Random assignment is one of the more difficult concepts in introductory statistics classes. Many textbook authors admonish students to check on the comparability of two randomly assigned groups by conducting statistical tests on pretest means to determine if randomization worked. A Monte Carlo study was conducted on a sample of n = 2 per group, where each participant's personality profile was represented by 7,500 randomly selected and assigned scores. These values were obtained from real data sets from applied education and psychology research. Then, independent samples t-tests were conducted at the 0.01 alpha level on these scores. Results demonstrated that x-bar(1) does not equal x-bar(2) for only 33 out of 7,500 variables, indicating that random assignment was successful in equating the two groups on 7,467 variables, even with a sample size of n = 2. The students' focus is redirected from the ability of random assignment to create comparable groups to testing the claims of randomization schemes.
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The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education