Analysis of Variance: Part 2

Transcription

1 Analysis of Variance: Part 2 Oneway Repeated Measures ANOVA

2 Threats to Internal Validity History Maturation Testing Instrumentation Statistical Regression Experimental Mortality Selection-maturation interaction

3 Instrumentation In which changes in the calibration of a measuring instrument or changes in the observers or scorers used may produce changes in the obtained measurements.

4 Statistical Regression Operating where groups have been selected on the basis of their extreme scores.

5 Experimental Mortality or differential loss of respondents from the comparison groups.

6 Partitioning the Variance: Repeated Measures Variance

7 Partitioning the Variance: Repeated Measures Variance Between Subjects Subjects

8 Partitioning the Variance: Repeated Measures Variance Between Subjects Error Treatment Subjects

9 Between Subjects Variance The variance in the data that can be attributed to differences among the subjects. Irrelevant to the Hypothesis.

10 Subjects Variance Variance between subject s own scores on each repeated assessment. Treatment effects Error variance Variances among treatment means for each condition.

11 F-Ratio F= Treatment Variance Error Variance

12 Assumptions Treatments are not Independent Dependent Variable is measured on at least an ordinal scale Dependent Variable is normally distributed

13 When to use Repeated Measures ANOVA Same Subjects are in each treatment. There are 2 means or more to compare. (Can use for 2 groups: t is easier)

14 How to set up the ANOVA Summary Table

15 How to set up the ANOVA Summary Table

16 How to set up the ANOVA Summary Table Between Treatment Error

17 How to set up the ANOVA Summary Table Between Treat. Error Sums of SS S SS IV SS E SS T

18 How to set up the ANOVA Summary Table Between Treat. Error Sums of SS S SS IV SS E df df S df IV df E SS T df T

19 How to set up the ANOVA Summary Table Sums of df Mean Between SS S df S Treat SS IV df IV MS IV Error SS E df E MS E SS T df T

20 How to set up the ANOVA Summary Table Sums of df Mean F Between SS S df S MS S Treat SS IV df IV MS IV F Error SS E df E MS E SS T df T

21 Calculating the F Statistic Calculate Sums of Calculate df Calculate Mean Calculate F

22 How to Calculate the Sums of Between Sums of Between Treat. SS S SS IV p ( X ) k 2 T N 2 Error SS E SS T

23 How to Calculate the Sums of Between Sums of Sum of scores for each subject Between Treat. SS S SS IV p ( X ) k 2 T N 2 Error SS E SS T

24 How to Calculate the Sums of Between Between Treat. Error Sums of SS S SS IV SS E T== Sum of all scores. p ( X ) k 2 T N 2 SS T

25 How to Calculate the Sums of Between Sums of Between Treat. SS S SS IV p ( X ) k 2 T N 2 k=number treatments Error SS E SS T

26 How to Calculate the Sums of Between Between Treat. Error Sums of SS S SSN= IV number of scores SS E p ( X ) k 2 T N 2 SS T

27 How to Calculate the Sums of Sums of Between SS S Treat. SS IV Error SS E SS T X 2 T N 2

28 How to Calculate the Sums of Sums of Between SS S Treat. SS IV Error SS E Sum of all scores squared first SS T X 2 T N 2

29 How to Calculate the Sums of Sums of Between SS S for treatment j Treat. Error SS IV SS E j X n 2 2 T N SS T

30 How to Calculate the Sums of Sums of Between SS S Treat. Error SS IV SS E j X n 2 2 T N Number of subjects SS T

31 How to Calculate the Sums of Between Treat. Error Sums of SS S SS IV SS E SS T -SS IV -SS E SS T

32 How to Calculate the Degrees of Freedom Between Treat. Error Sums of SS S SS IV SS E df n-1 SS T df T

33 How to Calculate the Degrees of Freedom Between Treat. Error Sums of SS S SS IV SS E df n- 1 n is the number of subjects SS T df T

34 How to Calculate the Degrees of Freedom Between Treat. Error Sums of SS S SS IV SS E df n-1 k-1 SS T df T

35 How to Calculate the Degrees of Freedom Between Treat. Error Sums of SS S SS IV SS E df n-1 k-1 (n-1)(k-1) SS T df T

36 How to Calculate the Degrees of Freedom Between Treat. Error Sums of SS S SS IV SS E SS T df n-1 k-1 (n-1)(k-1) N-1

37 How to Calculate the Mean Sums of df Mean Between SS S df S Treat SS IV df IV MS IV Error SS E df E MS E SS T df T

38 How to Calculate F Sums of df Mean F Between SS S df S MS S Treat SS IV df IV MS IV Error SS E df E MS E = F SS T df T

39 Determining the Critical F Alpha =.05 Find Column for df Treatment Find Row for df Error Compare Critical F to Obtained F

40 Statistical Decision Making If Critical F > Obtained F failed to reject null hypothesis If Critical F < Obtained F reject the null hypothesis

41 Interpreting the Results Graph Means Use a multiple Comparison test to determine which means are significantly different

42 Multiple Comparisons Honestly Significant Difference Test HSD HSD = q a MS n error

43 Multiple Comparisons Honestly Significant Difference Test HSD HSD = q a MS n error Studentized Range Statistic (from Table)

44 Multiple Comparisons Honestly Significant Difference Test HSD Mean Square Error (from ANOVA) HSD = q a MS n error

45 Multiple Comparisons Honestly Significant Difference Test HSD HSD = q a MS n error Number of Subjects