This week's assignment requires you to complete a mixed design analysis. The data is a subset of a theoretical experiment in which the researcher hypothesized that engineering students would have a more developed sense of shape and symmetry than do psychology students. Three types of shapes were presented to samples of psychology and engineering students under sub-optimal viewing conditions on a monitor screen. All three shapes were presented to each subject and the order of presentation was counterbalanced. The dependent variable is the number of shapes correctly identified. See the unit 6 datafile for all the data needed for this activity.

Analysis Guidelines

Each week there will be a weekly assignment, not to be confused with the study assignments, which are more inclusive. The weekly assignment will require data analysis and interpretation. All weekly assignments are due by the end of the week on Sunday at 11:59 pm CST. For each assignment, any needed data will be provided and the required analysis will be described. Use a narrative format and organization for all weekly assignments.

The format of the data analysis and interpretation assignments should be narrative with supporting statistical output (table and graphs) integrated into the narrative in the appropriate place (not all at the end of the document).

SPSS output can be selectively copied and pasted into Word by using the Copy Objects command:

• Click on the SPSS object in the Viewer Window .
• Right click for options.
• Select the Copy Objects command.
• Paste into a Microsoft Word document.

The Copy Objects command will preserve the formatting of the SPSS tables and charts when pasting into Microsoft Word.

For the data analysis assignments, organize the narrative report with a section heading for each of the four sections described below. Label all tables and graphs in a manner consistent with APA style. Citations, if needed, should be included in the text and references included in a reference section at the end of the report. The organization of the report should include the following four sections:

Section I-Data File Description (one paragraph)

• The source of the database.
• Any history or "story" that provides context for the data.
• All variable(s) that are used in the analysis, including the measurement scale associated with each variable and any missing cases.
• The number of cases (sample size).
• The presumed population.
• Any other general information that describes the data file and variables.

Section II-Assumptions, Data Screening, and Verification of Assumptions(multiple paragraphs)

• Clearly identify and verify any assumptions and requirements underlying the use of each inferential statistical procedure.
• Systematically verify each assumption and requirement for the variables that will be used in the analysis.
• If an assumption or requirement cannot be verified with the given information, indicate what information would be needed to provide verification.
• If the assumption or requirement is not consistent with the variables in the data file, indicate what remediation might be undertaken to ameliorate the problem.
• Screen the data for out-of-bound values and outliers.

Section III-Inferential Procedure, Hypotheses, Alpha Level (one paragraph)

• State the alpha level (use .05 unless otherwise indicated).
• State the research question(s).
• State the statistical hypotheses, both null and alternative.
• Indicate what the calculated statistic will be that addresses each of the hypotheses.

Section IV-Interpretation (multiple paragraphs)

• Indicate the results and interpret the meaning of the results for each inferential analysis and do this specifically for the variables that are being analyzed.
• State your conclusions, as they relate directly to the research questions and hypotheses, based on the interpretation of the results.
• Indicate any limitations or constraints regarding these conclusions.

SPSS Hints

At this point in the course, you should be able to get SPSS to run the appropriate analyses without help, but here are a few tips:

• Select Analyze / GLM / Repeated Measures .
• The within-subjects factor will be identified as "shape" and it has three levels. Press Add .
• Then select Define and move these three within-subjects variables ( Triangle, Square, and Rectangle ) over from the left side box to the Within-Subjects Variables box.
• Move the remaining variable category (the between-subjects factor with two groups) over to the Between-Subjects Factors box.
• Select the Plots option, identify Category as the horizontal axis, and shape to separate lines.
• For post-hoc, select Category and Bonferonni.
• For options, select whatever marginal means you would like to see.

The format and organization of this model should be used for all subsequent data analysis assignments. See the Instructor's Expectations in the course syllabus for additional details. Please note that all tables and figures are clearly and appropriately identified.

Section I-Data file description

• The source of the database.
• Any history or "story" that provides context for the data.
• All variable(s) that are used in the analysis, including the measurement scale associated with each variable and any missing cases.
• The number of cases (sample size).
• The presumed population.
• Any other general information that describes the data file and variables.

The data file was provided by David Howell from a study that he initially conducted in 1965. Howell and Huessy (1985) published a long-term follow-up study with 386 children who were included in the original 1965 research and who, during childhood, had or had not exhibited symptoms of attention deficit disorder (ADD).

There were only two variables, ENGL and IQ, that were used in this exercise from the Howell and Huessy data file. ENGL is a categorical variable used to represent the level of English class in ninth grade: 1 = college prep, 2 = general, 3 = remedial. IQ is a presumably interval scaled variable obtained from a group administered IQ test.

Table 1 below presents the case summary for IQ by ENGL groups. As can be seen, the total non-missing (valid) N is 227, with most participants (N=164) in the general (level 2) English classes. It is notable that in each group there were between 26.1% and 35.4% missing cases, presumably because the IQ score was not available for some students. Although Howell reports that the sample size was 386, this data file contained a total of only 342 participants. Since the original 1965 sample was composed of children enrolled in second grade from 18 rural schools within 40 miles of Burlington, Vermont, the presumed population for the follow-up study would be all ninth grade students attending rural public schools within 40 miles of Burlington, Vermont.

Table 1

Case Summary for IQ by ENGL Group

Section II--Assumptions, data screening, and verification of assumptions:

• Clearly identify and verify any assumptions and requirements underlying the use of each inferential statistical procedure.
• Systematically verify each assumption and requirement for the variables that will be used in the analysis.
• If an assumption or requirement cannot be verified with the given information, indicate what information would be needed to provide verification.
• If the assumption or requirement is not consistent with the variables in the data file, indicate what remediation might be undertaken to ameliorate the problem.
• Screen the data for out-of-bound values and outliers.

ANOVA is a parametric statistical procedure that includes several assumptions and requirements. These include

1. Random sampling.
2. Interval or ratio measurement for the dependent variable.
3. Normally distributed groups.
4. Equal variance between groups (homoscedasticity).

Based on the published results of the study conducted by Howell and Huessy, it will be assumed that the participants were randomly selected. Inspection of the dependent variable and prior practice within the research community indicates that IQ can be treated as an interval scaled variable, although this assumption is open to debate.

Table 2 below provides a descriptive summary of the distribution of IQ for each ENGL group. It can be noted that groups 1 and 2 are somewhat negatively skewed, while group 3 has a positive skewness. Likewise, groups 1 and 2 appear to have similar variances, while the variability of group 3 is greater than either group 1 or 2. All values of ENGL and IQ appear to be within an expected possible range for each variable.

Table 2

Descriptive Statistics for IQ by ENGL Group

Figure 1 below shows box plots of the IQ distribution for each ENGL group. Figure 2 provides historgrams showing the distribution of IQ for each ENGL group. Again, some negative skewness is noticeable for groups 1 and 2. For group 2, this negative skewness appears to be related to the possible influence of an outlier with an IQ score of 55. (See Table 3 below for a listing of extreme values by group.) An IQ of 55 is unusually low for a general education class and for this reason this case might be considered an outlier and removed from the database. However, for this analysis, it was retained.

Figure 1

Boxplots of IQ by ENGL Group

At this point, the prior tables and graphs indicate that the assumptions of normality and equal variances across groups may be questionable for this data. Additional consideration is warranted. Table 4 represents the outcomes of two statistical tests of the normality assumption. For each of these tests, the null hypothesis is that the distributions are consistent with a normal distribution. Since none of the significance (sig.) values are less than .05, this assumption cannot be rejected and therefore the assumption of normality does, in fact, appear reasonable. Table 5 presents the Levene test of homogeneity of variance. The null hypothesis is that the variances between groups are equal. Since the sig. value is greater than .05, the assumption of equal variances also appears appropriate.

Table 4

Tests of Normality for IQ by ENGL Group

Section III-Inferential procedure, hypotheses, alpha level

• State the alpha level (use .05 unless otherwise indicated).
• State the research question(s).
• State the statistical hypotheses, both null and alternative.
• Indicate what the calculated statistic will be that addresses each of the hypotheses.

Alpha level = .05

The reason question is, "Are there mean differences in IQ among the three ninth-grade English level classes?"

Ho: The mean IQs of the three ENGL groups are equal; or

Ho: µ 1 = µ 2 = µ 3

H1: The mean IQs of the three ENGL groups are not equal; or

H1: µ1 ? µ2 ? µ3

The statistical procedure that will be used to test this hypothesis is one-way ANOVA. The calculated statistical result will be an F value.

Section IV-Interpretation

• Indicate the results and interpret the meaning of the results for each inferential analysis and do this specifically for the variables that are being analyzed.
• State your conclusions, as they relate directly to the research questions and hypotheses, based on the interpretation of the results.
• Indicate any limitations or constraints regarding these conclusions.

Table 6 provides the result of the ANOVA analysis. The F of 12.850 is statistically significant at and below the .05 level. Thus, the null hypothesis is rejected and the initial conclusion is that the mean IQs of the three ENGL groups are not equal. Since there are more than two ENGL groups, additional analysis is needed to identify exactly which groups have significantly different means and how these means differ.

Table 7 indicates that all possible pairs of ENGL groups are significantly different. Table 8 shows that the College Bound English group (group 1) had a mean IQ of 111.03, while the general English classes had a mean IQ of 102.03 and the remedial English classes had a mean IQ of 95.98. Figure 3 illustrates these differences graphically.

These results might indicate that placement in ninth grade English is related to not only the student's competence in English but also to their IQ. Further information concerning how students are actually placed would be needed before any more definitive conclusions could be reached.

Table 6

ANOVA Results

This information supplements the assignment guidelines indicated in Unit 6 SPSS Hints and the Model Example. Please ensure that your submission coplies with the aforementioned assignment requirements.
Go to SPSS>Analyze> GLM>Repeated Measures>Factor 1>Number of Levels> 3>Add Within Subjects Factor name>Shape>Define>Triangle> 1 >Square>2>rectangle>3>category>Between Subjects factors>Plots>Category>Horizantal Axis>Factor 1 >Separate Lines>Add>Post Hoc>category>Post Hoc TestsFor>Options>Category, Factor 1, Category*Factor 1>Display Means For

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Solution: The downloadable solution consists of 9 pages, 468 words and 13 charts.
Deliverable: Word Document