Question

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. The superintendent is continuing to examine the data that has been reported for the district. Another question concerned the differences in performance on high stakes tests. To examine this issue, the superintendent obtained the average scale scores for schools that participated in the high stakes testing for the district and two comparison districts. The following scores were collected: Superintendent’s district: 281 301 297 312 344 306 326 279 306 317 299 302 Comparison district 1: 328 290 302 275 293 291 289 286 288 291 291 310 Comparison district 2: 283 279 274 304 291 278 271 304 269 281 291 278 1. What is the mean scale score for each district? 2. What is the standard deviation of the scale scores for each district? 3. State an appropriate null hypothesis for this analysis. 4. What is the observed or computed value of F? 5. What are the reported degrees of freedom for the Between Groups variance? 6. What are the reported degrees of freedom for the Within Groups variance? 7. What is the reported level of significance? 8. Based on the results of the one-way ANOVA, would you accept or reject the null hypothesis? 9. Based on the results of the LSD post hoc test, identify which districts are significantly different. 10. 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. I also need to know how to enter it into the SPSS Calculator

Answer 1

Answwer:

Answers to question 1 and 2.

Variable District N N* Mn standard deviatio Test dist1 14 0 301.29 19.27 dist_2 14 0301.29 19.27 superi 140 314.71 18.02

3) Ans:

Null hypothesis: The mean scores between each district are same.

Alternative Hypothesis: At least one district has difference mean score.

4)

Tests of Between-Subjects Effects Dependent Variable:Test Type III Sum of Squares Sig Source Corrected Model Intercept District Error Total Corrected Total df Mean Square 841.524 2.365 107 1683.048 3926594.381 1683.048 13874.571 3942152.000 15557.619 1 3926594.381 11037.255 841.524 2.365 355.758 107 39 42

The observed or computed value of F is 2.365.

5) Ans: The reported degrees of freedom for the Between Groups variance is 3-1=2.

6) Ans: The reported degrees of freedom for the Within Groups variance is 39.

7) Ans: The reported level of significance is 0.05 (standard).

8) Ans: Based on the results of the one-way ANOVA, we should accept the null hypothesis. Because the estimated p-value is 0.107 and larger than 0.05 level of significance.

9)

Multiple Comparisons TestLSD Interval Mean Difference (I-J) pper BoundBound ower (I) District dist1 (J) District dist_2 superi dist 1 superi dist 1 dist 2 Std. Error Sig. 7.12900 7.12900 7.12900 7.12900 7.12900 7.12900 1.000 -14.4198 14.4198 9912 1.000 -14.4198 14.4198 9912 067.9912 27.8483 .9912 27.8483 -13.4286 067 -27.8483 dist 2 -13.4286 13.4286 13.4286 067 -27.8483 superi 067-.9

From 8 we know that there is no significant difference in mean scores. Hence, the LSD post hoc test can not identify which districts are significantly different at 0.05 level of significance.