What is a hypothesis test?

A hypothesis test is a statistical method for making decisions about population parameters based on sample data. It involves setting up a null hypothesis (H₀) and an alternative hypothesis (Hₐ), then using sample data to determine whether there is sufficient evidence to reject the null hypothesis in favor of the alternative.

When should I use a t-test vs a z-test?

Use a t-test when the population standard deviation is unknown and must be estimated from sample data (most common). Use a z-test only when the population standard deviation is known, which is rare in practice. For large samples (n > 30), t-tests and z-tests give similar results.

What is a p-value and how do I interpret it?

A p-value is the probability of observing results as extreme as or more extreme than those in your sample, assuming the null hypothesis is true. A small p-value (typically < 0.05) suggests strong evidence against the null hypothesis, leading to its rejection. However, p-values should be interpreted in context with effect sizes and practical significance.

What is the difference between paired and two-sample t-tests?

A paired t-test is used when comparing two related measurements from the same subjects (e.g., before and after treatment). A two-sample t-test (like Welch's test) is used when comparing two independent groups. Paired tests are generally more powerful because they account for individual differences between subjects.

Hypothesis Tests

Perform t-tests, z-tests, and chi-square tests with comprehensive results, effect sizes, and assumption checking.

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