Directions:
1. The α level for all the significance tests on this exam will be .05.
2. Please use the SPSS data file in the same exam folder for this assignment.
3. No partial credit will be assigned for a correct verbal conclusion supported by incorrect statistics or an incorrect verbal conclusion supported by correct statistics.
4. Please don’t submit all your SPSS outputs to the instructor and expect him to find the relevant statistics for you.
5. Please submit your answers by the designated deadline. An overdue problem will be assigned 0 point.
A researcher intended to investigate if student midterm exam grades on a 0 - 30 scale would differ across weekly tutoring time in hours (i.e., 0, 1, 2, 3, & 4) in an intermediate statistics course. The omnibus research question was formulated as:
Will average midterm exam grades in an intermediate statistics course differ across weekly tutoring time? Or, equivalently, is weekly tutoring time related to midterm exam grade in an intermediate statistics course?
Due to consideration of the fairness issue, the researcher did not randomly assign students to groups of different weekly tutoring time. Instead, students voluntarily chose to receive tutoring in various hours each week. That is, students self-selected themselves into one of the following 5 weekly tutoring hour groups: (1) 0-hour group (Group 1)
(2) 1-hour group (Group 2)
(3) 2-hour group (Group 3)
(4) 3-hour group (Group 4)
(5) 4-hour group (Group 5)
Please conduct the one-way ANOVA with the SPSS to answer the following questions:
(a) Is the assumption of homogeneity of variances violated? Please supported your verbal conclusion with the Levene’s test results in APA style? (3 points)
(b) What is your conclusion regarding the omnibus research question? Due to the use of a nonexperimental design, don’t try to make a causal inference from the results. Given no violation of the homogeneity of variances assumption, please use the Fisher’s F test results in APA style to support your verbal conclusion. Given the violation of the homogeneity of variances assumption, please make an informed decision of the research questions based on the results of the Brown-Forsythe test and the Welch test. (3 points)
Based on the literature review, the researcher also formed two focused research questions:
i. Will midterm exam grades differ between no weekly tutoring time (i.e., Group 1) and at least some weekly tutoring time (i.e., Group 2, Group 3, Group 4, & Group 5 together) in an intermediate statistics course?
ii. Will midterm exam grades differ between short weekly tutoring time (i.e., Group 2) and long weekly tutoring time (i.e., Group 5) in an intermediate statistics course?
Please conduct the planned comparisons with the SPSS to address the above two focused research questions then answer the following questions:
(a) What will be the null hypothesis for the first focused research question? (3 points)
(b) What will be the null hypothesis for the second focused research question? (3 points)
(c) What is your verbal conclusion for the first focused research question supported by the relevant F test results and the effect size index (η2) in APA style? (3 points)
(d) What is your verbal conclusion for the second focused research question supported by the relevant F test results and the effect size index (η2) in APA style? (3 points)