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Dependent t-tests When the two samples are correlated (i.e. not independent) 1

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KNR 445 Statistics Dependent t Slide 2 Dependent? Whats that? Well, not independent2 ways Same individuals measured twice (known as repeated measures, or within subjects variables) Pre-test, post-test Each person receiving both experimental conditions Matched subjects Form pairs based upon pairs similarity on a variable; then assign one of each pair to condition A, & one to condition B Twins studies are an example of this (matched on genes, therefore - supposedly - matching on all sorts of other things) 1 2

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KNR 445 Statistics Dependent t Slide 3 Standard deviation of the dist n. SE M of difference between dependent means Key point: SE M is reduced in proportion with the correlation between the 2 sets of scores (in comparison with independent formula for SE M ) 1

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KNR 445 Statistics Dependent t Slide 4 So why use paired samples? Because of that correlation The larger the r, the larger the reduction in SE M, and the likelier it is youll get significant results Wise use of dependent samples will normally increase power, increase effect size, increase likelihood of significant result 1

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KNR 445 Statistics Dependent t Slide 5 Dependent t-test in SPSS Data format: Data from each sample must now be placed in separate columns. Note each persons data (one pair of scores) fits on each row 1 2

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KNR 445 Statistics Dependent t Slide 6 Dependent t-test in SPSS SPSS procedure: choose the appropriate command 1

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KNR 445 Statistics Dependent t Slide 7 Dependent t-test in SPSS Choose variables: slide the pair over from here Choose variables: to here And select ok 1

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KNR 445 Statistics Dependent t Slide 8 Dependent t-test in SPSS SPSS output Significance level r between samples (justification for choosing the test) Descriptives 1 2 3

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KNR 445 Statistics Dependent t Slide 9 Note: what if wed assumed independence? Weird: now its significantbut I thought the dependent t-test was more powerful??? 1

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KNR 445 Statistics Dependent t Slide 10 Note: what if wed assumed independence? But look you subtract the product of r and the SE M. & r was negative, right? So that means the SE term grows rather than shrinks in the paired t-test meaning less likelihood of significance 1 2 3

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How dependent samples normally work To prove the point KNR 445 Statistics Dependent t Slide 11 1 2

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How dependent samples normally work To prove the point KNR 445 Statistics Dependent t Slide 12 1

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How dependent samples normally work To prove the point KNR 445 Statistics Dependent t Slide 13 1 2 3 4

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Finally, for the skeptics Comparing same data via independent t-tests KNR 445 Statistics Dependent t Slide 14 2 3 4 1

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Finally, for the skeptics Comparing same data via independent t-tests KNR 445 Statistics Dependent t Slide 15 2 1