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Chapter 11 Hypothesis Tests: Two Related Samples

Chapter 11 Hypothesis Tests: Two Related Samples. Overview. Learning objectives Vocabulary lesson again Introduce t test for related samples Advantages and disadvantages An example Review questions. Learning Objectives.

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Chapter 11 Hypothesis Tests: Two Related Samples

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  1. Chapter 11 Hypothesis Tests: Two Related Samples

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

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

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

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

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

  7. Matched-samples • 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 • Also called matched pairs or pairwise t test

  8. Difference Scores • Calculate difference between first and second score (between individual scores or matched pairs) • e. g. Difference = Before – After • D = X2-X1 • Base subsequent analysis on difference scores

  9. The Formulas

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

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

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

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

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

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

  16. The Data: Therapy for PTSD

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

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

  19. Step 4 • The critical value with 8 df, α=.05, two-tailed = +2.306 • We calculated t = 6.85 • Since 6.85 > 2.306, reject H0 • Conclude that the mean number of symptoms after therapy was less than mean number before therapy. • Supportive counseling seems to work.

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

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

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

  23. Review Questions--cont. • Why do we usually test H0: mD = 0? • Why do we have 8 df in our sample when we actually have 18 observations? • What are the advantages and disadvantages of related samples?

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