# factorial ANOVA/multiple categorical predictors

library(tidyverse)
library(lmSupport)

# read in data, explore its structure
eysenck <- read.csv("http://whlevine.hosted.uark.edu/psyc5143/eysenck.csv")
glimpse(eysenck)
head(eysenck, 20)
str(eysenck)

# factorize variables, provide labels for levels
eysenck$ageF <- factor(eysenck$age, labels = c("young", "old"))
eysenck$processF <- factor(eysenck$process, labels = c("shallow", "deep"))

glimpse(eysenck)
head(eysenck, 20)

# always check your work
table(eysenck$ageF, eysenck$age)
table(eysenck$process, eysenck$processF)
table(eysenck$ageF, eysenck$processF)

# summary data for cells
aggregate(data = eysenck, recall ~ age*process, mean)
aggregate(data = eysenck, recall ~ age*process, sd)

# summary data for age effect
aggregate(data = eysenck, recall ~ ageF, mean)

# summary data for processing effect
aggregate(data = eysenck, recall ~ processF, mean)

# another quick-and-easy way to explore the data (not very visually-pleasing,
# but easy!)
interaction.plot(x.factor = eysenck$ageF,            # x-axis factor
                 trace.factor = eysenck$processF,    # the other factor
                 response = eysenck$recall)          # the DV

# the ANOVA table using the aov function (OG ANOVA)
summary(aov(recall ~ ageF*processF, eysenck))

# exploring the default coding that R gives to factors
contrasts(eysenck$ageF)
contrasts(eysenck$processF)

# create contrast codes (no worries about orthogonality with only two levels)
eysenck <- eysenck %>% 
	mutate(age.contrast = ifelse(ageF == "young", 0.5, -0.5),
				 process.contrast = ifelse(processF == "deep", 0.5, -0.5))

# fit the model
model.contrasts <- lm(recall ~ age.contrast * process.contrast, eysenck)

# the summary
summary(model.contrasts)

# for comparison, back to the ANOVA
summary(aov(recall ~ ageF*processF, eysenck)) # t^2 = F, p is the same, df is the same, etc.

# testing simple effects (the effect of each factor at one level of the other)

# requires dummy coding
eysenck <- eysenck %>% 
	mutate(age.young.dummy = ifelse(ageF == "young", 0, 1),
				 age.old.dummy = ifelse(ageF == "old", 0, 1),
				 process.shallow.dummy = ifelse(processF == "shallow", 0, 1),
				 process.deep.dummy = ifelse(processF == "deep", 0, 1))

# reminder of cell means
aggregate(data = eysenck, recall ~ ageF*processF, mean)
aggregate(data = eysenck, recall ~ ageF, mean)
aggregate(data = eysenck, recall ~ processF, mean)
# the simple effect/slope of age when doing deep processing
summary(lm(recall ~ age.contrast * process.deep.dummy,  eysenck))

# the simple effect/slope of age when doing shallow processing
summary(lm(recall ~ age.contrast * process.shallow.dummy, eysenck))

# the simple effect/slope of processing among the young
summary(lm(recall ~ process.contrast * age.young.dummy, eysenck))

# the simple effect/slope of processing among the old
summary(lm(recall ~ process.contrast * age.old.dummy, eysenck))