Basic Statistics

REFERENCES 199

can be computed on the ranks, which is Spearman’s rho. SAS, Stata, and SPSS
will compute Spearman’s rank correlation and give the p-value for the test that the
correlation is zero. StatXact gives exact p-values.

PROBLEMS

13.1 In Problem 8.2, the null hypothesis of equal weight of the male and female mice

was tested using the t test. Use the exact sign test with Q = .05. Compare the

results from the sign test with those from the t test.

13.2 Repeat the results from the sign test using the normal approximation. Compare

the results with those obtained using the exact test.

13.3 In Table 7.2, weights for two time periods on the same adults and weight loss

were evaluated. Note that the tests requested here and in Problem 13.5 have

smaller than recommended sample sizes to make it simpler to do with a hand

calculator.

13.4 The visual analog scale is often used to measure pain. The worst possible score is

10. Thirty patients who had the same operation were questioned about their pain
    two days post-operation. Fifteen of the patients were assigned to the standard
    analgesic and 15 received the standard analgesic plus pulsed electromagnetic
    field treatment. What statistical test would you use to test if the two treatments
    were equally effective? What statistical program would you use to obtain the
    results?
    13.5 Perform a Wilcoxon rank sum test on the following data on the length of time
    that it took to perform two types of operations. For type 1, six patients were
    operated on in 45,47,50,53,58, and 62 minutes. In the second type of operation
    it took 51, 56, 60, 63, 64, 69, and 70 minutes. Use the normal approximation.
    13.6 Compute the usual correlation and Spearman’s rho for the data in Table 12.2
    and compare the results you obtained.

REFERENCES

Bergmann, R., Ludbrook, J. and Sporeen, W. P. J. M. [2000]. Different outcomes of the

Wilcoxon-Mann-Whitney test from different statistic packages, The American Statisti-

cian, 54,72-71.

Conover, W. J. [1999]. Practical Nonparametric Statistics, 3rd ed., Hoboken, NJ, Wiley,

Daniel, W. W. [ 19781. Applied Nonparametric Statistics, Boston, MA: Houghton Mifflin,

Dixon, W. J. andMassey, F. J. [ 19831. Introduction to StatisticalAnalysis, NewYork: McGraw-

Gibbons, J. D. [ 19931. Nonparametric Statistics: An Introduction, Newbury Park, CA, Sage,

157-164,271-281,314-318,352-359,510-512,542.

31-37,82-87, 130-134,300-306.

Hill.

6-22,30-42.