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Unit 10 lesson 1

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Unit 10 lesson 1

  1. 1. Unit 10: Repeated Measures ANOVA Lesson 1: Further Applications of the ANOVA EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas Time Score Next Slide
  2. 2. Paired Samples t-test Occasion 3 12 11 12 15 16 14 Next Slide Occasion 2 9 8 7 8 9 8 Occasion 1 5 4 4 5 6 5 Person 1 Person 2 Person 3 Person 4 Person 5 Person 6 t-test t-test t-test
  3. 3. Repeated Measures ANOVA Where X ik is person i ’s score in group k T is the sum of all scores N is the total number of observations Next Slide NOTICE: No means!!!
  4. 4. Sum of Squares Total SS T = 54.667 Next Slide ANOVA Repeated Measures
  5. 5. Why Do Repeated Measures? In ANOVA: SS T = SS B + SS W <ul><li>In Repeated Measures ANOVA: </li></ul><ul><li>variation among individuals (SS I ) </li></ul><ul><li>variation among occasions (SS O ) </li></ul><ul><li>residual variation or error (SS Res ) </li></ul>Next Slide SS T SS W SS B SS T SS Res SS O SS I
  6. 6. Why Do RM? (cont). 1. The partitioning of the variation in the ANOVA needs to be adjusted so that we are using the correct df (and SS) to compute F-calc based on the corrected MS error . 2. We may or may not improve our chances of obtaining statistical significance. 3. Since we are partitioning out the variation due to individual differences from the residual variation (error), we will most likely note a larger eta-squared (this is an artificial eta-squared, however). Next Slide
  7. 7. Setting Up The Data Use the same example data for repeated measures as is in your book Mean test1 = 6.1 Mean test2 = 10.6 Mean test3 = 15.3 Next Slide
  8. 8. Using SPSS for Analysis Analyze  General Linear Model  Repeated Measures Next Slide
  9. 9. Analyzing the Data Next Slide
  10. 10. The Sphericity Assumption <ul><li>Put succinctly, the sphericity assumption (also called compound symmetry) states that the variance at each measurement occasion should be equal. </li></ul><ul><li>Interpret results the same way we would Levine’s test for homogeneity of variance in ANOVA. </li></ul>Next Slide
  11. 11. What if we don’t meet the sphericity assumption? Use a “correction” for the df: <ul><li>Greenhouse-Geisser </li></ul><ul><li>Huynh-Feldt </li></ul><ul><li>Lower-bound </li></ul>These all correct the df in an analysis and make it more difficult to find statistically significant results Next Slide
  12. 12. Reading the Results Next Slide Occasions Residual Individuals
  13. 13. The “Correct” Summary Table Next Slide
  14. 14. ANOVA vs. Repeated Measures Next Slide Data treated as a One-Way ANOVA with 3 levels 3 Repeated Measurements
  15. 15. Eta-squared in Repeated Measures Next Slide SS T SS Res SS O SS I In ANOVA: In Repeated Measures ANOVA:
  16. 16. The Final Summary Table Next Slide
  17. 17. Polynomial Trends Next Slide Linear Trend Quadratic Trend test1 test2 test3 Mean 6.1 10.6 15.3
  18. 18. Polynomial Trends (cont.) Next Slide Cubic Trend 5 data points Cubic Trend 4 data points
  19. 19. Unit 10: Repeated Measures ANOVA Lesson 1: Further Applications of the ANOVA EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas Time Score

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