Overview
This lecture explains hypothesis testing in statistics, focusing on the difference between one-tailed and two-tailed tests using real-world traffic examples.
Hypothesis Testing Basics
- Hypothesis testing checks if data supports a specific idea (hypothesis) about reality.
- The null hypothesis (H₀) assumes no effect or no difference between groups.
- The alternative hypothesis (H₁) predicts a specific effect or difference.
Statistical Tails and Significance
- Tails of a distribution represent the extreme ends where rare or extreme values occur.
- The significance level (commonly 0.05) defines how much of each tail is in the "critical region" for rejecting H₀.
- A normal (bell-shaped) distribution allows use of standard hypothesis tests.
Two-Tailed Tests
- Used when looking for any difference between groups, regardless of direction.
- Critical regions are located in both tails of the distribution.
- If the test statistic falls in either tail's critical region, H₀ is rejected.
- Example: Joan compares traffic in two neighborhoods to see if there's any difference.
One-Tailed Tests
- Used when interested in a difference in a specific direction (e.g., more or less).
- The critical region is only in one tail, making the test more sensitive for effects in that direction.
- Example: Noah tests if traffic increased after building a park in a specific neighborhood.
Choosing the Right Test
- Decide on one- or two-tailed test before collecting or analyzing data.
- Switching from a two-tailed test to a one-tailed test after seeing results biases findings and is considered unethical.
- One-tailed tests have more power to detect effects in one direction but miss effects in the other.
Key Terms & Definitions
- Null Hypothesis (H₀) — the assumption that there is no effect or difference.
- Alternative Hypothesis (H₁) — the belief that there is an effect or difference.
- Significance Level (α) — the probability threshold (often 0.05) for rejecting H₀.
- Critical Region — part(s) of the distribution where, if the test statistic falls, H₀ is rejected.
- One-Tailed Test — checks for an effect in only one direction.
- Two-Tailed Test — checks for any difference, regardless of direction.
Action Items / Next Steps
- Review how to select between one-tailed and two-tailed tests for different scenarios.
- Practice setting null and alternative hypotheses for sample situations.
- Ensure ethical statistical testing by choosing the test type before analyzing data.