Assignment 05_answers

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University of West Alabama *

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582

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Statistics

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Apr 3, 2024

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Assignment 5: Analysis of Variance and Post Hoc Tests Directions Using the information from the following scenario, conduct a one-way ANOVA and specify the LSD post hoc test. Remember: Round descriptive statistics to two decimal places. You should NOT round the test statistic or p-values. Scenario After seeing that students performed significantly higher on their tests after participating in the after-school tutoring pilot program, the superintendent decided to explore more options for the program. Because resources are scarce, the superintendent wants the tutoring program to be as efficient as possible and thus wants to see if the number of days a student participates in tutoring impacts scores. To determine this, he collects student score data from three different schools, each with a tutoring program that meets a different number of days a week. School A conducts tutoring 2 days per week, School B conducts tutoring 3 days per week, and School C conducts tutoring 4 days per week. Use the data below to help the superintendent determine whether or not there is a significant difference between the mean scores of the three groups. School A Test Scores (Tutoring 2 days/week) School B Test Scores (Tutoring 3 days/week) School C Test Scores (Tutoring 4 days/week) 115 116 120 103 101 113 88 103 106 96 104 100 111 116 120 70 109 110 91 101 115 94 103 110 100 90 120 82 110 90 112 120 120 106 104 115 100 102 119 Page 1 of 3

Questions 1. When is appropriate to use a One Way Analysis of Variance? (2 points) When comparing the means of three or more independent groups. 2. What is the mean score for each school? (3 points) School A- M=97.54 School B- M=106.08 School C- M=112.15 3. What is the standard deviation of the scores for each school? (3 points) School A- Sd=12.77 School B- Sd=8.00 School C- Sd=9.11 4. State an appropriate null hypothesis for this analysis. (1 point) Bonus (1 pt): State an appropriate research hypothesis for this analysis. Null hypothesis-There will be no statistically significant difference among the three school groups with respect to the number of tutoring days per week. Hypothesis-There will be a difference among the three school groups with respect to the number of tutoring days per week. 5. What is the observed or computed value of F? (1 point) F= 6.779 6. What are the reported degrees of freedom for the Between Groups variance? (1 point) df=2 7. What are the reported degrees of freedom for the Within Groups variance? (1 point) df=36 8. What is the reported level of significance? (1 point) p= .003 9. Based on the results of the one-way ANOVA, would you accept or reject the null hypothesis? Why? (1 point) No, reject the null hypothesis because .003 < .05. We have a significant difference. 10. Based on the results of the SNK post hoc test, identify which schools have scores that are significantly different. Justify your answer. (2 points) School A is different from School B and C. There is no significantly difference between School B and School C, but there is a significant difference between School A and School B and School C. School B and School C are in the same column meaning no significant difference between them. School A is in it’s own column because it is different then the other two schools. Page 2 of 3

11. Present the results as they might appear in an article. This must include a table and narrative statement that reports the results of the one-way ANOVA and LSD post hoc test. (4 points) The results of the one-way ANOVA indicated a statistically significant difference, F(2,36) = 6.779, p = .003, among the three schools with respect to the number of days for tutoring services in a week. The LSD post hoc tests showed that there was a statistically significant difference between School A (M = 97.54, SD = 12.77) and School B (M = 106.08, SD = 8.00). It also shows there is a significant difference between School A (M = 97.54, SD = 12.77) and School C (M= 112.15, SD= 9.11). It shows that there is not a significant difference between School B (M = 106.08, SD = 8.00) and School C (M= 112.15, SD= 9.11). Table 1 Analysis of Variance Results for Interpretation Anxiety Source df MS F p Between Groups 2 1.82 2.500 .086 Within Groups 117 .728 Note: The table must be created using your word processing program. Tables that are copied and pasted from SPSS are not acceptable. Remember, you can find an example of how to report the results of a One-way ANOVA in table and narrative format in the supporting materials folder for this lesson. Page 3 of 3

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