SPSS Problem # 7

2. SPSS Problem # 7 • Page 467 • 13.5 • Page 416 • 12.2

3. Cookbook due WednesdayMay 4th!!

4. What if. . . • You were asked to determine if psychology and sociology majors have significantly different class attendance (i.e., the number of days a person misses class) • You would simply do a two-sample t-test • two-tailed • Easy!

5. But, what if. . . • You were asked to determine if psychology, sociology, and biology majors have significantly different class attendance • You would do a one-way ANOVA

6. But, what if. . . • You were asked to determine if psychology majors had significantly different class attendance than sociology and biology majors. • You would do an ANOVA with contrast codes

7. But, what if. . . • You were asked to determine the effects of both college major (psychology, sociology, and biology) and gender (male and female) on class attendance • You now have 2 IVs and 1 DV • You could do two separate analyses • Problem: “Throw away” information that could explain some of the “error” • Problem: Will not be able to determine if there is an interaction

8. Factorial Analysis of Variance • Factor = IV • Factorial design is when every level of every factor is paired with every level of every other factor

9. Main effect of gender

10. Main effect of major

11. Interaction between gender and major

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

13. SStotal = (2-2.06)2+ (3-2.06)2+ . . . . (1-2.06)2 = 30.94 *What makes this value get larger?

14. SStotal = (2-2.06)2+ (3-2.06)2+ . . . . (1-2.06)2 = 30.94 *What makes this value get larger? *The variability of the scores!

15. Sum of Squares • SS A • Represents the SS deviations of the treatment means around the grand mean • Its multiplied by nb to give an estimate of the population variance (Central limit theorem) • Same formula as SSbetween in the one-way

16. SSA = (3*3) ((1.78-2.06)2+ (2.33-2.06)2)=1.36 *Note: it is multiplied by nb because that is the number of scores each mean is based on

17. SSA = (3*3) ((1.78-2.06)2+ (2.33-2.06)2)=1.36 *What makes these means differ? *Error and the effect of A

18. Sum of Squares • SS B • Represents the SS deviations of the treatment means around the grand mean • Its multiplied by na to give an estimate of the population variance (Central limit theorem) • Same formula as SSbetween in the one-way

19. SSB = (3*2) ((3.17-2.06)2+ (2.00-2.06)2+ (1.00-2.06)2)= 14.16 *Note: it is multiplied by na because that is the number of scores each mean is based on

20. SSB = (3*2) ((3.17-2.06)2+ (2.00-2.06)2+ (1.00-2.06)2)= 14.16 *What makes these means differ? *Error and the effect of B

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

22. SSCells = (3) ((2.67-2.06)2+ (1.00-2.06)2+. . . + (0.33-2.06)2)= 24.35

23. SSCells = (3) ((2.67-2.06)2+ (1.00-2.06)2+. . . + (0.33-2.06)2)= 24.35 What makes the cell means differ?

24. Sum of Squares • SS Cells • What makes the cell means differ? • 1) error • 2) the effect of A (gender) • 3) the effect of B (major) • 4) an interaction between A and B

25. Sum of Squares • Have a measure of how much cells differ • SScells • Have a measure of how much this difference is due to A • SSA • Have a measure of how much this difference is due to B • SSB • What is left in SScells must be due to error and the interaction between A and B

26. Sum of Squares • SSAB = SScells - SSA – SSB • 8.83 = 24.35 - 14.16 - 1.36

27. Sum of Squares • SSWithin • The total deviation in the scores not caused by • 1) the main effect of A • 2) the main effect of B • 3) the interaction of A and B • SSWithin = SSTotal – (SSA + SSB + SSAB) 6.59 = 30.94 – (14.16 +1.36 + 8.83)

28. Sum of Squares • SSWithin

29. SSWithin = ((2-2.67)2+(3-2.67)2+(3-2.67)2) + . .. + ((1-.33)2 + (0-.33)2 + (0-2..33)2 = 6.667

30. SSWithin = ((2-2.67)2+(3-2.67)2+(3-2.67)2) + . .. + ((1-.33)2 + (0-.33)2 + (0-2..33)2 = 6.667 *What makes these values differ from the cell means? *Error

31. Compute df

32. dftotal = N - 1

33. dftotal = N – 1 dfA = a – 1 dfB = b - 1

34. dftotal = N – 1 dfA = a – 1 dfB = b – 1 dfAB = dfa * dfb

35. dftotal = N – 1 dfA = a – 1 dfB = b – 1 dfAB = dfa * dfb dfwithin= ab(n – 1)

36. Compute MS

37. Compute MS

38. What does each MS mean?

39. Compute F

40. Compute F

41. Test each F value for significance F critical values (may be different for each F test) Use df for that factor and the df within.

42. Test each F value for significance F critical A (1, 12) = 4.75 F critical B (2, 12) = 3.89 F critical AB (2, 12) = 3.89

43. Test each F value for significance F critical A (1, 12) = 4.75 F critical B (2, 12) = 3.89 F critical AB (2, 12) = 3.89

45. Interpreting the Results • Main Effects • Easy – just like a one-way ANOVA

47. Interpreting the Results • Interaction • Does the effect of one IV on the DV depend on the level of another IV?

48. Want to plot out the cell means

49. Sociology Psychology Biology

50. Practice • 2 x 2 Factorial • Determine if • 1) there is a main effect of A • 2) there is a main effect of B • 3) if there is an interaction between AB