1. Chapter 11 Hypothesis Tests: Two Related Samples

2. 2 Overview u Learning objectives u Vocabulary lesson again u Introduce t test for related samples u Advantages and disadvantages u An example u Review questions

3. 3 Learning Objectives u Difference between independent-measures & related-samples experimental design u Difference between repeated-measures & matched-subjects experimental design u Compute t test for dependent groups u Advantages and disadvantages u Measures of effect size

4. 4 Vocabulary u Related-samples t statistic Repeated- measures design u Matched-samples design u Difference scores (estimated standard error of D-bar) u Individual differences u Carry-over effects

5. 5 Related-samples t statistic u Two forms Repeated-measures design Matched-samples design u Use difference scores between two measurement points rather than means

6. 6 Repeated-measures u The same participants give us data on two measures (e. g. Before and After treatment) Aggressive responses before video and aggressive responses after u Accounts for the fact that if someone is high on one measure probably high on other.

7. 7 Matched-samples u Individuals in one group are matched to individuals in a second sample Matching based on variables thought to be relevant to the study Not always perfect match u Also called matched pairs or pairwise t test

8. 8 Difference Scores u Calculate difference between first and second score (between individual scores or matched pairs) e. g. Difference = Before – After D = X 2 -X 1 u Base subsequent analysis on difference scores

9. 9 The Formulas

10. 10 Hypothesis Testing u Null states that The population of difference scores has a mean of zero No systematic or consistent difference between the conditions u Alternative states that There is a real difference

11. 11 Advantages of Related Samples u Eliminate subject-to-subject variability Makes the test more powerful u Control for extraneous variables u Need fewer subjects

12. 12 Disadvantages of Related Samples u Order effects u Carry-over effects u Subjects no longer naïve u Change may just be a function of time u Sometimes not logically possible

13. 13 An Example u Therapy for rape victims Foa, Rothbaum, Riggs, & Murdock (1991) u A group (n=9) received Supportive Counseling u Measured post-traumatic stress disorder symptoms before and after therapy

14. 14 Step 1 u Null: there is no difference in symptoms in individuals after treatment u Alternative: there is a difference in symptoms u α=.05, two tailed

15. 15 Step 2 u With a sample of 9 df = n-1 = 9-1 = 8 Critical value = +2.306 u Sketch

16. 16 The Data: Therapy for PTSD

17. 17 Eye test of Results u The Supportive Counseling group decreased number of symptoms u Was this enough of a change to be significant? u Before and After scores are not independent; use related-samples t test

18. 18 Step 3 df = n - 1 = 9 - 1 = 8 Compute t test for related samples

19. 19 Step 4 u The critical value with 8 df, α=.05, two- tailed = +2.306 u We calculated t = 6.85 u Since 6.85 > 2.306, reject H 0 u Conclude that the mean number of symptoms after therapy was less than mean number before therapy. u Supportive counseling seems to work.

20. 20 SPSS u Next slide shows SPSS Printout Similar printout from other software Results match ours

21. 21

22. 22 Magnitude of difference by computing effect size u Two methods for computing effect size u Cohen’s d u r2

23. 23 Review Questions u Why do we say that the two sets of measures are not independent? u What are other names for “related samples?” u How do we calculate difference scores? What happens if we subtract before from after instead of after from before? Cont.

24. 24 Review Questions--cont.  Why do we usually test H 0 :  D = 0? u Why do we have 8 df in our sample when we actually have 18 observations? u What are the advantages and disadvantages of related samples?