Self-Assessment Module 12




Introduction Instructions Resources Assessment 1. Algebraic Notation and Operations 2. Descriptive Statistics 3. Tabular Displays of Data 4. Graphical Displays of Data 5. Research Topics, Theory, Constructs, Questions, and Hypothesis 6. Research Designs 7. Measurement 8. Sampling 9. Probability 10. Basics of Inferential Statistics 11. One-Group Inferential Statistics 12. Two-Group Inferential Statistics 13. Critiquing Education and Social Science Research Answer Key		Module 12: Two-Group Inferential Statistics This section assesses skills in conducting and interpreting inferential statistical analysis for comparisons between two groups. These procedures are widely used in education and social science research, usually to address associational and causal questions. Answer all the questions in this section in respect the following fictitious situation: You randomly sample 72 students from a high school of 1,200 and randomly assign 36 to the school's normal mathematics instruction and 36 to a new artificial intelligence computerized tutorial system. Each group receives the same hours of instruction. At the end of the school year both groups are assessed with a well developed and widely used standardized test of mathematics and with several questions about students' interests in mathematics. The normal instruction group had a mean score of 60 and a variance of 25 on the math test; the computerized tutorial group had a mean score of 65 and a variance of 16. Question 1: What statistical test should be used to judge whether the computerized tutorial program is more effective in respect to the given math test than the normal instruction? A. Chi-Square test B. F-test C. t-test D. z-test E. None of the above Question 2: What assumptions of that test have to be met in order to be valid? A. The math scores should be approximately normally distributed B. The two groups should be approximately binomially distributed C. There should be approximate homogeneity of variance D. Both (A) and (C) E. Both (B) and (C) Question 3: Would the difference cited above be statistically significant at the .05 level using that test? A. Insufficient information is provided B. Yes, it would be significant C. It would be on the border of being significant D. No, it would not be significant at the .05 level E. None of the above Question 4: Approximately what would be the .95 confidence interval about the difference in the mean math scores? A. -30 to +21 B. -5 to + 5 C. 0 to +10 D. 5 to 10 E. None of the above Question 5: The students were asked to respond to several questions about their interests in mathematics, including: "Students who like math are mostly: smart cool nerds bad-looking." In response to that question, the frequency distribution of students in the traditional program was: 8 0 18 10, respectively. The distribution for the students using the computerized tutorial was: 12 10 8 6. What statistical test should be used to judge whether the responses for the computerized tutorial program differ from those of the normal instruction? A. Chi-Square test B. F-test C. t-test D. z-test E. None of the above Question 6: If, in the experiment described at the beginning of this module, the students were first matched into pairs based on their math skills, and then one from each pair was randomly assigned to the computerized tutorial and the remaining one assigned to the normal mathematics instruction, could the test of the effectiveness of the computerized tutorial be more powerful, equally powerful, or less powerful than if the experiment was conducted as originally described? A. Insufficient information for judging B. More C. Equally D. Less E. None of the above Question 7: What statistical test should be used to assess the association between the math scores and the perceptions indicated in Question 12-4? A. Chi-Square test B. F-test C. t-test D. z-test E. None of the above