Brief Description of Study.

In this study, the researchers were interested in the self-perceptions of scholastic competence for normal achieving children, low achieving children, and children with learning disabilities. The researchers examined 3 groups of children: (a) normally achieving children (NA group, coded as GROUP =1) composed of children whose reading and math scores on the Stanford Achievement Test were in the average range, (b) low achieving children (LA group, coded as GROUP =2) composed of children who scored at or below the 25 th percentile (below average range) in reading or math on the Stanford Achievement Test, and (c) children with learning disabilities (LD group, coded as GROUP =3) composed of children who had been identified as having learning disabilities by a multidisciplinary evaluation team and who had a significant discrepancy between IQ on the Wechsler Intelligence Scale for Children - Revised and Reading, Spelling, or Arithmetic subtest scores on the Wide Range Achievement Test.

The dependent variable was children's self-perception of scholastic competence as measured by the Scholastic Competence subscale of the Self-Perception Profile for Children (Harter, 1985). The subscale consists of six items. "The score for each item

can range from 0 (least favorable self-perception) to 5 (most favorable). Subscale scores are derived by averaging item scores in the respective domains" (p. 130). The Scholastic Competence subscale is used in this study.

The researchers provide a clear, specific, a priori hypotheses about student self-perceptions of scholastic competence: "We expected that self-perceptions of scholastic competence among children with LD and LA, because of their academic deficiencies, would be lower than those of NA children" (p. 127).

This study is cleverly extracted and barely adapted from a study by Clever, Bear, and Juvonen (1992). The actual data in this take home examination is fictitious and some aspects of the research have been modified to be consistent with our current level of skills. The data set is available as 'scholast12.dat' on Blackboard in course documents, Week 3, Take Home I.

If you experience any difficulty retrieving the data set, please contact me as soon as possible. Each line of the data file contains three numbers. The first number is a subject identification number, the second number is the subject's group coded as \(1=\) NA. \(2=\mathrm{LA}, 3=\mathrm{LD}\). The third number is the child's score on the Scholastic Competence subscale of the Self-Perception Profile for Children. Use the description of the study, the data file, and SPSS to answer the following questions.

Questions

1. A first step in analysis is to examine the data and determine if any distributional assumptions have been violated in a way that would compromise our findings and conclusions. Use SPSS to describe the distribution of scores overall and for each group.

1. Using the histograms and boxplots, describe the shape of the distribution of scores overall and for each group. Do you observe any problems with the distribution of scholastic competence scores that would compromise your conclusions in an Analysis of Variance? Identify, describe, and evaluate 3 essential assumptions. ( 3 points)
2. Summarize in an APA formatted table the sample size, center and variability of the distributions both overall and for each group. ( 5 points)

2. The researchers clearly have an a priori theoretical prediction about the pattern of group means that they expect to see. "We expected that self-perceptions of scholastic competence among children with $\mathrm{LD}$ and LA, because of their academic deficiencies, would be lower than those of NA children" Specify a planned comparison (or a priori contrast) that would represent the researchers prediction. You must report the set of contrast weights or specify the null hypothesis in sufficient detail to obtain contrast coefficients to answer this question. Do not test this prediction, just specify the contrast coefficients. (3 points)

3. No research project is completed until the papers are submitted. The researchers are interested in reporting achievement group effects on scholastic competence in a scholarly journal that uses APA style guidelines.

1. Specify a research question relevant to this study that addresses a relation between variables for a population. (2 points)
2. Describe your IV and DV providing the information a statistician and researcher would need to analyze and interpret the findings. ( 2 points)
3. Report the results of the analysis of variance as a summary table using APA format. The table must be neatly typewritten or word processed and follow all APA guidelines identified on the APA table checklist and in the APA publication manual. (6 points)
4. Write a short statement of your findings using APA style that would be appropriate for inclusion in a published article. The statement must be neatly typewritten or word processed and follow all APA guidelines identified on the APA statistics in text checklist and in the APA publication manual. Make sure your statement includes the name of the analysis you conducted, the name and description of variables, and statement of findings. (6 points)
5. How much of the variance in scholastic competence is explained by knowing student's achievement group? How would you interpret the percent of variance explained (i.e., is it small, moderate, large)? (3 points)

4. Flummox and Baffle (2006) replicated this study with the same groups of students (although they used a different sample of students in each group), but they used dummy coding and a set of indicator variables to represent the groups. They reported the following table of regression coefficients from their analysis:

Parameter Estimates

Dependent Variable: Comp

How does the mean of the LA group from your study compare to the mean of the LA group (Group 2) obtained by Flummox and Baffle (2006)? Make sure you show your work including the regression equation and the predicted mean obtained from Flummox and Baffle (2006). (3 points)

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