Introduction to Hypothesis Testing

Hypothesis testing is a statistical method to determine whether there is enough evidence to reject a null hypothesis.

Null and Alternative Hypothesis

In hypothesis testing:

• The null hypothesis (H₀) assumes no effect or difference.
• The alternative hypothesis (H₁) suggests an effect or difference.

Performing a t-Test

A t-test checks if two groups have significantly different means.

data1 <- c(5.1, 6.2, 5.8, 6.5, 5.9)
data2 <- c(7.0, 6.8, 7.5, 7.1, 6.9)
t.test(data1, data2)

Interpreting p-values

The p-value helps decide whether to reject H₀:

• If p-value < 0.05, reject H₀ (significant result).
• If p-value > 0.05, fail to reject H₀ (not significant).

Chi-Square Test

The chi-square test checks if categorical variables are independent.

observed <- matrix(c(20, 30, 50, 40), nrow=2)
chisq.test(observed)

ANOVA Test

ANOVA compares means across multiple groups.

group1 <- c(5.1, 6.2, 5.8)
group2 <- c(7.0, 6.8, 7.5)
group3 <- c(4.9, 5.5, 5.2)
data <- data.frame(value = c(group1, group2, group3), 
                   group = rep(c('A', 'B', 'C'), each=3))
aov_test <- aov(value ~ group, data = data)
summary(aov_test)

Effect Size

Effect size measures the strength of a result, helping determine practical significance.

Limitations of Hypothesis Testing

Hypothesis testing relies on assumptions and can be influenced by sample size and data quality.

Summary

In this lesson, you learned:

• How to perform hypothesis testing.
• How to use t-tests, chi-square, and ANOVA.
• The importance of p-values and effect sizes.