1 Assignment 7 FOUN 823 Directions: (1) Please email your assignment answers in an MS Word file to the instructor ( XXXXXXXXXX) by the designated deadline. No overdue assignment will be graded unless...

The assignment is five total ANOVA questions requiring SPSS due in three days.
For reference, I am attaching five documents:1) Assignment2) SPSS3) Class notes (mirror formatting of verbal conclusions)4+5) Two step-by-step SPSS files to detail expected operations.


1 Assignment 7 FOUN 823 Directions: (1) Please email your assignment answers in an MS Word file to the instructor (cyen@odu.edu) by the designated deadline. No overdue assignment will be graded unless a prior arrangement is made due to some extenuating circumstances. (2) For this assignment, please analyze the SPSS data file in the same assignment folder with within-subjects ANOVA to answer various assignment questions. (3) The alpha level (α) will be .05 for the hypothesis testing on this assignment. (4) No partial credits will be assigned to an incorrect verbal conclusion supported by the correct statistics or a correct verbal conclusion supported by the incorrect statistics. In addition, no partial credits will be assigned to an incorrect SPSS table. (5) Please contact me (cyen@odu.edu) for any questions regarding what you are required to do for this assignment. Don’t make your own assumption when an assignment question is unclear to you. 2 A researcher studied the change of the depressive symptoms over time among 30 patents. Please conduct a one-way within-subjects ANOVA on the depressive symptom data in the SPSS data file to answer the assignment questions: 1. According to the Mauchly’s test results, is the sphericity assumption violated? Please support your verbal conclusion with the relevant statistics in APA style. (1 Point) 2. What will be the sum of squares (SS) of Time variable? (1 Point) 3. What will be the sum of squares (SS) of Error? (1 Point) 4. Did patients’ depressive symptoms change over time? Given no violation of the sphericity assumption, please use the standard F test results to support you verbal conclusion. Given the violation of the sphericity assumption, please use the F tests with the Greenhouse-Geisser correction and the Huynh-Feldt correction to support your verbal conclusion (1 Point) 5. Please copy the Profile Plots graph from the SPSS outputs then paste it to your submitted assignment. (1 Point) Quantitative Method III 1 Within-Subjects (Repeated Measures) ANOVA FOUN 823 Cherng-Jyh Yen, Ph.D. 2 Within-Subjects (Repeated Measures) ANOVA • Within-Subjects ANOVA • Within-subjects independent variable • Same participants going through all levels of the within-subjects independent variable, such as treatment, time, and so forth • Repeated measures dependent variable • Same participants being measured on the same dependent variable at each level of the independent variable (repeated measures) • Main advantage over between-subjects ANOVA: Increased statistical power • Subjects serve as their own control • Remove the SS related to Subject from the error variance • Decomposition of SSTotal Between-subjects ANOVA: SSTotal = SSA + SSS/A Within-subjects ANOVA: SSTotal = SSA + (SSS + SSAxS); SSAxS as the error variance 3 Within-Subjects ANOVA • A Numerical Example Time 1 Time 2 Time 3 Time 4 Time 5 (Pretest 1) (Pretest 2) (Posttest 1) (Posttest 2) (Posttest 3) Subject 1 12 12 7 5 5 �̅�1. = 8.200 2 9 10 5 6 5 �̅�2. = 7.000 3 9 8 7 5 6 �̅�3. = 7.000 4 8 6 6 4 4 �̅�4. = 5.600 5 8 9 6 4 5 �̅�5. = 6.400 6 9 10 8 6 7 �̅�6. = 8.000 7 12 10 7 5 4 �̅�7. = 7.600 8 6 7 5 7 5 �̅�8. = 6.000 �̅�.1 = 9.125 �̅�.2 = 9.000 �̅�.3 = 6.375 �̅�.4 = 5.250 �̅�.5 = 5.125 �̅�T = 6.975 Within-subjects independent variable: Time Time 1: 1 week before the treatment Time 2: 1 hour before the treatment Time 3: 1 week after the treatment Time 4: 2 weeks after the treatment Time 5: 3 weeks after the treatment Repeated measures dependent variable: Symptom Severity Omnibus, unfocused research question related to the main effect of Time: Does depressive symptom severity change over time (i.e. differ over time points)? Focused research question related to the contrast of planned comparison: Does the average post-treatment depressive symptom severity differ from the average pre-treatment depressive symptom severity? 4 Within-Subjects ANOVA • Sphericity Assumption • Homogeneity of population variances and correlations of difference scores • Assumption violation → Incorrect observed p value → Incorrect decision of the null hypothesis → Incorrect verbal conclusion 5 Within-Subjects ANOVA • Mauchly’s test of sphericity assumption Observed p < →="" reject="" the="" null="" hypothesis="" of="" no="" violation="" of="" the="" sphericity="" assumption="" observed="" p=""> ? → Retain the null hypothesis of no violation of the sphericity assumption If ? = .05 Verbal Conclusion: The alpha level was set at .05. The results suggested the violation of the sphericity assumption, W (9) = .04, p = .043. Mauchly's Test of Sphericitya Measure: MEASURE_1 Within Subjects Effect Mauchly's W Approx. Chi-Square df Sig. Epsilonb Greenhouse- Geisser Huynh- Feldt Lower- bound Time .036 17.995 9 .043 .488 .674 .250 Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. a. Design: Intercept Within Subjects Design: Time b. May be used to adjust the degrees of freedom for the averaged tests of significance