tTests.R

########################################
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# 
# Conducting t-tests in R
# 
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########################################
# One-sample t-tests
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set.seed(0)

# Say we're looking at tree volumes
# in a lumber shipment
treeVolume <- c(rnorm(75, mean = 36500, sd = 2000))

# one-sample t-test for equality of means
t.test(treeVolume, mu = 39000) # Ho: mu = 39000

# Visualize as a histogram
hist(treeVolume, freq = TRUE, density = 150, col = "dodgerblue4",
     border = "black", breaks = 15, 
     main = "Histogram of Douglas Fir Volumes",
     xlab = "Volume (cubic feet)", xlim = c(30000, 44000),
     ylim = c(0, 225))

segments(39000, 0, 39000, 225, lwd = 3,
         lty = 2)
text(41000, 190, "Population mean")
text(41000, 175, "volume")

segments(mean(treeVolume), 0, mean(treeVolume), 225,
         lwd = 3, lty = 2, col = "gray70")
text(33500, 190, "Sample mean volume", col = "gray35")


########################################
# Paired-samples t-test
########################################

set.seed(2820)

# Say we're looking at pre- and
# post-treatment systolic blood
# pressures for people taking
# a medication to manage
# hypertension
preTreat <- c(rnorm(1000, mean = 145, sd = 9))
postTreat <- c(rnorm(1000, mean = 138, sd = 8))

# Visualize the pre- and post-treat
# differences in distributions
x <- seq(from = 110, to = 174, by = 0.5)
y1 <- dnorm(x, mean = 145, sd = 9)
y2 <- dnorm(x, mean = 138, sd = 8)
plot(x, y1, type="l", lwd=2, col="red",
     main="Systolic Blood Pressure Before and After Treatment",
     xlab = "Systolic Blood Pressure (mmHg)",
     ylab = "Frequency", yaxt="n",
     xlim = c(110, 175), ylim = c(0, 0.05))
lines(x, y2)
polygon(c(110,x,175),c(0,y2,0), col="firebrick3", density = 100,
        border = "black")
polygon(c(117,x,175),c(0,y1,0), col="dodgerblue4", density = 100,
        border = "black")

ylab=c(seq(from=0, to=175, by=25))
y=c(seq(from=0, to=0.05, length.out = 8))
axis(2,at=y,labels=ylab)

text(x = 120, y = 0.045, "- Pre-Treatment BP", col = "dodgerblue4", cex = 0.9)
text(x = 120, y = 0.04, " - Post-Treatment BP", col = "firebrick3", cex = 0.9)
points(109, 0.0445, pch = 15, col = "dodgerblue4")
points(109, 0.0395, pch = 15, col = "firebrick3")

# Conduct a paired-samples t-test
t.test(preTreat, postTreat, paired = TRUE)


########################################
# Independent samples t-test
########################################

# Independent 2-group t-test
# where y1 and y2 are numeric
set.seed(0)
ClevelandSpending <- rnorm(50, mean = 250, sd = 75)
NYSpending <- rnorm(50, mean = 300, sd = 80)
t.test(ClevelandSpending, NYSpending, var.equal=TRUE)

# Independent 2-group t-test
# where y1 is numeric and y2 is binary
spending <- c(ClevelandSpending, NYSpending)
city <- c(rep("Cleveland", 50), rep("New York", 50))
t.test(spending~city, var.equal=TRUE)

# Independent 2-group t-test
# Equal variances not assumed
t.test(ClevelandSpending, NYSpending, var.equal=FALSE)