Lecture slides stats1.13.l18.air
- 1. Statistics One Lecture 18 Repeated measures ANOVA 1
- 2. Two segments • Repeated measures: Pros & Cons • Repeated measures: Example 2
- 3. Lecture 18 ~ Segment 1 Repeated measures Pros & Cons 3
- 4. Repeated measures: Pros & cons • Pros – Less cost (fewer subjects required) – More statistical power • This is the important new concept
- 5. Repeated measures: Pros & cons • Working memory training example • Four independent groups (8, 12, 17, 19) – There were 20 subjects per group – Total N = 80 5
- 6. Repeated measures: Pros & cons • Working memory training example • Repeated measures design – N = 20 6
- 7. Repeated measures: Pros & cons • More statistical power – Variance across subjects may be systematic – If so, it will not contribute to the error term
- 8. Between groups design (SS) Systematic/ Between (A) Unsystematic/ Within (S/A)
- 9. Repeated measures design (SS) Between (A) Subjects(S) Unsystematic = (AxS) Error in a repeated measures design is the inconsistency of subjects from one condition to another Therefore: FA = MSA / MSAxS
- 10. MS and F • MSA = SSA / dfA • MSAxS = SSAxS / dfAxS • F = MSA / MSAxS
- 11. Repeated measures: Pros & cons • Cons – Order effects – Counterbalancing – Missing data – Extra assumption
- 12. Counterbalancing • Consider a simple design with just two conditions, A1 and A2 • One approach is a Blocked Design – Subjects are randomly assigned to one of two “order” conditions • A1, A2 • A2, A1
- 13. Counterbalancing • Another approach is a Randomized Design – Conditions are presented randomly in a mixed fashion • A2, A1, A1, A2, A2, A1, A2…..
- 14. Counterbalancing • Now suppose a = 3 and a blocked design • There are 6 possible orders (3!) • • • • • • A1, A2, A3 A1, A3, A2 A2, A1, A3 A2, A3, A1 A3, A1, A2 A3, A2, A1
- 15. Counterbalancing • To completely counterbalance, subjects would be randomly assigned to one of 6 order conditions • The number of conditions needed to completely counterbalance becomes large with more conditions – 4! = 24 – 5! = 120
- 16. Counterbalancing • With many levels of the IV a better approach is to use a “Latin Squares” design • Latin Squares designs aren’t completely counterbalanced but every condition appears at every position at least once
- 17. Counterbalancing • For example, if a = 3, then – A1, A2, A3 – A2, A3, A1 – A3, A1, A2
- 18. Missing data • Two issues to consider – Relative amount of missing data – Pattern of missing data
- 19. Missing data ~ Relative amount • How much is a lot? – No hard and fast rules – A rule of thumb is • Less than 10% on any one variable, OK • Greater than 10%, not OK
- 20. Missing data ~ Pattern? • Is the pattern random or lawful? – This can easily be detected – For any variable of interest (X) create a new variable (XM) • XM = 0 if X is missing • XM = 1 if X is not missing – Conduct a t-test with XM as the IV – If significant then pattern of missing data may be lawful
- 21. Missing data ~ Remedies • Drop all cases without a perfect profile – Drastic – Use only if you can afford it • Keep all cases and estimate the values of the missing data points – There are several options for how to estimate values
- 22. Sphericity assumption • Homogeneity of variance • Homogeneity of covariance
- 23. Sphericity assumption • How to test? – Mauchly’s test – If significant then report an adjusted p-value • Greenhouse-Geisser • Huyn-Feldt
- 24. Segment summary • Pros – Less cost (fewer subjects required) – More statistical power • This is the important new concept 24
- 25. Segment summary • Cons – Order effects – Counterbalancing – Missing data – Extra assumption 25
- 26. END SEGMENT 26
- 27. Lecture 18 ~ Segment 2 Repeated measures ANOVA Example 27
- 28. Repeated measures: Pros & cons • Working memory training example • Four independent groups (8, 12, 17, 19) – There were 20 subjects per group – Total N = 80 28
- 29. Repeated measures: Pros & cons • Working memory training example • Repeated measures design – N = 20 29
- 31. Common dataframe subject A1 (8) A2 (12) A3 (17) A4 (19) 1 2 3 4 5 6 … 31
- 32. R dataframe subject 1 1 1 1 2 2 … condition A1 (8) A2 (12) A3 (17) A4 (19) A1 (8) A2 (12) IQ 32
- 34. Results: Post-hoc tests (Holm) 34
- 35. Results: Post-hoc tests (Bonferroni) 35
- 36. Results: Paired t-test 12 vs. 17 36
- 37. Comparison of procedures Procedure p-value for 12 vs. 17 Paired t-test 0.0065 Holm 0.0192 Bonferroni 0.0391 37
- 38. Repeated measures ANOVA • Appropriate when comparing group means – Three or more group means – Same subjects tested in each condition – F-test – Post-hoc testss 38
- 39. END SEGMENT 39