Chapter 10 The t Test for Two Independent Samples

1. Chapter 10The t Test for Two Independent Samples PSY295 Spring 2003 Summerfelt

2. Overview • Introduce the t test for two independent samples • Discuss hypothesis testing procedure • Vocabulary lesson • New formulas • Examples

3. Learning Objectives • Know when to use the t test for two independent samples for hypothesis testing with underlying assumptions • Compute t for independent samples to test hypotheses about the mean difference between two populations (or between two treatment conditions) • Evaluate the magnitude of the difference by calculating effect size with Cohen’s d or r2

4. Introducing the t test for two independent samples • Allows researchers to evaluate the difference between two population means using data from two separate samples • Independent samples • Between two distinct populations (men vs. women) • Between two treatment conditions (distraction v. non-distraction) • No knowledge of the parameters of the populations (μ and σ2)

5. Vocabulary lesson • Independent measures/Between-subjects design • Design that uses separate sample for each condition • Repeated measures/Within-subjects design • Design that uses the same sample in each condition • Pooled variance (weighted mean of two sample variances) • Homogeneity of variance assumption

6. Discuss hypothesis testing procedure • State hypotheses and select a value for α • Null hypothesis always state a specific value for μ • Locate a critical region (sketch it out) • Add the df from each sample and use the t distribution table • Compute the test statistic • Same structure as single sample but now we have two of everything • Make a decision • Reject or “fail to reject” null hypothesis

7. The t Test formula • Difference in the means over the standard error One Sample Two Samples

8. Formula for the degrees of freedom in a t test for two independent samples

9. Estimating Population Variance • Need variance estimate to calculate the standard error • Since these variances are unknown, we must estimate them • Pooling the sample variances proves to be the best way • Add the sums of squares for each sample and divide by the sum of the df of each sample

10. Calculating the Standard Error for the t statistic • Using the pooled variance estimate in the original formula for standard error

11. Magnitude of difference by computing effect size • Two methods for computing effect size • Cohen’s d • r2

12. Example • Researcher wants to assess the difference in memory ability between alcoholics and non-drinkers • Sample of n=10 alcoholics, sample of n=10 non-drinkers • Each person given a memory test that provides a score • Alcoholics; mean=43, SS=400 • Non-Drinkers; mean=57, SS=410

13. Example, continued • What if the introduction read… • A researcher wants to assess the damage to memory that is caused by chronic alcoholism • Would that change the analysis?