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- 1. Split Plot Analysis of Variance Designs PSYCHOLOGY 3800, LAB 003
- 2. • two-way ANOVA assignment feedback (short version) • split plot ANOVA overview • example analysis • example output of overall effects • example post hoc investigation • assignment In Lab Today…
- 3. Assignment #4: Feedback
- 4. Assignment #4: Feedback • keep your report organized o introduction o assumptions o interaction + simple main effects o main effect 1 (self-esteem) o main effect 2 (difficulty) + post hoc tests o conclusion • tell a story o make clear what you are seeing o describe effects o write concluding sentences
- 5. Assignment #4: Feedback Description of Effects • be specific about the nature of the effect observed Example No significant main effect was found when comparing the low self-esteem group (M = 30.67, SE = 1.79) to the high self-esteem group (M = 31.23, SE = 1.09), F(1, 54) = 0.23, ns, η2 = 00, power = .08. …need to add to this to clarify the effect… Therefore, participants in low self-esteem groups did not differ significantly from those in the high self-esteem on their test performance.
- 6. Assignment #4: Feedback • example two-way ANOVA results section posted on lab blog http://psych3800g.tumblr.com/post/44614034425/two-way-anova-example-report
- 7. Split Plot ANOVA: Overview
- 8. • extension of the completely randomized factorial design o two or more factors (independent variables) o each factor has multiple levels o measuring one dependent variable o can have main effects and interaction o interested in differences between means • main design difference o two-way ANOVA: both factors are independent o split plot ANOVA: one factor is independent, one is correlated Split Plot ANOVA: Overview
- 9. • independent factor = between-subjects factor o composed of 2 (or more) levels of completely different people • correlated factor = within-subjects factor o composed of 2 (or more) levels that consist of the same people (repeated) What kind of study would use this design? Split Plot ANOVA: Overview
- 10. Does a participant’s level of amusement after watching different types of ‘80s action movies change depending on their level of sleep deprivation? 1. obtain a sample of participants 2. randomly assign participants to either sleep deprivation or lots of sleep condition 3. have each person watch 3 different ‘80s action movies 4. record participants’ amusement level after each movie (1 = not at all amused, 5 = extremely amused) Research question: Procedure: Split Plot ANOVA: Example
- 11. Sleep status Action movie from 1980s Ghostbusters The Terminator Indiana Jones Sleep deprived Tons of sleep Split Plot ANOVA: Example Each participant experiences only one combination of variables. Two-Way Factorial Design
- 12. Sleep status Action movie from 1980s Ghostbusters The Terminator Indiana Jones Sleep deprived Tons of sleep Split Plot ANOVA: Example Split Plot Design Participants get assigned to a group, and experience all levels of second factor in that group.
- 13. Sleep status Action movie from 1980s Ghostbusters The Terminator Indiana Jones Sleep deprived 4.105 3.975 2.425 Tons of sleep 3.540 3.555 2.970 3.823 3.765 2.698 3.502 3.355 Split Plot ANOVA: Effects The types of values that we can calculate are similar to those obtained via a two-way factorial design (in a two-way ANOVA)…
- 14. main effect of sleep (if significant, know that these means differ significantly) Split Plot ANOVA: Effects Sleep status Action movie from 1980s Ghostbusters The Terminator Indiana Jones Sleep deprived 4.105 3.975 2.425 Tons of sleep 3.540 3.555 2.970 3.823 3.765 2.698 3.502 3.355
- 15. Sleep status Action movie from 1980s Ghostbusters The Terminator Indiana Jones Sleep deprived 4.105 3.975 2.425 Tons of sleep 3.540 3.555 2.970 main effect of movies (if significant, know that at least two of these means differ significantly) Split Plot ANOVA: Effects 3.823 3.765 2.698 3.502 3.355
- 16. Sleep status Action movie from 1980s Ghostbusters The Terminator Indiana Jones Sleep deprived 4.105 3.975 2.425 Tons of sleep 3.540 3.555 2.970 interaction effect (if significant, know that cell means differ significantly) From here, we must decide on an approach to interpreting interaction effect. (same as in two-way ANOVA) Split Plot ANOVA: Effects
- 17. Sleep status Action movie from 1980s Ghostbusters The Terminator Indiana Jones Sleep deprived 4.105 3.975 2.425 Tons of sleep 3.540 3.555 2.970 Split Plot ANOVA: Effects Interpreting the Interaction: Option #1 o simple main effects of movie at each level of sleep Sleep deprived: G vs. T G vs. I T vs. I Tons of Sleep: G vs. T G vs. I T vs. I 6 comparisons
- 18. Sleep status Action movie from 1980s Ghostbusters The Terminator Indiana Jones Sleep deprived 4.105 3.975 2.425 Tons of sleep 3.540 3.555 2.970 Split Plot ANOVA: Effects Interpreting the Interaction: Option #2 o simple main effects of sleep at each level of movie Ghostbusters: sleep deprived vs. tons of sleep 3 comparisonsTerminator: sleep deprived vs. tons of sleep Indiana Jones: sleep deprived vs. tons of sleep
- 19. As in two-way ANOVA, we are interested in three main hypotheses: 1. interaction hypotheses H0: a significant interaction does not exist between sleep status and movies HA: a significant interaction exists between sleep status and movies 2. main effect for variable 1 (sleep status) H0: µDEPRIVED = µLOTS HA: µDEPRIVED ≠ µLOTS 3. main effect for variable 1 (movie) H0: µGHOSTBUSTERS = µTERMINATOR = µINDIANA HA: at least two means differ significantly Split Plot ANOVA: Hypotheses
- 20. 1. independent random sampling 2. normality 3. homogeneity of variance (2 parts) Split Plot ANOVA: Assumptions
- 21. Homogeneity of Variance • Levene’s test (F) o between-groups variances are homogenous (as in previous tests) o e.g., is variance of the DV (amusement scores) equal for both for sleep-deprived versus sleep-affluent people at each movie? • Mauchly’s test (W) o circularity of the pooled variance-covariance matrix o variances of difference scores are the same (as in repeated ANOVA) o regardless of results, always report Greenhouse-Geisser corrected values Significant results suggest that assumption has been violated (applicable to both tests). Split Plot ANOVA: Assumptions
- 22. Split Plot ANOVA: Example Analysis in SPSS
- 23. with-subjects factor (as labeled) between-subjects factor (1 = deprived, 2 = lots) scores on DV, 1-5 (level of amusement) 40 cases First participant: -randomly assigned to “lots of sleep” condition -rated Ghostbusters and Terminator as highly amusing, Indiana Jones as low Split Plot ANOVA: Example Data *ignore the 5th column for now
- 24. Analyze General Linear Model Repeated Measures specify repeated (within-subjects) factor name and number of levels, click “Add” when info added (as shown) click “Define” Split Plot ANOVA: SPSS Analysis
- 25. define each level of within-subjects variable as in a repeated measures ANOVA (select level on right, click on corresponding movie on left, click ) Split Plot ANOVA: SPSS Analysis
- 26. define the between-subjects variable by moving Sleep_Status into the Between-Subjects Factor(s) box (click on variable in left panel, click on beside Between-Subjects box) Split Plot ANOVA: SPSS Analysis
- 27. Options Menu provides Levene’s test output for between-subjects factor (Sleep Status) gives descriptive values for within-subjects factor (Movies) and interaction Split Plot ANOVA: SPSS Analysis
- 28. Split Plot ANOVA: SPSS Analysis Plots Menu request both types of plots to help you decide in which way you would like to frame/interpret the interaction
- 29. Once all selections have been made, click “OK” to run the analyses. Split Plot ANOVA: SPSS Analysis
- 30. Split Plot ANOVA: Example Output for Overall Effects
- 31. Descriptive Statistics Split Plot ANOVA: SPSS Output • these are the cell means representing the effect of one variable at each level of the other (will use when assessing interaction) • standard errors are not provided and so will have to be calculated by hand: € SE = s n
- 32. Descriptive Statistics Split Plot ANOVA: SPSS Output • these are the group means for the movie levels (one mean for each movie) and will be assessed when we examine the main effects of the within-subjects factor • standard errors are not provided and so will have to be calculated by hand: € SE = s n
- 33. Split Plot ANOVA: SPSS Output Descriptive Statistics: Obtaining Data for the Between-Subjects Factor • need to create a single variable that represents the mean enthusiasm for each participant, collapsed across the movies (average movie scores per participant) • I have already done this for you in your data file
- 34. Split Plot ANOVA: SPSS Output Descriptive Statistics: Obtaining Data for the Between-Subjects Factor Analyze Descriptive Statistics Explore specify that the averaged scores represent your DV, which you are examining at each level of your Sleep Status IV (request statistics only)
- 35. Split Plot ANOVA: SPSS Output Descriptive Statistics: Obtaining Data for the Between-Subjects Factor • these are the group means for the sleep levels (one mean for each sleep group) and will be assessed when we examine the main effects of the between-subjects factor • standard errors are provided
- 36. Mauchly’s W = 0.863, χ2(2) = 6.388, p < .05 * significant effect = assumption of circularity has been violated Test of Assumptions: Mauchly’s Test Split Plot ANOVA: SPSS Output
- 37. Test of Assumptions: Levene’s Test Split Plot ANOVA: SPSS Output Ghostbusters: Levene F(1, 38) = 1.048, ns Terminator: Levene F(1, 38) = 0.427, ns Indiana Jones: Levene F(1, 38) = 1.867, ns Equal variances are assumed on the DV for the sleep groups at each level of the within-subjects (repeated) variable.
- 38. F(2, 66) = 5.652, p < .01, η2 = .129, power = .806 • significant interaction exists between movies and sleep status • proceed with simple main effects Split Plot ANOVA: SPSS Output Omnibus Test: Interaction
- 39. F(2, 66) = 24.928, p < .001, η2 = .396, power = 1.000 • significant main effect exists for the repeated variable of Movies • proceed with post hoc tests (Tukey’s HSD) Split Plot ANOVA: SPSS Output Omnibus Test: Within-Subjects Effects (Movie)
- 40. Split Plot ANOVA: SPSS Output Omnibus Test: Between-Subjects Effects (Sleep Status) F(1, 38) = 0.405, ns, η2 = .011, power = .095 • no significant main effect for sleep status exists • no Tukey’s HSD post hoc tests required
- 41. Split Plot ANOVA: SPSS Output So far, we know: • significant interaction between level of sleep and movie type • significant within-subjects main effect for movie type • non-significant between-subjects main effect for level of sleep Next steps: • investigation of simple main effects for interaction • post hoc tests (Tukey’s HSD) for main effect of movies
- 42. Split Plot ANOVA: Post Hoc Analyses
- 43. Split Plot ANOVA: Post Hoc Analyses Interaction 1: Simple Main Effects of Movie at Each Level of Sleep i.e. simple main effects of within-subjects factor at each level of between-subjects factor 0 1 2 3 4 5 Sleep deprived Lots of Sleep MeanAmusementRating Sleep Status
- 44. Split Plot ANOVA: Post Hoc Analyses Step 1: Run a MANOVA using the syntax option in SPSS File New Syntax levels of within-subjects factor (movie) between-subjects factor (sleep) with coding name of within-subjects factor (number of levels) comparing means of within-subject factor (movie) at first level of sleep-status (sleep-deprived) Interaction 1: Simple Main Effects of Movie at Each Level of Sleep
- 45. Split Plot ANOVA: Post Hoc Analyses movies at sleep-deprived: F(2, 76) = 27.13, p < .001 movies at tons-of-sleep: F(2, 76) = 3.45, p < .05 Reading the very bottom table of the MANOVA output… at least two movie means differ significantly at each sleep level proceed with Tukey’s HSD to pinpoint differences Interaction 1: Simple Main Effects of Movie at Each Level of Sleep
- 46. Split Plot ANOVA: Post Hoc Analyses Step 2: follow up with separate Tukey’s HSD analyses for applicable levels using the POSTHOC program (use sphericity assumed values, no pooled error term) Interaction 1: Simple Main Effects of Movie at Each Level of Sleep Example: SME of Movies at Sleep Deprived from “Tests of Within- Subjects Effects” table Report as: q(k, dferror) q(3, 76) k = # of means compared dferror = same as what you gave to POSTHOC *compare against q-critical from tables
- 47. Split Plot ANOVA: Post Hoc Analyses Interaction 2 : Simple Main Effects of Sleep at Each Level of Movie i.e. simple main effects of between-subjects factor at each level of within-subjects factor 0 1 2 3 4 5 Ghostbusters Terminator Indiana Jones MeanAmusementRating Action Movie from the 1980s
- 48. Split Plot ANOVA: Post Hoc Analyses Analyze Compare Means One-Way ANOVA Interaction 2 : Simple Main Effects of Sleep at Each Level of Movie Step 1: run a one-way ANOVA in SPSS for all variables
- 49. Split Plot ANOVA: Post Hoc Analyses • the output is not the results of our simple main effects analysis (sorry!) • this is a way for us to get the necessary info to calculate our needed statistics • pull out the Mean Square and df values for the “Between Groups” effects (the rest of the info is meaningless) Interaction 2 : Simple Main Effects of Sleep at Each Level of Movie
- 50. Split Plot ANOVA: Post Hoc Analyses Option #1: by hand Interaction 2 : Simple Main Effects of Sleep at Each Level of Movie € Pooled MSerror = SSerror1 + SSerror2 dferror1 + dferror2 € Pooled dferror = (SSerror1 + SSerror2)2 SSerror1 2 dferror1 + SSerror2 2 dferror2 where… SSerror1 = sums of squares for error, sphericity assumed (Tests of Within-Subjects Effects table) dferror1 = degrees of freedom for error, sphericity assumed (Tests of Within-Subjects Effects table) SSerror2 = sums of squares for error (Tests of Between-Subjects Effects table) dferror2 = degrees of freedom for error (Tests of Between-Subjects Effects table) Step 2: Calculate pooled error terms for the analysis
- 51. Split Plot ANOVA: Post Hoc Analyses Option #2: POSTHOC program • enter in all cell means (found in your descriptive values output) • specify the nature of the sample (group size, all groups equal) • identify two Mean Square Error (MSE) values and their degrees of freedom (df) MSE1 and df1 Tests of Within-Subjects Effects table, Error section, sphericity assumed value MSE2 and df2 Tests of Between-Subjects Effects table, Error row Interaction 2 : Simple Main Effects of Sleep at Each Level of Movie
- 52. Split Plot ANOVA: Post Hoc Analyses this is your pooled error term (when reporting it in your results, the convention is to round it down… so, it would be 93) Option #2: POSTHOC program Interaction 2 : Simple Main Effects of Sleep at Each Level of Movie
- 53. Split Plot ANOVA: Post Hoc Analyses Step 3: Calculate F-obtained values for each comparison by hand Interaction 2 : Simple Main Effects of Sleep at Each Level of Movie € F = MSBG MSerror where… MSBG = between-groups MS value of interest (one-way ANOVA output) MSerror = pooled MS error value (from POSTHOC or by hand) F(dfBG, dferror) = calculated value where… dfBG = between-groups df value of interest (one-way ANOVA output) dferror = pooled df error value, rounded down (from POSTHOC or by hand)
- 54. Split Plot ANOVA: Post Hoc Analyses Step 3: Calculate F-obtained values for each comparison by hand Interaction 2 : Simple Main Effects of Sleep at Each Level of Movie € F = MSBG MSerror = 3.192 .960333 = 3.324 Example: sleep-deprived versus lots-of-sleep after watching Ghostbusters F(1, 93) = 3.324
- 55. Split Plot ANOVA: Post Hoc Analyses Step 3: Compare F-obtained values against F-critical values to determine significance Interaction 2 : Simple Main Effects of Sleep at Each Level of Movie • to find F-critical: use tables or website suggested by Dr. McRae • for F-tables: use the same degrees of freedom in looking up your critical value as you do when reporting your obtained value: F(dfBG, dferror) = critical value • reject H0 (and conclude significant difference) if F-obtained > F-critical
- 56. • use POST HOC program to output qobtained values for all comparisons • enter sphericity-assumed data (as in repeated ANOVA) • no pooled error term needed • compare qobtained values against qcritical value from tables q (k, dferror) = obtained or critical value where: k number of within-subjects factor levels dferror error df from Tests of Within-Subjects Effects table (sphericity assumed) …also include significance info for qobtained Split Plot ANOVA: Post Hoc Analyses Main Effect: Within-Subjects (Repeated) Variable
- 57. Assignment #6
- 58. • 3-page report in APA-style • two main sections: 1) response to question #1 (part A in point-form, part B in sentence form) 2) APA-style results section describing overall results • all output o SPSS output (Split Plot analysis, One-Way ANOVA, MANOVA, descriptives) o POST HOC output (post hoc tests for any significant main effects, post hoc tests for simple main effects when needed) Assignment: What to Submit
- 59. Assignment: What to Report for Question 1 Within-Subjects Variable at Each Level of Between-Subjects Variable (movies at each level of sleep status) • simple main effect of movies for sleep deprived participants MG = 4.11, MT = 3.98, MI = 2.42 F(2, 76) = 27.13, p < .001 q(3, 76) = 0.72, ns (Ghostbusters = Terminator) q(3, 76) = 9.42, p < .01 (Ghostbusters > Indiana Jones) q(3, 76) = 8.69, p < .01 (Terminator > Indiana Jones) • simple main effect of movies for tons-of-sleep participants MG = 3.54, MT = 3.56, MI = 2.97 etc… Example: Method 1 of Interpreting Interaction
- 60. Assignment: What to Report for Question 1 Between-Subjects Variable at Each Level of Within-Subjects Variable (sleep status at each level of movie) • simple main effect of sleep status for Ghostbusters MDEPRIVED = 4.11, MLOTS = 3.54 F(1, 93) = 3.324, p < .05 • simple main effect of movies for Terminator MDEPRIVED = 3.98, MLOTS = 3.56 etc… Example: Method 2 of Interpreting Interaction Don’t forget to address part B!
- 61. • introductory paragraph o general overview of study o provide design being used (split plot) o identify IVs (and levels) specify which is between-subjects, within-subjects o identify DV • tests of assumptions o Levene’s test for between-subjects factor (all F-values applicable) o Mauchly’s test for within-subjects factor o write a concluding sentence for each test, stating what we can conclude on basis of results Assignment: What to Report in Results Section
- 62. • interaction effect o report F-statistics (with df and p-value), effect size, power o if significant, report one set of simple main effects (repeat of question 1); no critical values need to be included in your report) o provide interpretation and caution regarding interpretation of main effects • main effect for within-subjects variable (Concept) o descriptive values o report F-statistics (with df and p-value), effect size, power o if significant, post hoc tests (with qcritical and qobtained values) o provide interpretation • main effect for between-subjects variable (groups) o report F-statistics (with df and p-value), effect size, power o if significant, post hoc tests (with qcritical and qobtained values) o provide interpretation and caution if interaction significant • general conclusion Assignment: What to Report in Results Section
- 63. • use Greenhouse Geisser corrected values for the ANOVA (where applicable… within-subjects and interaction) but use sphericity assumed values for post hoc tests • use the appropriate error term in reporting your results o Tests of Within-Subjects Effects: overall interaction (adjusted), overall within- subjects main effect (adjusted), post hoc for within-subjects main effect (unadjusted) o Tests of Between-Subjects Effects: overall between-subjects main effect, post hoc for between-subjects main effect o pooled error term (POST HOC program or hand calculation): SME of between-subjects factor at leach level of within-subjects factor o MANOVA output: SME of within-subjects factor at each level of between- subjects factor Helpful Hints
- 64. Good Friday: Update • Friday lab section has been re-scheduled as follows: Wednesday, March 27, 2013 10:30 AM – 12:30 PM SSC 1020 (computer lab in basement of SSC) • will be sending out a general e-mail outlining who I have attending which lab section (mine, Sarah’s, Paul’s) if there is an error or if you have changed your preference, let me know I will be forward a list of student names to Sarah/Paul, so they know how many students to expect • deadline for the assignment that week will be Thursday, March 28, 5:00 PM can submit earlier
- 65. Make sure you have and understand all output Before you leave lab today!

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