A clinic has four doctors.They wish to compare the amount of time that doctors spend with their patients.It is suspected that times may not be normally distributed but are otherwise assumed similar except in center,so a nonparametric test was chosen.The Kruskal-Wallis test results are shown below. Which is the best conclusion at α = .01?
A)The doctors have the same median times.
B)The doctors have different median times.
C)The sample size is insufficient for this kind of test.
D)A one-factor ANOVA would be a better kind of test.

Question

A clinic has four doctors.They wish to compare the amount of time that doctors spend with their patients.It is suspected that times may not be normally distributed but are otherwise assumed similar except in center,so a nonparametric test was chosen.The Kruskal-Wallis test results are shown below.  Which is the best conclusion at α = .01?
A)The doctors have the same median times. 
B)The doctors have different median times. 
C)The sample size is insufficient for this kind of test. 
D)A one-factor ANOVA would be a better kind of test.

Quizplus · Accepted Answer

The Kruskal-Wallis test is a nonparametric test used to compare the medians of two or more groups. The test statistic obtained is compared to the critical value in the Kruskal-Wallis table. In this case, the test statistic (χ2 = 7.6) is greater than the critical value (χ2 = 9.488), which means that we reject the null hypothesis of equal medians and conclude that at least one doctor has a different median time from the others. Therefore, the best conclusion is that the doctors have different median times (Option B). Option A is incorrect because if the medians were the same, we would not have rejected the null hypothesis. Option C is incorrect because the sample size is sufficient for the Kruskal-Wallis test. Option D is incorrect because a one-factor ANOVA assumes normality of the data, which is not the case here.

A Clinic Has Four Doctors