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 one- sample and two-sample comparisons

Previous Statistical Knowledge  Students have learned how to calculate the mean and standard deviation  Students have learned about the t- distribution  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,

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 one- sample 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.  Assessment Two Sample Comparison Assessment