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

KNR 445 Statistics Dependent t Slide 2 Dependent? What’s that?  Well, not independent…2 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

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

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 you’ll get significant results  Wise use of dependent samples will normally increase power, increase effect size, increase likelihood of significant result 1

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 person’s data (one pair of scores) fits on each row 1 2

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

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

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

KNR 445 Statistics Dependent t Slide 9 Note: what if we’d assumed independence? Weird: now it’s significant…but I thought the dependent t-test was more powerful??? 1

KNR 445 Statistics Dependent t Slide 10 Note: what if we’d 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

How dependent samples normally work…  To prove the point… KNR 445 Statistics Dependent t Slide

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

How dependent samples normally work…  To prove the point… KNR 445 Statistics Dependent t Slide

Finally, for the skeptics…  Comparing same data via independent t-tests… KNR 445 Statistics Dependent t Slide

Finally, for the skeptics…  Comparing same data via independent t-tests… KNR 445 Statistics Dependent t Slide