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

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

Learning Objectives o Know when to use the t test for two independent samples for hypothesis testing with underlying assumptions o Compute t for independent samples to test hypotheses about the mean difference between two populations (or between two treatment conditions) o Evaluate the magnitude of the difference by calculating effect size with Cohen’s d or r 2

Introducing the t test for two independent samples o Allows researchers to evaluate the difference between two population means using data from two separate samples o Independent samples o Between two distinct populations (men vs. women) o Between two treatment conditions (distraction v. non- distraction) o No knowledge of the parameters of the populations (μ and σ 2 )

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

Discuss hypothesis testing procedure 1. State hypotheses and select a value for α o Null hypothesis always state a specific value for μ 2. Locate a critical region (sketch it out) o Add the df from each sample and use the t distribution table 3. Compute the test statistic o Same structure as single sample but now we have two of everything 4. Make a decision o Reject or “fail to reject” null hypothesis

The t Test formula o Difference in the means over the standard error One Sample Two Samples

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

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

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

Magnitude of difference by computing effect size o Two methods for computing effect size o Cohen’s d o r 2

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

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