Week 6 Factorial ANOVA Problem.

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.

Here are the elements of this Assignment.

1) Create the Null and Alternative Hypotheses. See my examples;

2) 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)

3) Write an APA formatted Summary of the Results. The first thing that you should do is conduct Levene’s test for equality of variances, and report the findings (state whether the data meets the assumption of homogeneity of variances, be sure to present the appropriate statistics to support your conclusion.). 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. That is, 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 Figure (Graph) – See my sample summary). Please keep in mind that you must fully explain the results. I’ve provided a sample summary to show you what to include in the summary, how to present the statistics in the summary, tables, and figure (graph). Model your summaries after mine.

PS: The following Syntax will produce all of the statistics required:

UNIANOVA ERT BY Sex Approach
/Method=SSTYPE(3)
/INTERCEPT=INCLUDE
/PLOT=PROFILE(Approach*Sex)
/EMMEANS=TABLES(Sex) COMPARE ADJ(BONFERRONI)
/EMMEANS=TABLES(Approach) COMPARE ADJ(BONFERRONI)
/EMMEANS=TABLES(Sex*Approach) COMPARE (Sex) ADJ(BONFERRONI)
/EMMEANS=TABLES(Sex*Approach) COMPARE (Approach) ADJ(BONFERRONI)
/PRINT=ETASQ HOMOGENEITY DESCRIPTIVE
/CRITERIA=ALPHA(.05)
/DESIGN=Sex Approach Sex*Approach.

SPSS Syntax for the 95% CIs

EXAMINE VARIABLES=ERT
/PLOT BOXPLOT STEMLEAF
/COMPARE GROUPS
/STATISTICS DESCRIPTIVES
/CINTERVAL 95
/MISSING LISTWISE
/NOTOTAL.