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Two-Sample Comparison: A Classroom Activity Presented by Carol Kuper Jo Wilson Grace Zhang Learning Objectives Explain the importance of data accuracy Compare means of two independent groups using a t test. Explain the difference between onesample and two-sample comparisons Previous Statistical Knowledge Students have learned how to calculate the mean and standard deviation Students have learned about the tdistribution Students will have conducted a single sample t-test Background for Instructors Verbal Fluency—The ability to generate words rapidly Research has shown that women (girls) have higher verbal fluency than men (boys) Recent reference: Burton, L.A., Henninger, D., & Hafetz, J. (2005). Gender differences in relations of mental rotation, verbal fluency, and SAT scores to finger length ratios as hormonal indexes. Developmental Neuropsychology, 28, 493.505. Data Collection Procedure Before discussing the hypothesis, give the students 3 minutes to list things that are yellow on a sheet of paper. Ask the students to exchange papers with a neighbor and verify that all items are in fact yellow (instructor’s note: encourage class discussion about the integrity of the data). Have the students switch back and count the number of correctly identified items that are yellow. Hypothesis Formulation Define verbal fluency for the class, and discuss gender differences. Ask the class to formulate the null and alternative hypotheses. Hypothesis formulation usually comes before data collection, but the data will be biased if students know about gender differences related to verbal fluency. Data Analysis Procedure List data on the board under two columns male and female. (instructor’s note: be sure not to have the column headings on the board prior to data generation). Have students calculate the mean and standard deviation. Construct a histogram of the means for males and females. Calculate t-test statistic and complete hypothesis testing. Connecting Past to Present Knowledge. Discuss the difference between a onesample t-test and a two-sample t-test. One group vs. two groups The differences in stating the null hypotheses. Discuss data integrity and sampling problems. Checking data for accuracy Controlling for age and education level Follow up Paired t-test—May refer back to the independent sample design and emphasize the difference between independent and dependent samples. Regression—May use gender as an indicator variable. ANOVA—Compare a two-sample design to a multivariate or multisample design. Summary Data that have not been verified and checked will lack integrity and will lead to erroneous conclusions. When you have two independent samples, you can use a two-sample t test to test for differences between the means. For a one sample t test, the null hypothesis is µ = k. For a two sample t test, the null hypothesis is 1 2 . Assessment Two Sample Comparison Assessment