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# Factorial ANOVA of Instructional Approaches

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A school psychologist is asked to assess the effectiveness of three instructional approaches to teaching reading to second grade elementary school children. The different approaches are whole language, phonic, and blended instruction. The "Whole Language Approach" is a method of teaching children to read by recognizing words as whole pieces of language. The "phonics approach" teaches children to decode words by sounds, rather than recognizing whole words. And the "Blended Approach" incorporates elements of both the whole language and phonics.

A sample of 15 boys and 15 girls are randomly assigned to one of the three teaching instructional conditions. Therefore, five boys and five girls were randomly assigned to one of the three instructional conditions.

Following 10 weeks of daily reading instruction, all students were administered the Elementary Reading Test (ERT; Smith and Jones, 2007)). Therefore, in the present study Instructional Condition (i.e., approach to teaching reading) is the Independent Variable, Sex is a Subject Variable (and possible moderator variable) and ERT score is the Dependent variable.

Using the attached data file, conduct a 3 (Instructional Condition) x 2 (Sex) Factorial ANOVA to examine the main and interaction effects for Instructional Approach and Sex.

1) Describe the research question and the research design.
2) Create the Null and Alternative Hypotheses. Use statistical notation to state the main effects and see Warner p. 505 on how to state the interaction hypotheses.
3) Conduct the Factorial ANOVA, including. Levene's test, Simple Effects Analyses (the simple effect of instructional method for sex), Post Hoc Tests (Bonferroni). and Effect Size (Eta-Square)
4) Write a summary of the results including appropriate tables and figures.

Be sure first to conduct Levene's test for equality of variances, and report the findings (state whether the data meet the assumption of homogeneity of variances, be sure to present the appropriate statistics to support your conclusion.) Regardless of the results of the Levene test, continue with the remainder of the assignment. Then, be sure to interpret the main and interaction effect. You'll find that the interaction of Sex x Instructional Condition is statistically significant, therefore you must conduct and interpret the findings for the Simple Effects Analyses - that is: a) The Simple Effect for Instructional Condition for Males, and b) the Simple Effects for Instructional Condition for females. If either of these simple effects are significant (and they will be) conduct Bonferroni's Post Hoc tests to determine within each Sex which means differ significantly. SPSS does not make obtaining the simple effects easy. The quickest way to obtain the simple effects is to do the General Linear Model univariate analysis and paste the syntax into file. Then add the following command to the syntax file. Make it the last line of the syntax before the period in the syntax file.

/EMMEANS=Tables(Sex*Approach) Compare(Approach).

The simple effects will provide, within each Sex which reading approach produces the best/worst outcomes. Be sure to report and interpret the effect sizes (Eta-Square (η2). Include the appropriate Tables and Figures (Graph) using APA style.