Question

In a classic study, which predates the existence of the EPO drug, Melvin Williams of Old Dominion University actually injected extra oxygen-bearing red cells into the subjects’ bloodstream just prior to a treadmill test. Twelve long-distance runners were tested in 5-mile runs on treadmills. Essentially, two running times were obtained for each athlete, once in the treatment or blood-doped condition after the injection of two pints of blood and once in the placebo control or non-blood-doped condition after the injection of a comparable amount of a harmless red saline solution. The presentation of the treatment and control conditions was counterbalanced, with half of the subjects unknowingly receiving the treatment first, then the control, and the other half receiving the conditions in reverse order.

Since the difference scores, as reported in the *New York
Times,* on May 4, 1980, are calculated by subtracting
blood-doped running times from control running times, a positive
mean difference signifies that the treatment has a facilitative
effect, that is, the athletes’ running times are shorter when blood
doped. The 12 athletes had a mean difference running time,
*D*, of 51.33 seconds with a standard deviation, *s
D* , of 66.33 seconds.

a) Calculate Cohen's d for these results

b) interpret the effect size

c) How might this result be reported in literature?

d) Why is it important to counterbalnce the presentation of blood-doped and control the conditions?

e) Comment on the wisdom of testing each subject twice—once under the blood-doped condition and once under the control condition—during a single 24-hour period. (Williams actually used much longer intervals in his study.)

Answer #1

(a)Test the null hypothesis at the .05 level of significance.H0: μd ≤ 0H1: μd>0´D= 51.33sD= 66.33s´D= 66.33/√12=19.1478t=51.33/19.1478=2.680723tcrit=1.796Reject null hypothesis at the .05 level of significance because t=2.680723 which exceeds 1.796.This indicates that blood doping facilitates running which causes a decline in running times.(b)Specify the p -value for this result.p< .05(c)Would you have arrived at the same decision about the null hypothesis if the difference scores had been reversed by subtracting the control times from the blood-doped times?Yes, although the mean difference score would appear negative. After doing the rest of the calculations it would be the same.14

(d)If appropriate, construct and interpret a 95 percent confidence interval for the true effect of blood doping.confidence interval=51.33±(2.201) (19.1478)={93.47439.185692We can claim with 95% confidence that the true effect of blood doping is between 9.19 and 93.47 seconds.(e)Calculate and interpret Cohen’s d for these results .d=51.33/66.33= .077, This is a large effect(f)How might this result be reported in the literature?For athletes who serve as their own controls, blood doping causes a decline inmean runningtime. (´D= 51.33 , sD= 66.33, p < .05, d = 0.77).

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