In a study on the effect of caffeine on muscle metabolism, nine male volunteers

Question

In a study on the effect of caffeine on muscle metabolism, nine male volunteers from a random group of men underwent arm exercise tests on two separate occasions. On one occasion the volunteer took a placebo capsule an hour before the test; on the other occasion he received a capsule containing caffeine. The order of these treatments was randomised for each participant. During each exercise test, the ratio of carbon dioxide produced to oxygen consumed (respiratory exchange ratio or "%RER") was measured. The data are as follows: Volunteer 1 2 4 6 Placebo: 105 109 93 96 101 96 95 98 Caffeine a) Are these data paired or unpaired? Explain briefly the advantages of this type of b) What conditions are needed to proceed with inference using this data? What type of 96 89 95 95 93 study design. plot would be necessary as a check? Perform a basic, quick check to show that the conditions are valid. Calculate the relevant summary statistics from the data? Calculate a 90% confidence interval for the mean change in %RER with use of caffeine. Show all working c) d) e) Based on that confidence interval, is there sufficient evidence to conclude that caffeine consumption affects the mean % RER? f) Conduct a test of significance (at a significance level of 5%) to determine if there is evidence of a difference in % RER between the two treatment groups: placebo and caffeine. Follow all steps clearly and write a clear conclusion

Explanation / Answer

Unpaired Test.

Mann-Whitney

The non-parametric equivalent to the independent samples t-test is the Mann-Whitney test. The null hypothesis for the test is H0: The population medians are equal. The non-directional alternative hypothesis is H1: The population medians are not equal.

The medians show that, on average, caffeine appears to have reduced RER from about 98% to 94%, a reduction of 6%. However, there is a great deal of variation between the data values in both samples and considerable overlap between them. So is the difference between the two medians simply due to sampling variation or does the data provide evidence that caffeine does, on average, reduce RER?

The null hypothesis is that caffeine intake by men does not affect their median RER. The alternative hypothesis is that caffeine intake by men does affect their median RER. In Minitab the estimated medians for the two samples are calculated, together with an approximate 95% confidence interval for the difference between the medians.

The conclusion that we "cannot reject at alpha = 0.05" in Minitab means we "cannot reject the null hypothesis at the 5% level of significance", although in this case with a p-value of 0.0521, there is some evidence of a difference between the medians. Indeed, the SPSS output from a Mann-Whitney test gives p=0.046, which would give evidence to reject the null hypothesis!

The Mann-Whitney Test using Minitab

To perform this test use Stat > Nonparametrics > Mann-Whitney... and the following output is obtained:

Mann-Whitney Confidence Interval and Test

Caffeine N = 9 Median = 94.00
Placebo N = 9 Median = 98.00
Point estimate for ETA1-ETA2 is -6.00
95.8 Percent CI for ETA1-ETA2 is (-12.00,-0.00)
W = 63.0
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0521
The test is significant at 0.0512 (adjusted for ties)
Cannot reject at alpha = 0.05

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