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Hypothesis Tests: Two Related Samples

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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.

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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

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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

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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

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Therapy for PTSD

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Results 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.

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Results--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

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t test D and s D = mean and standard deviation of differences. df = n - 1 = 9 - 1 = 8 Cont.

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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.

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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

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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

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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.

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Effect Size, cont. Cont.

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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.

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IQ Pill

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Computing t

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Interpreting t t(4) = 1.236, p >.05. Do not reject null hypothesis Sample came from population in which mean difference score = 0 IQ scores after taking the pill (M = 102.4) were not significantly higher than IQ scores before taking the pill (M = 99.4), t(4) = 1.24, p >.05.

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