What is the primary goal of a two-sample test?

To compare statistics between two different groups.

If your p-value is greater than your alpha level, what should you do?

Fail to reject the null hypothesis.

Two Sample Hypothesis Testing Cheat Sheet

This cheat sheet covers the process of conducting two-sample hypothesis tests to compare means or proportions between two groups. It outlines the steps, key formulas, and interpretation of results.

Core Principles

Two-sample tests compare statistics between two distinct groups.
The steps of hypothesis testing (assumptions, hypotheses, test statistic, comparison, conclusion) remain consistent.
Distinguish between testing for differences in means versus proportions.
Understand the concepts of Type I and Type II errors in hypothesis testing.
Significance tests help determine if observed differences are likely due to chance or a real effect.

Action Steps

Step 1: Confirm assumptions (random sampling, independent samples).
Step 2: State the null ($H_0$) and alternative ($H_A$) hypotheses.
Step 3: Calculate the appropriate test statistic (t-statistic for means, z-statistic for proportions).
Step 4: Compare the test statistic to the critical value or determine the p-value.
Step 5: Draw a conclusion: reject $H_0$ if the test statistic is extreme enough (or p-value < alpha), otherwise fail to reject $H_0$.

Formulas

For means: $t = \frac{(\bar{y}_1 - \bar{y}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_{y_1}^2}{n_1} + \frac{s_{y_2}^2}{n_2}}}$
Standard error of difference in means: $s_{\bar{y}_1-\bar{y}_2} = \sqrt{\frac{s_{y_1}^2}{n_1} + \frac{s_{y_2}^2}{n_2}}$
For proportions: $z = \frac{(p_1 - p_2) - (\pi_1 - \pi_2)}{\sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}}$
Standard error of difference in proportions: $s_{p_1-p_2} = \sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}$

Key Terms

Null Hypothesis ($H_0$): A statement of no effect or no difference between groups.
Alternative Hypothesis ($H_A$): A statement that there is an effect or difference.
Significance Level (alpha, $\alpha$): The probability of rejecting the null hypothesis when it is true (Type I error rate).
Test Statistic: A value calculated from sample data used to test a hypothesis.
Critical Value: The threshold value that determines whether to reject the null hypothesis.
p-value: The probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.
Type I Error: Rejecting a true null hypothesis (false positive).
Type II Error: Failing to reject a false null hypothesis (false negative).

Timeline

March 10, 2026: Lecture on Hypothesis Testing II: Two Sample Tests.
March 13: Sleep Log due.
March 17: Assignment 8 and Reading Report due.
March 31st: Final Test.

People

Instructor: Leads Sociology 222 course, covering 'Measuring the Social World'.

Quiz

What is the primary goal of a two-sample test?: To compare statistics between two different groups.
If your p-value is greater than your alpha level, what should you do?: Fail to reject the null hypothesis.