1 / 80

Remember

Dive into the impact of a "magic math pill" on test scores through a repeated measures design with Repeated Measures ANOVA tests. Learn to analyze within and between-group variability and conduct F-tests for significance. Explore correlations and differences between subjects and treatment conditions.

lilianadavis
Download Presentation

Remember

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Remember • You just invented a “magic math pill” that will increase test scores. • On the day of the first test you give the pill to 4 subjects. When these same subjects take the second test they do not get a pill • Did the pill increase their test scores?

  2. What if. . . • You just invented a “magic math pill” that will increase test scores. • On the day of the first test you give a full pill to 4 subjects. When these same subjects take the second test they get a placebo. When these same subjects that the third test they get no pill.

  3. Note • You have more than 2 groups • You have a repeated measures design • You need to conduct a Repeated Measures ANOVA

  4. Tests to Compare Means

  5. What if. . . • You just invented a “magic math pill” that will increase test scores. • On the day of the first test you give a full pill to 4 subjects. When these same subjects take the second test they get a placebo. When these same subjects that the third test they get no pill.

  6. Results

  7. For now . . . Ignore that it is a repeated design

  8. Between Variability = low

  9. Within Variability = high

  10. Notice – the within variability of a group can be predicted by the other groups

  11. Notice – the within variability of a group can be predicted by the other groups Pill and Placebo r = .99; Pill and No Pill r = .99; Placebo and No Pill r = .99

  12. These scores are correlated because, in general, some subjects tend to do very well and others tended to do very poorly

  13. Repeated ANOVA • Some of the variability of the scores within a group occurs due to the mean differences between subjects. • Want to calculate and then discard the variability that comes from the differences between the subjects.

  14. Example

  15. Sum of Squares • SS Total • The total deviation in the observed scores • Computed the same way as before

  16. SStotal = (57-75.66)2+ (71-75.66)2+ . . . . (96-75.66)2 = 908 *What makes this value get larger?

  17. SStotal = (57-75.66)2+ (71-75.66)2+ . . . . (96-75.66)2 = 908 *What makes this value get larger? *The variability of the scores!

  18. Sum of Squares • SS Subjects • Represents the SS deviations of the subject means around the grand mean • Its multiplied by k to give an estimate of the population variance (Central limit theorem)

  19. SSSubjects = 3((60.33-75.66)2+ (72.33-75.66)2+ . . . . (93.66-75.66)2) = 1712 *What makes this value get larger?

  20. SSSubjects = 3((60.33-75.66)2+ (72.33-75.66)2+ . . . . (93.66-75.66)2) = 1712 *What makes this value get larger? *Differences between subjects

  21. Sum of Squares • SS Treatment • Represents the SS deviations of the treatment means around the grand mean • Its multiplied by n to give an estimate of the population variance (Central limit theorem)

  22. SSTreatment = 4((74-75.66)2+ (75-75.66)2+(78-75.66)2) = 34.66 *What makes this value get larger?

  23. SSTreatment = 4((74-75.66)2+ (75-75.66)2+(78-75.66)2) = 34.66 *What makes this value get larger? *Differences between treatment groups

  24. Sum of Squares • Have a measure of how much all scores differ • SSTotal • Have a measure of how much this difference is due to subjects • SSSubjects • Have a measure of how much this difference is due to the treatment condition • SSTreatment • To compute error simply subtract!

  25. Sum of Squares • SSError = SSTotal - SSSubjects – SSTreatment 8.0 = 1754.66 - 1712.00 - 34.66

  26. Compute df df total = N -1

  27. Compute df df total = N -1 df subjects = n – 1

  28. Compute df df total = N -1 df subjects = n – 1 df treatment = k-1

  29. Compute df df total = N -1 df subjects = n – 1 df treatment = k-1 df error = (n-1)(k-1)

  30. Compute MS

  31. Compute MS

  32. Compute F

  33. Test F for Significance

  34. Test F for Significance F(2,6) critical = 5.14

  35. Additional tests Can investigate the meaning of the F value by computing t-tests and Fisher’s LSD

  36. Remember

  37. Pill vs. Placebo

  38. Pill vs. Placebo t=1.23

  39. Pill vs. Placebo t=1.23 t (6) critical = 2.447

  40. Pill vs. Placebo t=1.23 Pill vs. No Pill t =4.98* t (6) critical = 2.447

  41. Pill vs. Placebo t=1.23 Pill vs. No Pill t =4.98* Placebo vs. No Pill t =3.70* t (6) critical = 2.447

  42. Practice • You wonder if the statistic tests are of all equal difficulty. To investigate this you examine the scores 4 students got on the three different tests. Examine this question and (if there is a difference) determine which tests are significantly different.

  43. SPSS Homework – Bonus 1) Determine if practice had an effect on test scores. 2) Examine if there is a linear trend with practice on test scores.

More Related