Advanced Data Analysis Quiz: Repeated Measures ANOVA Insights
School
University of Waterloo**We aren't endorsed by this school
Course
PSYCH 391
Subject
Psychology
Date
Dec 12, 2024
Pages
11
Uploaded by CorporalFire15272
Name ________________ ID# ________________ 1 Psychology 391: Advanced Data AnalysisQuiz #3aDecember 11th, 2023 Instructions: a)You have 2.5 hours. b)You should have a 11-page exam with 11 questions totaling 60 marks. c)Use an alpha of .05 for all of the questions unless otherwise stated. d)GOOD LUCK! (1)Answer the following questions based on the following repeated measures ANOVA: Source Df SS MS F Between Subjects 17 103.28 Time 3 62.28 20.76 8.29 Error 51 127.72 2.50 Total 71 293.28 (a) Report the F-statement in APA format for this analysis (1 Mark). (b) How many participants were involved in this study (1 Mark)? ________ (c) If you were to reanalyze these data as a One-Way between-subjects ANOVA, what would the new F value be (4 Marks)? Be sure to show all your work that helped you determine this. (d) In general, why are repeated measures designs more powerful than between-subjects designs (2 Marks)?
Name ________________ ID# ________________ 2 (2) In class, we discussed how there are two sources of individual differences in repeated measures ANOVAs that reflect how participants varied on the dependent variable. Briefly explain what these two sources of individual differences are (2 Marks). (3)Briefly describe what is meant by the assumption of Sphericity (1 Mark) and explain how the Greenhouse-Geisser correction (that we apply when we violate that assumption) affects the probability of making Type 1 errors (1 Mark). (4)Why do we not get a test of Sphericity when we only have two levels of an independent variable in a within-subjects design (1 Mark)?
Name ________________ ID# ________________ 3 (5)You just ran a 2 (between) x 4 (repeated) mixed design where the df for the error term of the within-subjects component of the analysis was 138. (a)How many factors (i.e., independent variables) are in this experiment (1 Mark)? ________ (b)What would the degrees of freedom for the interaction be (1 Mark)? ________ (c)What would the degrees of freedom for the between-subjects error term be (1 Mark)? ________ (d)What would the critical value of F for the within-subjects factor be (1 Mark)?________ (e)How many participants were in this experiment (1 Mark)? ________ (f)How many cells are in this design (1 Mark)? ________ (6)We discussed in class that we can use the same multiple comparison procedures (Tukey, Fishers Protected t-tests, etc.) for between subjects designs and repeated measures without changing the formulas. Why is that the case (i.e., why don’t we have to use different formulas) (2 Mark)? (7)By now we all know that an interaction between two variables basically means that the effect of one independent variable depends on the level of the other. Given that, explain how you can test for an interaction in a 2 x 2 design by doing a single t-test. Make sure you provide enough detail to make it clear what calculations are necessary (3 Marks).
Name ________________ ID# ________________ 4 (7)A sport psychologist is interested in the effects of strength training on running speed for young and old runners. She measured 4 young and 4 older runners’ performance on a 400m track before training and after 1 month of training. Her data are provided below (rounded to the nearest second), along with various marginal means. (a) Compute the SS calculation for SS Cells (3 Marks). (b) Imagine the SS for the main effect of Age was 27.56 and the main effect of Time was 22.56. What would the SS for the interaction be (1 Mark)?______ (c) The above table also includes “Subject Means”. How are subjects means used in the mixed ANOVA (i.e., what do you do with them (2 Marks)? Don’t actual do any calculations, just explain how they are used. (d) Using SPSS, a researcher decides to do simple effects analyses for the data, splitting the file on Age and looking at the effect of time separately. What are the drawbacks of this approach rather than doing it by hand (2 Marks)?Subject Pre-Test Post-Test Subject Mean Young 1 73.00 71.00 72.00 2 68.00 68.00 68.00 3 70.00 68.00 69.00 4 62.00 62.00 62.00 Mean68.2567.2567.75 Old1 80.00 75.00 77.50 2 74.00 66.00 70.00 3 68.00 67.00 67.50 4 67.00 64.00 65.50 Mean 72.25 68.00 70.13 Grand Means70.25 67.63 68.94
Name ________________ ID# ________________ 5 (8)Answer the following questions for the following output: (a)Write out the full F-statement for the two main effects and interaction in APA format assuming that the assumption of sphericity was violated for Factor_B only (3 Marks). (b)How many participants were in this experiment (1 Mark)? _______ (c)Given that there was an interaction in these data, describe how you would test for the locus of the interaction using SPSS (2 Marks)?
Name ________________ ID# ________________ 6 (9)In class, we have spent a lot of time talking about the MSE term in ANOVA’s. We have also spent a lot of time learning hand calculations for several simple effects procedures (e.g., SScontrasts, Fisher’s t-tests, etc) that all incorporate the MSE. (a) In general, what is the MSE a measure of (2 Marks)? (b) What is different about the MSE in a within- versus between-subjects design (2 Marks)? (10) In the graphs below:(a)Draw a 3-way interaction between Age, Drug, and Season (2 Marks). Age Young - - - - - - Old Summer Winter Y Placebo Drug Placebo Drug Drug Drug (b)In a few sentences, describe what simple effects analyses you would do to follow up this 3-way interaction (3 Marks)
Name ________________ ID# ________________ 7 (11)You and a colleague ran an experiment looking at the effects of Caffeine on Ziptoids and Bliptoids (two alien species from the Andromeda Galaxy) ability to throw a 16 pound bowling ball (yes… they are unusually strong). You measured the distance the aliens could throw the blowing ball (in meters) after consuming (a) no caffeine, (b) 50mg, (c) 100mg, and (d) 150mg of caffeine. Both groups of aliens participated in each of the four caffeine conditions on different days. The data and analyses are below (note the means for each condition are displayed on the graph): 14.817.521.718.614.512.911.814.80510152025Omg50mg100mg150mgDistane in MetresCaffeine DosageZiptoidsBliptoids
Name ________________ ID# ________________ 8 (a) How many participants in total were run in this study (1 Mark)? ________ (b) Calculate Partial h2for the main effect of Dosage (1 Mark). ________ (c) Why might partial h2be a better measure of effect size than regular h2 for these data (1 Mark)? (d) Given the initial findings (i.e., the omnibus ANOVA), conduct further statistical analyses of your choice (e.g., post hoc/simple effects) that will help explain the interaction (8 Marks). (e) Provide a brief rationale for your choice of the simple effects analyses that you used in the previous question (2 Marks).
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