Introduction
Hypothesis testing is a statistical method for making decisions about populations based on sample data.
T-Test
# One-sample t-test
t.test(x, mu = 0)
# Two-sample t-test
t.test(group1, group2)
# Paired t-test
t.test(before, after, paired = TRUE)
# With confidence interval
t.test(x, mu = 0, conf.level = 0.95)
Chi-Square Test
# Chi-square test of independence
chisq.test(matrix(c(10, 20, 30, 40), nrow = 2))
# Chi-square goodness of fit
chisq.test(c(10, 20, 30), p = c(1/3, 1/3, 1/3))
ANOVA
# One-way ANOVA
anova(lm(value ~ group, data = df))
# Or using aov
aov(value ~ group, data = df)
# Two-way ANOVA
aov(value ~ factor1 + factor2, data = df)
Interpretation
# Extract results
result <- t.test(x, mu = 0)
result$statistic # t-value
result$p.value # p-value
result$conf.int # Confidence interval
result$estimate # Sample mean
Summary
Hypothesis testing determines if results are statistically significant. Interpret p-values carefully.