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SPSS

SPSS. Collect. Chapter 12. A Priori and Post Hoc Comparisons Multiple t-tests Linear Contrasts Orthogonal Contrasts Trend Analysis Bonferroni t Fisher Least Significance Difference Studentized Range Statistic Dunnett’s Test. Multiple t-tests.

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SPSS

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  1. SPSS • Collect

  2. Chapter 12 • A Priori and Post Hoc Comparisons • Multiple t-tests • Linear Contrasts • Orthogonal Contrasts • Trend Analysis • Bonferroni t • Fisher Least Significance Difference • Studentized Range Statistic • Dunnett’s Test

  3. Multiple t-tests • Good if you have just a couple of planned comparisons • Do a normal t-test, but use the other groups to help estimate your error term • Helps increase you df

  4. Hyp 1: Juniors and Seniors will have different levels of happiness Hyp 2: Seniors and Freshman will have different levels of happiness

  5. Chapter 12 • A Priori and Post Hoc Comparisons • Multiple t-tests • Linear Contrasts • Orthogonal Contrasts • Trend Analysis • Bonferroni t • Fisher Least Significance Difference • Studentized Range Statistic • Dunnett’s Test

  6. Linear Contrasts • You think that Freshman and Seniors will have different levels of happiness than Sophomores and Juniors

  7. Linear Contrasts • Allows for the comparison of one group or set of groups with another group or set of groups

  8. Linear Contrasts a = weight given to a group

  9. Linear Contrasts 1 2 3 4 a1 = 0, a2 = 0, a3 = 1, a4 = -1 L = -23 a1 = 1, a2 = 0, a3 = 0, a4 = -1 L = -9 a1 = .5, a2 = -.5, a3 = -.5, a4 = .5 L = 80.5 – 67 = 13.5

  10. SS Contrast • You can use the linear contrast to compute a SS contrast • SS contrast is like SS between • SS contrast has 1 df • SS contrast is like MS between

  11. SS Contrast

  12. SS Contrasts a1 = .5, a2 = -.5, a3 = -.5, a4 = .5 L = 80.5 – 67 = 13.5

  13. SS Contrasts a1 = .5, a2 = -.5, a3 = -.5, a4 = .5 L = 80.5 – 67 = 13.5 n = 6 L = 13.5 Sum a2 = .52+-.52+ -.52 + .52 = 1

  14. SS Contrasts a1 = .5, a2 = -.5, a3 = -.5, a4 = .5 L = 80.5 – 67 = 13.5 n = 6 L = 13.5 Sum a2 = .52+-.52+ -.52 + .52 = 1

  15. SS Contrasts a1 = 1, a2 = -1, a3 = -1, a4 = 1 L = 161 – 134 = 27

  16. SS Contrasts a1 = 1, a2 = -1, a3 = -1, a4 = 1 L = 161 – 134 = 27 n = 6 L = 27 Sum a2 = 12+-12+ -12 + 12 = 4

  17. SS Contrasts a1 = 1, a2 = -1, a3 = -1, a4 = 1 L = 161 – 134 = 27 n = 6 L = 27 Sum a2 = 12+-12+ -12 + 12 = 4

  18. F Test Note: MS contrast = SS contrast

  19. F Test Fresh & Senior vs. Sophomore & Junior

  20. F Test Fresh & Senior vs. Sophomore & Junior

  21. F Test Fresh & Senior vs. Sophomore & Junior F crit (1, 20) = 4.35

  22. SPSS

  23. Make contrasts to determine • If seniors are happier than everyone else? 2) If juniors and sophomores have different levels of happiness?

  24. If seniors are happier than everyone else? a1 = -1, a2 = -1, a3 = -1, a4 = 3 L = 45 F crit (1, 20) = 4.35

  25. 2) If juniors and sophomores have different levels of happiness? a1 = 0, a2 = -1, a3 = 1, a4 = 0 L = -10 F crit (1, 20) = 4.35

  26. Chapter 12 • A Priori and Post Hoc Comparisons • Multiple t-tests • Linear Contrasts • Orthogonal Contrasts • Trend Analysis • Bonferroni t • Fisher Least Significance Difference • Studentized Range Statistic • Dunnett’s Test

  27. Contrasts • Some contrasts are independent • Freshman vs. Sophomore (1, -1, 0, 0) • Junior vs. Senior (0, 0, 1, -1) • Some are not • Freshman vs. Sophomore, Junior, Senior (3, -1, -1, -1) • Freshman vs. Sophomore & Junior (2, -1, -1, 0)

  28. Orthogonal Contrasts • If you have a complete set of orthogonal contrasts • The sum of SScontrast = SSbetween

  29. Orthogonal Contrasts • 1) ∑ aj = 0 • Already talked about • 2) ∑ aj bj = 0 • Ensures contrasts of independent of one another • 3) Number of comparisons = K -1 • Ensures enough comparisons are used

  30. Orthogonal Contrasts • ∑ aj bj = 0 • Fresh, Sophomore, Junior, Senior • (3, -1, -1, -1) and (2, -1, -1, 0) • (3*2)+(-1*-1)+(-1*-1) = 8

  31. Orthogonal Contrasts • ∑ aj bj = 0 • Fresh, Sophomore, Junior, Senior • (-1, 1, 0, 0) & (0, 0, -1, 1) • (-1*0)+(1*0)+(-1*0)+(1*0) = 0 • *Note: this is not a complete set of contrasts (rule 3)

  32. Orthogonal Contrasts • Lets go to five groups • What would the complete set contrasts be that would satisfy the earlier rules?

  33. Orthogonal Contrasts • General rule • There is more than one right answer

  34. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad Fresh & Soph vs. Jun, Sen, & Grad Fresh vs. Soph Jun & Sen vs. Grad Jun vs. Sen

  35. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad Fresh & Soph vs. Jun, Sen, & Grad Fresh vs. Soph Jun & Sen vs. Grad Jun vs. Sen 2 limbs are created The elements on different limbs can not be combined with each other Elements on the same limbs can be combined with each other (making new limbs)

  36. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad Fresh & Soph vs. Jun, Sen, & Grad Fresh vs. Soph Jun & Sen vs. Grad Jun vs. Sen

  37. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad Fresh & Soph vs. Jun, Sen, & Grad Fresh vs. Soph Jun & Sen vs. Grad Jun vs. Sen

  38. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad Fresh & Soph vs. Jun, Sen, & Grad Fresh vs. Soph Jun & Sen vs. Grad Jun vs. Sen

  39. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad Fresh & Soph vs. Jun, Sen, & Grad Fresh vs. Soph Jun & Sen vs. Grad Jun vs. Sen 3, 3, -2, -2, -2

  40. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad Fresh & Soph vs. Jun, Sen, & Grad Fresh vs. Soph Jun & Sen vs. Grad Jun vs. Sen 3, 3, -2, -2, -2 1, -1, 0, 0, 0

  41. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad Fresh & Soph vs. Jun, Sen, & Grad Fresh vs. Soph Jun & Sen vs. Grad Jun vs. Sen 3, 3, -2, -2, -2 1, -1, 0, 0, 0 0, 0, 1, 1, -2

  42. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad Fresh & Soph vs. Jun, Sen, & Grad Fresh vs. Soph Jun & Sen vs. Grad Jun vs. Sen 3, 3, -2, -2, -2 1, -1, 0, 0, 0 0, 0, 1, 1, -2 0, 0, 1, -1, 0

  43. Orthogonal Contrasts • 1) ∑ aj = 0 • 2) ∑ aj bj = 0 • 3) Number of comparisons = K -1 • 3, 3, -2, -2, -2 • 1, -1, 0, 0, 0 • 0, 0, 1, 1, -2 • 0, 0, 1, -1, 0

  44. Orthogonal Contrasts • 1) ∑ aj = 0 • 2) ∑ aj bj = 0 • 3) Number of comparisons = K -1 • 3, 3, -2, -2, -2 = 0 • 1, -1, 0, 0, 0 = 0 • 0, 0, 1, 1, -2 = 0 • 0, 0, 1, -1, 0 = 0

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