EPS 625 – INTERMEDIATE STATISTICSONE-WAY ANALYSIS OF VARIANCE – EXAMPLE 1Use the ANOVA – Example 1 data from the Web site and the following scenario:You are to investigate whether students’ scores on a reading midterm examination differ as afunction of the method of direction/instruction they received. For this study, 45 students havebeen randomly selected to participate. The students were then randomly assigned to one of threetreatment groups – to make 15 members in each group. All three groups are given the samerequired readings, but class time was spent differently in each group. Group 1 (Discussion) spentclass time in directed discussions of the assigned readings. Group 2 (No Class) was excused fromany obligations to attend class for the first half of the semester, but its members were givenadditional text materials they could use to help them understand the assigned readings. Group 3(Lecture) was instructed using the professor’s ordinary lecture methods. For this exercise, use ana priori alpha level of significance of α = 0.05 for each statistical analysis necessary to answerthe following questions.1. What would the null hypothesis be for this study? Show/write the appropriate symbols orexpression in words.H0:2. What would the research/alternative hypothesis be for this study? Show/write the appropriatesymbols or expression in words.Ha:3. Prior to examining whether group means differ, you need to test the assumption underlyingthe one-way ANOVA.a. Was the assumption of independence met for these data? Indicate how you made this determination.b. Was the assumption of normality met for these data? Indicate how you made this determination (using an alpha level of .01 for the Shapiro-Wilks test).c. Was the assumption of homogeneity of variance met for these data? Indicate how you made this determination.4. The next question that needs to be answered is whether all of the groups are the same on theirreading midterm examination. This is answered by conducting a One-way Analysis ofVariance using method of direction/instruction (group) as the independent variable andstudents’ scores on a reading midterm examination (test) as the dependent variable. What isyour conclusion (at this point) from this analysis? Indicate how you came to your conclusion.ANOVA – EXAMPLE 1PAGE 25. Calculate the measure of association and interpret its meaning.6. Assuming that you found a significant F, how do the pairs of groups differ? Indicate whichpost hoc procedure you used and why. Indicate your findings from the post hoc analysis. Thatis, how did you determine the pair to be significant or not (this must go beyond the * as anindication)? Be sure to discuss all unique pairwise comparisons.7. Then for all significant pairwise comparisons, calculate and report the effect size.ANOVA – EXAMPLE 1PAGE 38. Complete the three tables below that present your statistical results from these analyses. Usethe values reported in the SPSS output – you do not need to round (Note that in reportingyour data, APA suggests being consistent in your reporting of values, e.g., all rounded to twoor three decimals).Table 1Means and Standard Deviations of Midterm Reading Examination Scores by Treatment GroupTreatment Group n Mean SDDiscussionNo ClassLectureTotalTable 2Analysis of Variance for Midterm Reading Examination Scores by Treatment GroupSource SS df MS F pBetweenWithinTotalTable 3Post Hoc Results for Midterm Reading Examination Scores by Treatment GroupTreatment Group MeanMean Differences (jiXX )(Effect Sizes are indicated in parentheses)1 2 31. Discussion 0.002. No Class 0.003. Lecture 0.00*Significant at α = 0.05, ** Significant at α = 0.01, *** Significant at α = 0.001ANOVA – EXAMPLE 1PAGE