# January 31, 2024

library(tidyverse)

d <- tibble(group = factor(c(rep("exercise", 16), rep("control", 16))),
						stride = c(24, 25, 22, 24, 26, 17, 21, 22, 
											 22, 19, 24, 23, 23, 28, 25, 23,
											 26, 23, 20, 23, 20, 16, 21, 17,
											 18, 23, 16, 20, 25, 19, 17, 16))

d %>% group_by(group) %>% summarise(mean(stride))

# try +1/2 and -1/2
d <- d %>%
	mutate(groupHalfs = ifelse(group == "exercise", 0.5, -0.5))

modelBest <- lm(stride ~ groupHalfs, d)
modelSummary(modelBest)

ggplot(d, aes(groupHalfs, stride)) +
	geom_point() +
	geom_jitter(width = 0.1) +
	geom_smooth(method = "lm", se = F) +
	xlim(-1, 1) +
	geom_point(aes(x = -0.5, y = 20), color = "red", size = 5) +
	geom_point(aes(x = 0.5, y = 23), color = "red", size = 5) +
	geom_vline(xintercept = 0)

# try dummy coding (setting the control group to 0)
d <- d %>%
	mutate(groupDummy = ifelse(group == "control", 0, 1))

modelDummy <- lm(stride ~ groupDummy, d)
modelSummary(modelDummy)

ggplot(d, aes(groupDummy, stride)) +
	geom_point() +
	geom_jitter(width = 0.1) +
	geom_smooth(method = "lm", se = F) +
	xlim(-1, 2) +
	geom_point(aes(x = 0, y = 20), color = "red", size = 5) +
	geom_point(aes(x = 1, y = 23), color = "red", size = 5) +
	geom_vline(xintercept = 0)


# stuff need for laborious calculation of CI

# F-crit for 1, 30 df
Fcrit <- qf(p = .95, df1 = 1, df2 = 30)

# variance of X
varX <- var(d$groupHalfs)
var(d$groupDummy) # hey, it's the same; ponder why this is!

# CI half-width
CIhalf <- sqrt((Fcrit*8.8)/(31*varX))

# easier!
confint(modelBest)

# pooled variance

var1 <- var(d$stride[d$group == "exercise"])
var2 <- var(d$stride[d$group == "control"])

s2p <- (15*10.6667 + 15*6.9333) / 30
s2p_better <- (15*var1 + 15*var2) / 30

# SE of the difference between two independent means

SE <- sqrt(s2p/16 + s2p/16)

# t statistic

t <- (23 - 20)/SE

# more quickly!
t.test(stride ~ group, data = d, var.equal = T)

# Cohen's d
(23 - 20)/sqrt(s2p)

# a three-group design
threeGroups <- tibble(Y = c(2, 4, 6, 8, 10,
														5, 6, 8, 10, 11,
														10, 13, 14, 15, 18),
											group = factor(c(rep("group1", 5), 
																			 rep("group2", 5), 
																			 rep("group3", 5))))

# the case_when function will be introduced in drill next week; but it's very
# useful for assigning numerical values to a grouping variable with more than
# two levels ... but the syntax is tricky (I often forget commas or parentheses)
threeGroups <- threeGroups %>% 
	mutate(X = case_when(group == "group1" ~ 0,
											 group == "group2" ~ 1,
											 group == "group3" ~ 2))

ggplot(threeGroups, aes(X, Y)) +
	geom_point() +
	geom_smooth(method = "loess", se = F)