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### Nutrition example: Welch two-sample t-test in R ###
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# Read the two samples into R
xA = c(7.53, 7.48, 8.08, 8.09, 10.15, 8.4, 10.88, 6.13, 7.9)
xB = c(9.21, 11.51, 12.79, 11.85, 9.97, 8.79, 9.69, 9.68, 9.19)

# Perform Welch two-sample t-test
t.test(xB, xA)

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### Sleep medicine example: Paired t-test in R ###
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# Read the paired samples into R
x1 = c(.7,-1.6,-.2,-1.2,-1,3.4,3.7,.8,0,2)
x2 = c(1.9,.8,1.1,.1,-.1,4.4,5.5,1.6,4.6,3.4)

# Compute differences for the paired t-test
dif = x2 - x1

# Perform paired t-test
t.test(dif)

# Another way to perform the paired t-test
t.test(x2, x1, paired = TRUE)

# Normal Q-Q plots separately for each sample
qqnorm(xA, main = "Hospital A")
qqline(xA)
qqnorm(xB, main = "Hospital B")
qqline(xB)

# Multiple (simulated) Q-Q plots and sample A
require(MESS)
fitA <- lm(xA ~ 1)
qqnorm.wally <- function(x, y, ...) { qqnorm(y, ...); qqline(y, ...)}
wallyplot(fitA, FUN = qqnorm.wally, main = "")

# Multiple (simulated) Q-Q plots and sample B
fitB <- lm(xB ~ 1)
qqnorm.wally <- function(x, y, ...) { qqnorm(y, ...); qqline(y, ...)}
wallyplot(fitB, FUN = qqnorm.wally, main = "")

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### Example: Power-related calculations for t-tests ###
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# Power calculation (one-sample)
power.t.test(n = 40, delta = 4, sd = 12.21, type = "one.sample")

# Sample size calculation (one-sample)
power.t.test(power = .80, delta = 4, sd = 12.21, type = "one.sample")

# Power calculation (two-sample)
power.t.test(n = 10, delta = 2, sd = 1, sig.level = 0.05)

# Sample size calculation (two-sample)
power.t.test(power = 0.90, delta = 2, sd = 1, sig.level = 0.05)

# Detectable effect size (two-sample)
power.t.test(power = 0.90, n = 10, sd = 1, sig.level = 0.05)