simulate_correlation(n = 100, r = 0.5, mean = 0, sd = 1, names = NULL, ...)

simulate_ttest(n = 100, d = 0.5, names = NULL, ...)

simulate_difference(n = 100, d = 0.5, names = NULL, ...)

# Correlation --------------------------------
data <- simulate_correlation(r = 0.5)
plot(data$V1, data$V2)
cor.test(data$V1, data$V2)
summary(lm(V2 ~ V1, data = data))

# Specify mean and SD
data <- simulate_correlation(r = 0.5, n = 50, mean = c(0, 1), sd = c(0.7, 1.7))
cor.test(data$V1, data$V2)
round(c(mean(data$V1), sd(data$V1)), 1)
round(c(mean(data$V2), sd(data$V2)), 1)
summary(lm(V2 ~ V1, data = data))

# Generate multiple variables
cor_matrix <- matrix(c(
  1.0, 0.2, 0.4,
  0.2, 1.0, 0.3,
  0.4, 0.3, 1.0
),
nrow = 3
)

data <- simulate_correlation(r = cor_matrix, names = c("y", "x1", "x2"))
cor(data)
summary(lm(y ~ x1, data = data))

# t-test --------------------------------
data <- simulate_ttest(n = 30, d = 0.3)
plot(data$V1, data$V0)
round(c(mean(data$V1), sd(data$V1)), 1)
diff(t.test(data$V1 ~ data$V0)$estimate)
summary(lm(V1 ~ V0, data = data))
summary(glm(V0 ~ V1, data = data, family = "binomial"))

# Difference --------------------------------
data <- simulate_difference(n = 30, d = 0.3)
plot(data$V1, data$V0)
round(c(mean(data$V1), sd(data$V1)), 1)
diff(t.test(data$V1 ~ data$V0)$estimate)
summary(lm(V1 ~ V0, data = data))
summary(glm(V0 ~ V1, data = data, family = "binomial"))