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SPSS Series 3: Repeated Measures ANOVA and MANOVA

SPSS Series 3: Repeated Measures ANOVA and MANOVA. By Hui Bian Office for Faculty Excellence. List of topics. Repeated measures ANOVA with SPSS One-way within-subjects ANOVA with SPSS One between and one within mixed design with SPSS Repeated measures MANOVA with SPSS

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SPSS Series 3: Repeated Measures ANOVA and MANOVA

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  1. SPSS Series 3: Repeated Measures ANOVA and MANOVA By HuiBian Office for Faculty Excellence

  2. List of topics • Repeated measures ANOVA with SPSS • One-way within-subjects ANOVA with SPSS • One between and one within mixed design with SPSS • Repeated measures MANOVA with SPSS • How to interpret SPSS outputs • How to report results

  3. GLM Repeated Measures • When the same measurement is made several times on each subject or case, such as • Same group of people are pretested and post-tested on a dependent variable. • Comparing the same subjects under several different treatments. • Interested in the performance trends over time: is it linear, quadratic, or cubic?

  4. GLM Repeated Measures • Between and within factors • Between factors: a grouping or classification variables such as sex, age, grade levels, treatment conditions etc. • Within factors: is the one with multiple measures from a group of people such as time.

  5. Repeated measures • Assumptions • Independence of the observations • Violation is serious • Multivariate normality • Fairly robust against violation • Sphericity • Not necessary for the multivariate approach • The variance-covariance matrices are the same across the cells formed by the between-subjects effects.

  6. One-way within-subjects ANOVA • A simplest design • One within-subjects factor • One dependent variable • A group of subjects measured at different points in time

  7. One-way within-subjects ANOVA • Example: sample is from high school students. • Research questions: • 1. whether there is a significant change on frequency of drinking over time (3 months) before and after treatment; • 2. whether the relationship between the within factor (time) and frequency of drinking is linear, quadratic, or cubic. • Within-subjects factor: time. • Dependent variable: frequency of drinking (a28 and b28). • Two-time points data: a28 means baseline and b28 means 3-month posttest • Two conditions: before treatment and after treatment

  8. One-way within-subjects ANOVA • The design

  9. One-way within-subjects ANOVA • Select Intervention group as our sample • Go to Data Select Cases • Check If conditions… • Then click If

  10. One-way within-subjects ANOVA • Let Conditions = 1 • Then click Continue

  11. One-way within-subjects ANOVA • Run Repeated Measures analysis • Analyze General Linear Model Repeated Measures • Type Time as Within-Subject Factor Name, type 2 as Number of Levels, then click Add • Type dv1 as Measure Name (dv means dependent variable), then click Add

  12. One-way within-subjects ANOVA • Then click Define

  13. One-way within-subjects ANOVA • After Define you should get this window • Move a28 to (1, dv1) • Move b28 to (2, dv2)

  14. One-way within-subjects ANOVA • We don’t have any between-subjects factors • Click Options to get this Check Compare main effects even we have two levels for within-subjects factor. I just want to show the pair comparison function.

  15. One-way within-subjects ANOVA • Click Plots to get this window

  16. One-way within-subjects ANOVA • SPSS outputs • Descriptive statistic results

  17. One-way within-subjects ANOVA • SPSS outputs • Within-subjects effect: results of two tables are same.

  18. One-way within-subjects ANOVA Correction options include Geenhouse-Geisser, Huyn-Feldt, and Lower-bound when sphericity is not assumed. They produce more conservative estimates.

  19. One-way within-subjects ANOVA • SPSS outputs • Within-subjects effect: if there is no homogeneity of dependent variable covariance matrix, the Sphericity is not assumed. We should use the correction options.

  20. One-way within-subjects ANOVA • SPSS outputs • The mathematical properties underlying the relationship between within-subjects factor and dependent variable. Test linear component of Time effect The linear component is not significant

  21. One-way within-subjects ANOVA • SPSS outputs • Plot

  22. One-way within-subjects ANOVA Quadratic Cubic

  23. One-way within-subjects ANOVA • SPSS outputs • Pairwise comparisons: the within-subjects factor only has two levels. So we get the same results as multivariate tests table shows.

  24. One-way within-subjects ANOVA • Results • One-way within-subjects ANOVA was performed to test whether there was a difference of frequency of drinking between before-treatment and after-treatment conditions. The observed F value was not statistically significant, F(1, 136) = .42, p = .52, partial η2= .003, which indicated no difference of frequency of drinking over time.

  25. Two-way Mixed Design (ANOVA) • Two-way mixed design • Two independent factors: one is a between-subjects factor and one is a within-subjects factor • One dependent variable. • Tests null hypotheses about the effects of both the between-subjects factor and within-subjects factor. • Tests the effect of interactions between factors.

  26. Two-way Mixed Design (ANOVA) • Example: • Research questions: • whether there is a significant change on frequency of drinking over time (3 months) between intervention and control group. • Within-subjects factor: time. • Between-subjects factor: conditions (intervention vs. control). • Dependent variable: frequency of drinking (a28 and b28). • Two-time points data: a28 means baseline and b28 means 3-month posttest

  27. Two-way Mixed Design (ANOVA) • The design

  28. Two-way Mixed Design (ANOVA) • Run repeated measures analysis • Select all cases • Go to AnalyzeGeneral Linear ModelRepeated Measures • The same procedure to define the within-subjects factor and dependent variable. • Move Conditions to…

  29. Two-way Mixed Design (ANOVA) • Click Options • Click Plots

  30. Two-way Mixed Design (ANOVA) • SPSS outputs • Multivariate tests

  31. Two-way Mixed Design (ANOVA) • SPSS outputs • Estimated marginal means

  32. Two-way Mixed Design (ANOVA) • SPSS outputs • Plots

  33. Two-way Mixed Design (ANOVA) • Results • The intervention effect was analyzed using repeated measures ANOVA. There was no statically significant difference between intervention and control group over time on frequency of drinking, F(1,285) = .90, p = .34, partial η2 = .003.

  34. Two-way Mixed Design (MANOVA) • Example • Research questions: • whether there is a significant change on drinking behaviors over time (3 months) between intervention and control groups; or whether there is an intervention effect on drinking behaviors. • Within-subjects factor: time. • Between-subjects factor: conditions (two levels) • Dependent variables: frequency of drinking (a28 and b28), quantity of drinking (a31 and b31), and heavy drinking (a34 and b34). • Two-time points data: baseline and posttest

  35. Two-way Mixed Design (MANOVA) • Run repeated measures analysis • Go to Analyze General Linear Model Repeated Measures • We have three dependent variables • Still one within-subjects factor • Click Define

  36. Two-way Mixed Design (MANOVA) • Move a28/b28, a31/b31, and a34/b34 to…

  37. Two-way Mixed Design (MANOVA) • Options and Plots

  38. Two-way Mixed Design (MANOVA) • SPSS outputs • Multivariate tests

  39. Two-way Mixed Design (MANOVA) • SPSS outputs • Within-subjects effects

  40. Two-way Mixed Design (MANOVA) • SPSS outputs • Univariate tests

  41. Two-way Mixed Design (MANOVA) • SPSS outputs • Estimated marginal means

  42. Two-way Mixed Design (MANOVA) • SPSS outputs • Plots: dv1 (frequency of drinking)

  43. Two-way Mixed Design (MANOVA) • SPSS outputs • Plots: dv2 (quantity of drinking)

  44. Two-way Mixed Design (MANOVA) • SPSS outputs • Plots: dv3 (heavy drinking)

  45. Two-way Mixed Design (MANOVA) • Results • Repeated measures MANOVA test was conducted to test intervention effect on drinking behaviors. The results showed there was no difference between intervention and control group on frequency, quantity, and heavy drinking over time, F(3, 283) = 1.18, p = .32, η2 = .01. Univariate tests also indicated there was no intervention effect on individual drinking behavior, F(1, 285) = .90, p = .34, η2 = .003 for frequency, F(1, 285) = .67, p = .41, η2 = .002 for quantity, and F(1, 285) = .39, p = .53, η2 = .001 for heavy drinking.

  46. GLM Repeated Measures Contrasts • Example (planned comparisons) • One within-subjects factor: time • One between-subjects factor: living condition (11r) • One dependent variable: frequency of drinking (a28 and b28)

  47. GLM Repeated Measures Contrasts • Contrasts are used to test for differences among the levels of a between-subjects factor. • Go to Analyze General Linear Model Repeated Measures • The same procedure to define within-subjects factor and dependent variable • Click Contrasts

  48. GLM Repeated Measures Contrasts • You should get the left window • Choose Simple (simple means compares the mean of each level to the mean of a reference). Pull down

  49. GLM Repeated Measures Contrasts • Decide which category of between-subjects factor is a reference category. • The between-subjects factor is a11r: 1= Mother and father; 2 = Mother and stepfather; 3 = Mother; 4 = Others. • Use 1 = Mother and father as a reference. Check First, then click Change

  50. GLM Repeated Measures Contrasts • SPSS outputs

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