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Exam 16: Nonparametric Tests

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Question 1

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The Kruskal-Wallis test is analogous to the one-sample parametric t test for a mean.

A) True
B) False

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Question 2

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The dean of Oxnard business school wants to know if there is a difference in computer skills in four majors (marketing, finance, operations, accounting) . A 20-question skills test is given to 10 randomly chosen students in each major. Which nonparametric test could be used by the dean to see if there is a difference in computer skills of students in the various majors?

A) Wald-Wolfowitz test
B) Wilcoxon signed-rank test
C) Mann-Whitney test
D) Kruskal-Wallis test

E) A) and C)
F) None of the above

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Question 3

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Spearman's rank correlation is used to measure agreement in rankings of paired (x, y) data.

Which nonparametric test is analogous to a parametric two-sample t test for means?

The Kruskal-Wallis test does not require normal populations, but it does require them to be of similar shape.

Which nonparametric test is analogous to a parametric one-sample t test for differences in paired data?

The Friedman test requires groups of equal size.

The Wilcoxon signed-rank test does not assume a normal population, but it does require a roughly symmetric population.

Most nonparametric tests assume ordinal data.

Which parametric test resembles the nonparametric Spearman's rank test?

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. $\text { Kruskal-Wallis Test }$ $\begin{array}{ccrl}\hline \text { Wedian } & n & \text { Avg. Rank } & \\\hline 27.00 & 11 & 19.18 & \text { Doc A } \\28.50 & 14 & 15.93 & \text { Doc B } \\46.00 & 9 & 36.39 & \text { Doc C } \\31.00 & 11 & 24.86 & \text { Doc D } \\\hline 31.00 & 45 & & \text { Total }\end{array}$ 14.599 $\mathrm{H}$ (corrected for ties) 3 d.f. , 0022 p-value Which is the best conclusion?

Attendees at an outdoor concert can buy pavilion tickets (A) or lawn tickets (B) . Below is the output for the one-sample runs to test whether there is a pattern in 32 consecutive ticket purchases. Runs Test $\begin{array}{|l|l|l|}\hline\text { n }&\text { runs }\\\hline 21 & 6& \text { A }\\\hline 11 & 6& \text { B }\\\hline 32 & 12& \text { total }\\\hline\end{array}$ 15.44 expected value $2.50$ standard deviation $- 1.17 z$ $.2403$ p-value (two-tailed) The best conclusion at ? = .05 would be:

The Wilcoxon signed-rank test is less powerful than a one-sample test of a mean when the population is actually normal.

Delta Air Lines wants to determine if the number of no-shows for flights originating from Detroit is higher than from Minneapolis. A sample of 20 flights from each city is taken and the number of no-shows is determined for each flight. Which nonparametric test would you use to determine whether the number of no-shows is greater in Detroit?

Which nonparametric test would we use to compare ratings assigned to n pairs of bonds by two different rating agencies, if the bonds are rated on an ordinal scale (Aaa, Aa, A, Baa, Ba B, etc.) ?

The Mann-Whitney test is analogous to a one-sample t test comparing a mean with a benchmark.

The Friedman test is a nonparametric equivalent to a parametric one-sample t test comparing a mean with a benchmark.

The Spearman rank correlation test compares medians of two paired data sets.

The Mann-Whitney test is sometimes called the "Wilcoxon rank sum test" because it was formulated independently by different statisticians.

You do not wish to assume normality in the population, yet you wish to compare central tendency in c samples. You decide to utilize MINITAB, whose menu is shown here: Which menu would you choose?