# February 7, 2024

library(tidyverse)
library(lmSupport)

# a concrete example of a three-group design

threeGroups <- tibble(group = factor(c(rep("image", 10), rep("rhyme", 10), rep("control", 10))),
                      memory = c(15, 16, 6,  7, 13, 10, 13, 9, 12, 19,
                                 16,  8, 5, 10,  9, 13, 16, 3,  8, 12,
                                 11,  4, 8,  2, 10,  6,  2, 5,  7, 5))

threeGroups %>% group_by(group) %>% summarise(M = mean(memory))

# dummy codes
threeGroups <- threeGroups %>% 
	mutate(D1 = case_when(group == "image" ~ 1,
												group == "rhyme" ~ 0,
												group == "control" ~ 0),
				 D2 = case_when(group == "image" ~ 0,
				 							 group == "rhyme" ~ 1,
				 							 group == "control" ~ 0))


# the dummy-code model
modelDummy <- lm(memory ~ D1 + D2, threeGroups)
summary(modelDummy)

# notice that if you use the existing factor (that is, "group") as a predictor,
# the results are the same as the dummy-coded model; R dummy codes factors by
# default
modelDefault <- lm(memory ~ group, threeGroups)
summary(modelDefault)
summary(modelDummy)

# notice further that REGARDLESS of whether you use contrast or dummy or some
# other coding scheme for groups, the "model F" (which has as its compact model
# an intercept-only model) is identical
summary(modelDummy)$fstatistic    # F = 6.29
summary(modelDefault)$fstatistic  # F = 6.29

# let's use some strange numbers for the groups
threeGroups <- threeGroups %>% 
	mutate(strange1 = case_when(group == "image" ~ 2,
															group == "rhyme" ~ 7,
															group == "control" ~ 1),
				 strange2 = case_when(group == "image" ~ 3,
				 										 group == "rhyme" ~ 11,
				 										 group == "control" ~ 4))

modelStrange <- lm(memory ~ strange1 + strange2, threeGroups)
summary(modelStrange)$fstatistic  # F = 6.29

# the pairwise.t.test function is handy for getting p-values, but useless for
# getting t and df values; let's do the latter first

summary(modelDummy) # t = 3.48 for  I vs C; t = 2.32 for for R vs C

# getting the third t-test takes two steps
threeGroups$group <- relevel(threeGroups$group, ref = "image") # changes the reference group

summary(lm(memory ~ group, threeGroups)) # t = 1.16 for R vs I

pairwise.t.test(x = threeGroups$memory,           # the DV
								g = threeGroups$group,            # IV
								p.adjust.method = "none")         # method of adjustment (see ?p.adjust)

pairwise.t.test(x = threeGroups$memory,           # the DV
								g = threeGroups$group,            # IV
								p.adjust.method = "bonferroni")   # method of adjustment (see ?p.adjust)