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Understanding t-Test for Independent Samples in Hypothesis Testing

This chapter introduces the t-test for two independent samples, explaining the hypothesis testing procedure, vocabulary, formulas, and examples. Learn when and how to use this test to compare population means, compute effect sizes, and make informed decisions based on statistical analysis.

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Understanding t-Test for Independent Samples in Hypothesis Testing

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  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?

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