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Fundamental Statistics for the Behavioral Sciences, 5th edition David C. Howell

Chapter 13 Hypothesis Tests: Two Related Samples. Fundamental Statistics for the Behavioral Sciences, 5th edition David C. Howell. © 2003 Brooks/Cole Publishing Company/ITP     . Major Points. Related samples? Difference scores? An example t tests on difference scores

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Fundamental Statistics for the Behavioral Sciences, 5th edition David C. Howell

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

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

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

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

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

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

  8. Chapter 13 Hypothesis Tests: Two Related Samples 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. • See raw data • r = .64 Cont.

  9. Chapter 13 Hypothesis Tests: Two Related Samples Results--cont. • If no change, mean of differences should be zero • So, test the obtained mean of difference scores against m = 0. • Use same test as in Chapter 12. • We don’t know s, so use s and solve for t

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

  11. Chapter 13 Hypothesis Tests: Two Related Samples t test--cont. • With 8 df, t.025 = +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.

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

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

  14. Chapter 13 Hypothesis Tests: Two Related Samples Effect Size Again • We could simply report the difference in means. • Diff = 8.22 • But 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. Cont.

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

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

  17. Chapter 13 Hypothesis Tests: Two Related Samples SPSS • Next slide shows SPSS Printout • Similar printout from other software • Results match ours

  18. Chapter 13 Hypothesis Tests: Two Related Samples

  19. Chapter 13 Hypothesis Tests: Two Related Samples 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.

  20. Chapter 13 Hypothesis Tests: Two Related Samples Review Questions--cont. • Why do we usually test H0: mD = 0? • Why do we have 8 df in our sample when we have 18 observations? • What are the advantages and disadvantages of related samples? • What do effect sizes tell you in this case? • How would you calculate the confidence interval that SPSS produced?

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