285 1.013842 1.019041
#> Location:Diel 0.005277 2 0.184900 0.831187 1.010164 0.183040
#> Trophism:Diel 0.073769 3 2.584868 0.051365 1.012197 2.553721
#> Location:Trophism:Diel 0.011297 6 0.395837 0.882184 1.055660 0.374967
#> Error(between) 0.028539 Inf
#> pvalcorr
#> Location 0.382245
#> Trophism 0.018111
#> Diel 0.307548
#> Location:Trophism 0.410515
#> Location:Diel 0.832735
#> Trophism:Diel 0.053559
#> Location:Trophism:Diel 0.895351
#> Error(between)
corrected(w) # or uncorrected(w) for an abbreviated ANOPA table
#> MS df F correction Fcorr pvalcorr
#> Location 0.027449 2 0.961802 1.000112 0.961694 0.382245
#> Trophism 0.095656 3 3.351781 1.000115 3.351396 0.018111
#> Diel 0.029715 1 1.041227 1.000049 1.041176 0.307548
#> Location:Trophism 0.029485 6 1.033146 1.013842 1.019041 0.410515
#> Location:Diel 0.005277 2 0.184900 1.010164 0.183040 0.832735
#> Trophism:Diel 0.073769 3 2.584868 1.012197 2.553721 0.053559
#> Location:Trophism:Diel 0.011297 6 0.395837 1.055660 0.374967 0.895351
#> Error(between) 0.028539 Inf
explain(w) # for a human-readable ouptut ((pending))
#> [1] "method explain not yet done..."