Significance and Meaningfulness

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

KNR 445StatisticsDependent tSlide 2Dependent? Whats that?Well, not independent2 waysSame individuals measured twice (known as repeated measures, or within subjects variables)Pre-test, post-testEach person receiving both experimental conditionsMatched subjectsForm pairs based upon pairs similarity on a variable; then assign one of each pair to condition A, & one to condition BTwins studies are an example of this (matched on genes, therefore - supposedly - matching on all sorts of other things)12

KNR 445StatisticsDependent tSlide 3Standard deviation of the distn.SEM of difference between dependent means

Key point: SEM is reduced in proportion with the correlation between the 2 sets of scores (in comparison with independent formula for SEM)1

KNR 445StatisticsDependent tSlide 4So why use paired samples?Because of that correlationThe larger the r, the larger the reduction in SEM, and the likelier it is youll get significant resultsWise use of dependent samples will normally increase power, increase effect size, increase likelihood of significant result1

KNR 445StatisticsDependent tSlide 5Dependent 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 row12

KNR 445StatisticsDependent tSlide 6

Dependent t-test in SPSSSPSS procedure: choose the appropriate command1

KNR 445StatisticsDependent tSlide 7Dependent t-test in SPSS

Choose variables: slide the pair over from hereChoose variables: to hereAnd select ok1

KNR 445StatisticsDependent tSlide 8Dependent t-test in SPSSSPSS output

Significance levelr between samples (justification for choosing the test)Descriptives123

KNR 445StatisticsDependent tSlide 9Note: what if wed assumed independence?

Weird: now its significantbut I thought the dependent t-test was more powerful???1

KNR 445StatisticsDependent tSlide 10Note: what if wed assumed independence?But look you subtract the product of r and the SEM.

& r was negative, right? So that means the SE term grows rather than shrinks in the paired t-test meaning less likelihood of significance123

How dependent samples normally workTo prove the pointKNR 445StatisticsDependent tSlide 1112

How dependent samples normally workTo prove the pointKNR 445StatisticsDependent tSlide 121

How dependent samples normally workTo prove the pointKNR 445StatisticsDependent tSlide 131234

Finally, for the skepticsComparing same data via independent t-testsKNR 445StatisticsDependent tSlide 14

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Finally, for the skepticsComparing same data via independent t-testsKNR 445StatisticsDependent tSlide 1521