1. Statistics for the Social Sciences Psychology 340 Fall 2006 ANOVA: Book vs. instructor

2. Statistics for the Social Sciences Outline Comparing how the book computes ANOVA and how I compute ANOVA

3. Statistics for the Social Sciences Partitioning the variance Total variance Stage 1 Between groups variance Within groups variance Stage 2 Between subjects varianceError variance

4. Statistics for the Social Sciences Partitioning: Stage 1 PlaceboDrug ADrug BDrug C 3467 0336 2145 0134 0143 Total variance Stage 1 Between groups variance Within groups variance

5. Statistics for the Social Sciences Total variance Stage 1 Between groups varianceWithin groups variance Partitioning: Stage 1

6. Statistics for the Social Sciences The Between groups variance Assumes equal numbers of participants in each group Can use unequal numbers of participants in each group Variance of the distribution of means Sums of Squares for Between

7. Statistics for the Social Sciences The Within groups variance Adding Sums of Squares of each group Adding Variances of Each group

8. Statistics for the Social Sciences Partitioning: Stage 1 PlaceboDrug ADrug BDrug C 3467 0336 2145 0134 0143

9. Statistics for the Social Sciences PlaceboDrug ADrug BDrug C 3467 0336 2145 0134 0143 Partitioning: Stage 1

10. Statistics for the Social Sciences Partitioning: Stage 1

11. Statistics for the Social Sciences Partitioning the variance Total variance Stage 1 Between groups varianceWithin groups variance Stage 2 Between subjects varianceError variance

12. Statistics for the Social Sciences Partitioning the variance PlaceboDrug ADrug BDrug C 3467 0336 2145 0134 0143 What is ? The average score for each person Between subjects variance

13. Statistics for the Social Sciences Partitioning the variance PlaceboDrug ADrug BDrug C 3467 0336 2145 0134 0143 Between subjects variance

14. Statistics for the Social Sciences Partitioning the variance Between subjects variance

15. Statistics for the Social Sciences Partitioning the variance PlaceboDrug ADrug BDrug C 3467 0336 2145 0134 0143 Error variance

16. Statistics for the Social Sciences Partitioning the variance Error variance Do this for each score (so here you do it 20 times) PlaceboDrug ADrug BDrug C 3467 0336 2145 0134 0143

17. Statistics for the Social Sciences Reporting your results 1 Factor ANOVA –The observed difference –Kind of test –Degrees of freedom for the test –Computed F-ratio –The “p-value” of the test –Any post-hoc or planned comparison results “The mean score of Group A was 12, Group B was 25, and Group C was 27. A 1-way between groups ANOVA was conducted and the results yielded a significant difference, F(2,25) = 5.67, p < 0.05. Post hoc tests revealed that the differences between groups A and B and A and C were statistically reliable (respectively t(1) = 5.67, p < 0.05 & t(1) = 6.02, p <0.05). Groups B and C did not differ significantly from one another” “within”