Why is this important?

2. Why is this important? • Requirement • Understand research articles • Do research for yourself • Real world

3. The Three Goals of this Course • 1) Teach a new way of thinking • 2) Teach “factoids”

4. Mean

5. r =

6. What you have learned! • Describing and Exploring Data / The Normal Distribution • Scales of measurement • Populations vs. Samples • Learned how to organize scores of one variable using: • frequency distributions • graphs

7. What you have learned! • Measures of central tendency • Mean • Median • Mode • Variability • Range • IQR • Standard Deviation • Variance

8. What you have learned! • Z Scores • Find the percentile of a give score • Find the score for a given percentile

9. What you have learned! • Sampling Distributions & Hypothesis Testing • Is this quarter fair? • Sampling distribution • CLT • The probability of a given score occurring

10. What you have learned! • Basic Concepts of Probability • Joint probabilities • Conditional probabilities • Different ways events can occur • Permutations • Combinations • The probability of winning the lottery • Binomial Distributions • Probability of winning the next 4 out of 10 games of Blingoo

11. What you have learned! • Categorical Data and Chi-Square • Chi square as a measure of independence • Phi coefficient • Chi square as a measure of goodness of fit

12. What you have learned! • Hypothesis Testing Applied to Means • One Sample t-tests • Two Sample t-tests • Equal N • Unequal N • Dependent samples

13. What you have learned! • Correlation and Regression • Correlation • Regression

14. What you have learned! • Alternative Correlational Techniques • Pearson Formulas • Point-Biserial • Phi Coefficent • Spearman’s rho • Non-Pearson Formulas • Kendall’s Tau

15. What you have learned! • Multiple Regression • Multiple Regression • Causal Models • Standardized vs. unstandarized • Multiple R • Semipartical correlations • Common applications • Mediator Models • Moderator Mordels

16. What you have learned! • Simple Analysis of Variance • ANOVA • Computation of ANOVA • Logic of ANOVA • Variance • Expected Mean Square • Sum of Squares

17. What you have learned! • Multiple Comparisons Among Treatment Means • What to do with an omnibus ANOVA • Multiple t-tests • Linear Contrasts • Orthogonal Contrasts • Trend Analysis • Controlling for Type I errors • Bonferroni t • Fisher Least Significance Difference • Studentized Range Statistic • Dunnett’s Test

18. What you have learned! • Factorial Analysis of Variance • Factorial ANOVA • Computation and logic of Factorial ANOVA • Interpreting Results • Main Effects • Interactions

19. What you have learned! • Factorial Analysis of Variance and Repeated Measures • Factorial ANOVA • Computation and logic of Factorial ANOVA • Interpreting Results • Main Effects • Interactions • Repeated measures ANOVA

20. The Three Goals of this Course • 1) Teach a new way of thinking • 2) Teach “factoids” • 3) Self-confidence in statistics

22. 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?

23. 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.

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

25. Tests to Compare Means

26. 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.

27. Results

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

29. Between Variability = low

30. Within Variability = high

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

33. 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

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

35. 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.

36. Example

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

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

39. 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!

40. 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)

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

42. 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

43. 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)

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

45. 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

46. 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!

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

48. Compute df df total = N -1

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

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