DATA ANALYSIS

· Download the Excel data file for M5.

· Use this Word document to record your calculation/analysis processes and answers.

· Follow the instructions for each specific question as each will have different requirements.

· Upload the Word document when you are finished. Make sure the document has loaded successfully!

Information about the M5 data set for Q1 and Q3:

A longitudinal project was conducted to study the executive and memory functions of elderly residents in a community. The participants were assessed every few years with a set of cognitive tests. Demographic and health information was also collected. The data set for Q1 and Q3 has been adapted from the data from that project.

Data Preparation

Create an SPSS data file from the data set by importing the M5 Excel file into SPSS. Then configure the variables, the value labels, and the measures properly.

Q1. Perform and Interpret a One-Way ANOVA. (7 pts.)

The researchers would like to know if people’s education level affects the amount of decline in executive function as they age. For this analysis, education level ( Educ) is categorized into three levels and the change in executive function ( EFChange) has been calculated by subtracting the EF score at the first testing session from the EF score at the second testing session.

Use the EFChange and Educ data to perform a one-way ANOVA with α = .05 to answer the following question:

Is there a statistically significant difference in the change of executive function across different education levels?

A. What is the null hypothesis? (1)

B. What are the dependent variable (DV) and the independent variable (IV)? (1) must be completely correct to earn point

C. Perform the ANOVA in SPSS, including running descriptives and the homogeneity of variance test.

You MUST copy-and-paste the output from SPSS in order to earn points for Q1 D, E, F, G. (Note: There are two routes to run 1-way ANOVA and both outputs are acceptable.) (1) for pasting output

D. Was the test for homogeneity of variance significant? Explain what the results mean relative to the data. (1), -.5 for incorrect significance, -.5 for incorrect equal variances

F. Report the results of the one-way ANOVA using symbols in the APA format, including the F statistic, the p-value, and the effect size ƞ2. (See the APA guide for reporting statistics in the Resources for Assignments module.) (1) must be completely correct to earn point

G. What is the decision about the null hypothesis (reject or fail to reject) based on the test result?

(1) must be completely correct to earn point

H. Create a bar graph or line graph to show the mean change in executive function for the different education groups. (1) pasted graph

Data Preparation for Q2

For this question set, import the worksheet “Q2data” into SPSS to create a new data file. (Be sure to upload the Q2 data sheet and not the Q1-Q3 datasheet.) This data set contains reading comprehension scores from a group of elementary school children who were in a special reading program. These children were tested when they entered the reading program at third grade, and then tested again at fourth grade, and finally tested as they leave the program at fifth grade. Ensure that your data values, labels, and measures are correct before proceeding.

Q2. Perform and interpret a one-way repeated-measures ANOVA. (8 points)

To see if the reading program leads to significant improvement on reading comprehension, the researchers want to compare the three test scores at the three grade levels. Perform a one-way repeated-measured ANOVA to answer the following question:

Is reading comprehension significantly different across the three grade levels?

A. What is the null hypothesis? (1)

B. What are the DV and IV?

(1) must be completely correct to earn point

C. Run the ANOVA with the following options:

- Descriptives

- Estimate of effect size

Paste the entire output for this analysis here.

If any table is missing, no point will be earned for D, E, F in Q2.

D. Examine the Sphericity test result. Is the sphericity assumption met? How do you know?

(1), -.5 for incorrect assumption, -.5 if don’t mention p in reason

E. Report the test result in APA format (including F statistic, p value, and partial η2).

(2: Report the statistical result here, each error = -.5 up to 2 total).

F. What is the answer to the research question based on the test result?

(1)

G. Run the same ANOVA again, but this time request “contrasts” to compare each level with every other level. Follow the steps below to complete this question:

· Run the repeated-measures ANOVA, then request simple contrasts for the variable of “Grade”, with “Last” level as the reference category. This will compare each level with the “last” level. Paste the table of “Tests of Within-Subjects Contrasts” below (0.5)

· Run the repeated-measures ANOVA, then request simple contrasts for the variable of “Grade”, with “First” level as the reference category. This will compare each level with the “first” level. Paste the table of “Tests of Within-Subjects Contrasts” below (0.5)

· Report the result of each of the pair-wise contrasts, including F statistics (with df’s) and p value, in APA format.

· Determine whether there is a significant difference in reading comprehension in each contrast. Write all the pairs that have significant differences in reading comprehension.

(1: .5 for each error, maximum -1)

Q3. Perform and Interpret a Two-Way ANOVA. (10 pts.)

Use the same data set from Q1 for this item.

The researchers would also like to know whether or education levels ( Educ) significantly influences changes in memory over time ( MemChange). However, they suspect that education levels and gender ( Gender) may interact. In other words, the researchers want to investigate whether a statistically significant difference in the three education levels is dependent on gender.

Another way to say this is that the researchers want to investigate whether the magnitude of the difference in memory change scores between males and females at education level 1 is statistically significantly different from the magnitude of the difference in memory change scores between males and females at education levels 2 and 3, and so on. There are six groups formed by crossing gender (male, female) and education level (Levels 1, 2, and 3), resulting in the following research questions for the main effects and the interaction.

Main Effect (Gender)

Is there a statistically significant difference between genders in memory score changes?

Main Effect (Education Level)

Is there a statistically significant difference among education levels in memory score changes?

Interaction (Education Level x Gender)

Does a statistically significant difference in changes to memory scores among education levels depend on gender?

Perform a two-way ANOVA with α = .05 to answer the questions above.

A. What are the null hypotheses corresponding to our questions?

(1) must be completely correct to earn point

B. What are the two factors (i.e., IVs) and the DV.

(1) must be completely correct to earn point

C. Perform the initial 2x3 two-way ANOVA in SPSS.

· Upload the data from the Excel file. (Be sure to upload the Q1Q3 data sheet and not the Q2 datasheet.)

· Check that all variables are configured correctly in “Measure” under the “Variable View.”

· The “Values” for the nominal variables should be specified (e.g., use the codebook to enter labels that correspond to each value).

· Select “General Linear Model” from the analyze menu and then select “Univariate.”

· Enter the DV and IVs in the appropriate boxes. Note that the IVs are “Fixed Factors” because we did not randomly assign participants to their groups.

· Click on “Options” and check the box for “estimates of effect size”

D. What is the decision about the two main effect null hypotheses (reject or fail to reject) based on the initial test result?

· Report the main effects of the F test result in APA format including F, p and η2 . Be sure to paste the relevant output table here to support your answer. (1) must be completely correct to earn point (pasted table, F, p, η2 results)

[Paste output here.]

E. Report the result of the test on the Educ x Gender interaction effect:

· Report the test result on the interaction effect in APA format including F and p. (.5)

· Draw a conclusion from the hypothesis testing result and state the finding supported by the result. Be sure to explain what an “interaction” means.

(1 point: -.5 for each error, maximum -1).

F. Repeat the two-way ANOVA analysis, but with the following additional statistics requested before running the analysis.

· EM Means: Move Gender* Educ into the “display means for” box. “Compare simple main effects” should be checked and the “confidence interval adjustment” should be “LSD(none)”.

· Plots: Enter Educ into the “horizonal axis” box and Gender into the “separate lines” box. Also, click the “add” button, which will add the Educ x Gender variable. Chart type is set to ‘Line Chart’ already.

· Options: Check the boxes for “descriptive statistics” and “homogeneity tests.”

[Paste the entire output here.]

G. Examine the output for the descriptives. What observations can you make about the means of the different groups? (0.5)

H. Is the Levene’s Test significant? What does the result (significant or not significant) mean? Explain.

(1), -.5 for incorrect significance, -.5 if no explanation

I. What are the results of the Educ*Gender pair-wise comparisons between education levels? Report the result of each of the pair-wise contrasts, including the p value. Then, draw a conclusion based on the findings. Your conclusion should explain the findings and also indicate whether the post hoc test of Educ was necessary.

(2) -.5 for incorrect value up to -1.5; .5 for conclusion

J. Run a one-way ANOVA for the factor education levels ( Educ) using only the MemChange data for females. Similarly, run a one-way ANOVA for education levels using only the MemChange data for males. Paste your output and then draw a conclusion based on the findings. Your conclusion should explain the findings and also indicate whether this post hoc test was necessary. (1) -.5 if not pasted output , -.5 incorrect conclusion, -.5 post hoc test necessary incorrect, max -1)

K. Based on all of the analyses you have run for Q3, how would you summarize the findings in your own words? (1)