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Repeated Measures ANOVA

Repeated Measures ANOVA. One Factor, Correlated Measures: Same reasoning of Correlated Measures t-test More Power (and more efficient) Pulls out relatively small differences among treatments Relative to Big differences among subjects Removes Differences among subjects from error

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Repeated Measures ANOVA

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  1. Repeated Measures ANOVA • One Factor, Correlated Measures: • Same reasoning of Correlated Measures t-test • More Power (and more efficient) • Pulls out relatively small differences among treatments • Relative to Big differences among subjects • Removes Differences among subjects from error • term

  2. Subjects vs. Treatments  Large Differences (Error)   Small Differences (Effect) 

  3. Partitioning The Variance • SSTotal = SSSubjects + SSTreatment + SSError • SSError Is the Variability which a single subject would have • If you repeatedly measured him without changing treatment

  4. Partitioning The Variance Common Response to Tx Unique Response to Tx   • SSTotal = SSSubjects + SSTreatment + SSError • SSError Is the Variability which a single subject would have • If you repeatedly measured him without changing treatment

  5. The Structure of the ANOVA Partitioning the Total Sum of Squared Deviations From the Grand Mean • Spontaneous Variability of Subject • Change is not the same for each • Subject E.G., Strategies Subjects D.V.: Test Score • If you test your subjects repeatedly: • Counter Balance for (e.g.) practice effects/fatigue

  6. POC: Piece of Cake

  7. Step 1: Find The Total SS

  8. Step 2: Compute Between Subjects SS

  9. Step 3: Compute Treatment SS

  10. Step 4: Compute SS Error • This is the Same as the Interaction Term in a 2-Way ANOVA • IV1: Treatment • IV2: Subject • Interaction: Subject x Treatment

  11. Step 5: Determine Degrees of Freedom Just like Interaction df

  12. Step 6: Calculate MS & F

  13. If ANOVA is Significant Use Tukey Test to compare treatments • Nt is Number of Subjects in your • Experiment

  14. Caution • Caryover effects • Counter-balance • Vs. Trend Analysis • Populations Normally Distributed

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