M4 Assignment-Spring A 2024-1

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Arizona State University *

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330

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Statistics

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Feb 20, 2024

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Nelson Spring A 2024 M4 Assignment (35 points) INSTRUCTION: Use this Word document to fill in the answers to the questions. The answers must be supported either by typing out the calculation process or by pasting SPSS output or data as instructed. When prompted to paste something from the SPSS data or output file, you may use the copy/paste function or take a screenshot of the relevant part to paste in as a picture. Information about the data set for Q1 and Q2: 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 Q2 is based on part of the data from that project. Data Preparation for Q1 and Q2 (1 point: No point is earned if SPSS data file is missing) Create an SPSS data file from the data set by importing Q1Q2 data set (first ‘page’ of the Excel document, the Codebook for which is its second ‘page’) into SPSS and submit the file with your assignment. Make sure the SPSS data file meets the following criteria: (1 point total: deduct .5 for each error up to 1 point total.) - All variables are imported - All variables are configured correctly in “Measure” under the “Variable View” - The “Values” of the variables, “Marital”, “Sex”, and “EducR” should be specified under “Variable View” Q1. Perform and Interpret a One-Way ANOVA (15 points total, If SPSS output is missing for this analysis, 50% of the total number of earned points will be deducted) We are interested in whether executive function (EF1) is related to educational levels. To answer this question with a one-way ANOVA, education level (number of years of schooling) has been recoded to three levels as a new variable Educ-R: associate degree or under, bachelor’s degree, and graduate studies. A. What is the null hypothesis (in words)? What are the DV and IV? (3 points total: 1 for hypothesis, 1 for each variable) Null hypothesis: Executive function does not significantly differ between education levels. DV: executive function IV: educational levels B. Was the test for homogeneity of variances significant? What does it tell us about the ANOVA assumption of equal variances among the groups? -Be sure to paste the relevant output table here to support the answer. (2 points total: 1 for significance result, 1 for assumption result. No credit is earned if no table is pasted.)

Nelson Spring A 2024 Assuming alpha is .05, p = .459, p > alpha. We must fail to reject the null hypothesis and can assume variances are homogeneous and that the test is not significant. C. Report the results of the one-way ANOVA using symbols in the APA format. -Be sure to include the F -statistic, the p -value, and the effect size ƞ 2 . -Be sure to paste the relevant output table here to support the answer. -The calculation process for ƞ 2 must be shown, but separately from the line of APA report of the statistics. (5 points total: 1 point each for F , p , and ƞ 2 , 1 for calculation process for ƞ 2 , 1 for APA format. No credit is earned if no table is pasted.) F( 2,52) = .034, p = .967, ƞ 2 = .001 ƞ 2 = 6.594/5111.227 = .0012901 = .001 D. Make a decision about the null hypothesis (reject or fail to reject) based on the test result, and then write 1-2 sentences to directly answer the research question above based on the ANOVA result. (2 point, 1 for each question) Because p > alpha we fail to reject the null hypothesis. There is not a significant difference between the education level groups in regard to executive function. E. If post hoc analysis was necessary, discuss the findings in questions 1 and 2 below. Be sure to paste the relevant table here to support your answer. If post hoc analysis was not necessary, skip this question E and go to question F.

Nelson Spring A 2024 E1. Which test was used to compare the groups? (1 point) The LSD test. E2. Which groups are different significantly and which groups are not? Be specific about which group may have significantly higher or lower executive function compared to which other group, and include the p -values to support your answer. (2 points total: 1 point for correct statement as to which group(s) if any significantly different from which (other(s), and 1 point for correct statement of p -values, within a clear answer to the question. No credit earned if no table is pasted.) None of the groups are significantly different. This is because p > alpha for all groups. F. If post hoc analysis was not necessary, plot a bar or line graph to show the mean executive function for the different degree groups. (3 points total: 1 each for graph type, title/axis labels, and correct data.) n/a Q2. More One-Way ANOVA analysis (10 points total, If SPSS output is missing for this analysis, 50% of the total number of earned points will be deducted) Last week, we performed a t- test to compare unemployed and employed participants in terms of their age at the first testing session (age1). This question could also be answered by a one- way ANOVA: let’s now perform the ANOVA. (Note the dataset is different compared with that from last module’s assignment.) A. What is the null hypothesis (in words)? (note: if you misunderstood this last week, be sure to correct before copying the null hypothesis here!) (1 point, deduct .5 for any error) What are the DV (.5 point) and IV (.5 point) ? Null hypothesis: Employment status is not a potential factor in the effect of aging on cognitive functions. DV: effect of aging on cognitive function IV: Employment status

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Nelson Spring A 2024 B. Was the test for homogeneity of variances significant? What does it tell us about the ANOVA assumption of equal variances among the groups? Be sure to paste the relevant output table here to support the answer. (2 points total: 1 for significance result, 1 for assumption conclusion. No credit is earned if no table is pasted.) No, it was not significant. If we assume that alpha = .05, p > than alpha which means there is an equivalent of variances and ANOVA is not violated. C. Report the results using symbols in the APA format. -Be sure to include the F -statistic, the p -value, and the effect size ƞ 2 . -Be sure to paste the relevant output table to support your answer. -The calculation process for ƞ 2 must be shown, but separately from the line of APA report of statistics. (3.5 points total: 1 point each for F , p , and ƞ 2 , .5 for calculation process of ƞ 2 . No credit is earned if no table is pasted.) F( 1,53) = .394, p = .533, ƞ 2 = .001 ƞ 2 = 9.100/1232.435 = .00738375 = .007 D. Would you reject the null hypothesis? What is the answer to the research question? (2 points, 1 for each answer) Yes. Employment status is a potential factor in the effect of age on cognitive function. Data Preparation for Q3 (1 point: No point is earned if SPSS data file is missing) For this question set, import the worksheet “Q3data” (third ‘page’ of the Excel document, the Codebook for which is its fourth ‘page’) into SPSS to create a data file. Be sure to submit this SPSS data file with your assignment to earn this credit. (1 point total: deduct .5 for each error up to 1 point total)

Nelson Spring A 2024 Q3. Perform and interpret a one-way repeated-measures ANOVA (7 points total, If SPSS output is missing for this analysis, 50% of the total number of earned points will be deducted) This data set was adapted from one of Dr. Kuo’s own experiments. In this experiment, Dr. Kuo examined people’s memory for colors of drawings of ordinary objects while recording their brainwaves. Because Dr. Kuo needed to have a large number of trials to analyze the brainwave data properly and people couldn’t possibly remember that many pictures presented all at once, she tested the subjects in 3 separate sessions with breaks in between sessions. The dataset shows the percent correct for each subject in the 3 sessions. Because color memory test is a relatively difficult task, it was of interest to Dr. Kuo to see if there were significant differences across the sessions in performance. If there were changes in the upward direction, it may indicate some practice effect in the subjects’ color memory performance (that is, people get better at remembering colors after going through multiple sessions). For this question, perform a one-way repeated-measures ANOVA with the factor of “session” (3 levels) and the DV of color memory score. A. Determine if the assumption of sphericity has been met by our data. Report the test of sphericity result ( p-value ) and explain whether the assumption is met. Be sure to paste the relevant output tables here. (2 points total: 1 for each question. No credit is earned if no table is pasted.) (Note you will complete this entire question, regardless of whether the sphericity assumption is met.) p = .019 < alpha .05, the assumption is not met, we can not assume sphericity. B. Report the result of the statistical test that would need to be run, in order to find out what Dr. Kuo was seeking to discover. Be sure to do so in APA format (including F-statistic, p-value, and partial- η 2 ). Also be sure to paste the relevant output tables here to support your answer. (3 points total: 1 point for each statistic, df s must be correct for F to earn credit. No credit is earned if no table is pasted.) F( 2,38) = 1.149, p = .328, partial ƞ 2 = .06 Partial ƞ 2 = 573.673/9482.984 = .06049498 = .06

Nelson Spring A 2024 C. What is the answer to Dr. Kuo’s research question based on the test result? (1 point) Color memory improves with practice. D. Request simple contrasts for the variable of “session” if you did not do so when you ran the ANOVA. Examine the contrasts and discuss your observation regarding any significant difference (or lack of difference) between the different sessions, citing p values to support your answer. Be sure to paste the relevant output table here to support your answer. (2 points total: 1 for discussion of significance, 1 for discussion of p values. No credit is earned if no table is pasted.) I’ve pasted the two tables below for comparison. In regard to level 1 vs level 2 the repeated contrasts and the simple contrasts reflect the same data and significance. The p values are the same at p = .631. When reviewing repeated contrast vs simple contrast in regard to level 3, the comparison changes from comparing level 2 to level 3 in the repeated contrast, and level 1 and level 3 in the simple contrast. This presents a significant difference in data. In the repeated contrast table the p value is p = .427, but in the simple contrast table it is below alpha at p = .037

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M4 Assignment-Spring A 2024-1

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