1. Chapter 13 Hypothesis Tests: Two Related Samples Fundamental Statistics for the Behavioral Sciences, 5th edition David C. Howell © 2003 Brooks/Cole Publishing Company/ITP

2. 2Chapter 13 Hypothesis Tests: Two Related Samples Major Points Related samples?Related samples? Difference scores?Difference scores? An exampleAn example t tests on difference scorest tests on difference scores Advantages and disadvantagesAdvantages and disadvantages Effect sizesEffect sizes Review questionsReview questions

3. 3Chapter 13 Hypothesis Tests: Two Related Samples Related Samples The same participants give us data on two measuresThe same participants give us data on two measures Xe. g. Before and After treatment XAggressive responses before video and aggressive responses after With related samples, someone high on one measure is probably high on other.With related samples, someone high on one measure is probably high on other. Cont.

4. 4Chapter 13 Hypothesis Tests: Two Related Samples Related Samples--cont. Correlation between before and after scoresCorrelation between before and after scores XCauses a change in the statistic we can use Sometimes called matched samples or repeated measuresSometimes called matched samples or repeated measures

5. 5Chapter 13 Hypothesis Tests: Two Related Samples Difference Scores Calculate difference between first and second scoreCalculate difference between first and second score Xe. g. Difference = Before - After Base subsequent analysis on difference scoresBase subsequent analysis on difference scores XIgnoring Before and After data

6. 6Chapter 13 Hypothesis Tests: Two Related Samples An Example Therapy for rape victimsTherapy for rape victims XFoa, Rothbaum, Riggs, & Murdock (1991) One group received Supportive CounselingOne group received Supportive Counseling Measured post-traumatic stress disorder symptoms before and after therapyMeasured post-traumatic stress disorder symptoms before and after therapy

7. 7Chapter 13 Hypothesis Tests: Two Related Samples Therapy for PTSD

8. 8Chapter 13 Hypothesis Tests: Two Related SamplesResults The Supportive Counseling group decreased number of symptomsThe Supportive Counseling group decreased number of symptoms Was this enough of a change to be significant?Was this enough of a change to be significant? Before and After scores are not independent.Before and After scores are not independent. XSee raw data Xr =.64 Cont.

9. 9Chapter 13 Hypothesis Tests: Two Related SamplesResults--cont. If no change, mean of differences should be zeroIf no change, mean of differences should be zero  So, test the obtained mean of difference scores against  = 0. XUse same test as in Chapter 12. We don’t know , so use s and solve for tWe don’t know , so use s and solve for t

10. 10Chapter 13 Hypothesis Tests: Two Related Samples t test D and s D = mean and standard deviation of differences. df = n - 1 = 9 - 1 = 8 Cont.

11. 11Chapter 13 Hypothesis Tests: Two Related Samples t test--cont. With 8 df, t.025 = +2.306With 8 df, t.025 = +2.306 We calculated t = 6.85We calculated t = 6.85 Since 6.85 > 2.306, reject H 0Since 6.85 > 2.306, reject H 0 Conclude that the mean number of symptoms after therapy was less than mean number before therapy.Conclude that the mean number of symptoms after therapy was less than mean number before therapy. Supportive counseling seems to work.Supportive counseling seems to work.

12. 12Chapter 13 Hypothesis Tests: Two Related Samples Advantages of Related Samples Eliminate subject-to-subject variabilityEliminate subject-to-subject variability Control for extraneous variablesControl for extraneous variables Need fewer subjectsNeed fewer subjects

13. 13Chapter 13 Hypothesis Tests: Two Related Samples Disadvantages of Related Samples Order effectsOrder effects Carry-over effectsCarry-over effects Subjects no longer naiveSubjects no longer naive Change may just be a function of timeChange may just be a function of time Sometimes not logically possibleSometimes not logically possible

14. 14Chapter 13 Hypothesis Tests: Two Related Samples Effect Size Again We could simply report the difference in means.We could simply report the difference in means. XDiff = 8.22 XBut the units of measurement have no particular meaning to us—Is 8.22 large? We could “scale” the difference by the size of the standard deviation.We could “scale” the difference by the size of the standard deviation. Cont.

15. 15Chapter 13 Hypothesis Tests: Two Related Samples Effect Size, cont. Cont.

16. 16Chapter 13 Hypothesis Tests: Two Related Samples Effect Size, cont. The difference is approximately 2 standard deviations, which is very large.The difference is approximately 2 standard deviations, which is very large. Why use standard deviation of Before scores?Why use standard deviation of Before scores? Notice that we substituted statistics for parameters.Notice that we substituted statistics for parameters.

17. 17Chapter 13 Hypothesis Tests: Two Related SamplesSPSS Next slide shows SPSS PrintoutNext slide shows SPSS Printout XSimilar printout from other software XResults match ours

18. 18Chapter 13 Hypothesis Tests: Two Related Samples

19. 19Chapter 13 Hypothesis Tests: Two Related Samples Review Questions Why do we say that the two sets of measures are not independent?Why do we say that the two sets of measures are not independent? What are other names for “related samples?”What are other names for “related samples?” How do we calculate difference scores?How do we calculate difference scores? XWhat happens if we subtract before from after instead of after from before? Cont.

20. 20Chapter 13 Hypothesis Tests: Two Related Samples Review Questions--cont. Why do we usually test H 0 :  D = 0?Why do we usually test H 0 :  D = 0? Why do we have 8 df in our sample when we have 18 observations?Why do we have 8 df in our sample when we have 18 observations? What are the advantages and disadvantages of related samples?What are the advantages and disadvantages of related samples? What do effect sizes tell you in this case?What do effect sizes tell you in this case? How would you calculate the confidence interval that SPSS produced?How would you calculate the confidence interval that SPSS produced?