Essentials

64 ESSENTIALS OF STATISTICSless you are dealing with hundreds of participants, the critical t for the RM test willbe noticeably higher than for the corresponding two-group test. A higher criticalt is not good, but the calculated RM t value is usually so much higher than the calculatedtwo-group t value that the difference in critical values becomes unimportant.That is certainly the case in our weight loss example, as you will see next.Calculating the Repeated-Measures t TestLet us apply Formula 3.12 to the weight loss example. The numerator of the testis the mean of the difference scores, which is 2 (pounds). Note that the RM t testalways has the same numerator as the corresponding two-group test because thedifference of the two means is always the same as the mean of the differences (i.e.,if you subtract the mean of the after scores from the mean of the before scores,you get the same result as subtracting the after score from the before score separatelyfor each participant and then averaging these difference scores). The advantageof the RM test is in the denominator. The two-group t test is based on thevariability from person to person under each condition; for our example, the SDwas about 45 pounds. The RM t test is based instead on the variability of the differencescores. We have been saying that everyone lost “about” 2 pounds. To bemore specific, let’s say that the SD for the difference scores is 1.0 pounds (so mostparticipants lost between 1 and 3 pounds). Using Formula 3.12,2 2t 1 .3 16 6.33 10The RM t value is more than 60 times greater than the corresponding twogroupt value because the RM test avoids the large amount of person-to-personvariability and benefits from the consistency of the difference scores. Adding one500-pound person who loses 2 pounds would make the two-group t statistic evensmaller but would have very little effect on the RM test (in this case the effectwould be positive because adding a difference score of –2 would only make theSD smaller; plus you’d gain a degree of freedom). Of course, the difference scoresare not usually as consistent as in our example, but when it makes sense to createan RM design, the RM t statistic is almost always considerably larger than the correspondingindependent-group t.Other Repeated-Measures DesignsThe before-after design is not the best example of the RM t test because a controlgroup usually is required, which means that two groups are being measured at two