Statistics: Hypothesis Testing & p-Values
Statistics: Hypothesis Testing & p-Values
💡 Key Takeaways
- Formulate null and alternative hypotheses and choose the appropriate test statistic (e.g., z, t, chi-square) based on data and assumptions.
- Interpret the p-value correctly: quantify the probability of observing the data (or more extreme) under the null and compare it to your significance level.
- Differentiate one-tailed and two-tailed tests and know when to use each based on the research question and alternative hypothesis.
- Understand Type I and Type II errors, the concept of statistical power, and how sample size affects p-values and test conclusions.
❓ Frequently Asked Questions
What is the null hypothesis (H0) and the alternative hypothesis (H1) in hypothesis testing?
H0 states no effect or no difference (the status quo). H1 states there is an effect or a difference. We test H0 against H1 and reject H0 when the data are unlikely under H0.
What is a p-value and how is it used to decide whether to reject H0?
A p-value is the probability, under H0, of obtaining a test statistic as extreme as or more extreme than observed. If p ≤ α (the significance level), reject H0; otherwise, do not reject H0.
What is the difference between a one-tailed and a two-tailed test?
A one-tailed test checks for an effect in a specific direction (H1: μ > μ0 or μ < μ0). A two-tailed test checks for a difference in either direction (H1: μ ≠ μ0).
What are Type I and Type II errors, and how do α and β relate to them?
Type I error: reject H0 when H0 is true (false positive). Type II error: fail to reject H0 when H1 is true (false negative). α is the probability of a Type I error; β is the probability of a Type II error; power = 1 − β.