Exam 21: Nonparametric Techniques

Ten business people who fly frequently from Melbourne to Sydney were asked to rank four airlines in terms of the quality of service. The people assigned scores using a 5-point Likert scale where: 1 = bad, 2 = poor, 3 = average, 4 = good, and 5 = excellent. The results are shown below. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Airline }$ Person A B C D 1 5 5 2 1 2 3 3 4 2 3 2 3 4 3 4 1 1 4 3 5 4 1 5 3 6 2 3 4 2 7 1 3 5 2 8 3 3 5 1 9 1 3 5 2 10 2 4 3 1 Can we conclude at the 5% significance level that there are differences in service quality among the four airlines?

The non-parametric counterpart of the parametric one-way analysis of variance F-test is the:

A large faculty at a university is deciding to upgrade their computers. They have narrowed their selection down to two different brands of computers. The keyboard design for each of these two brands is different, and faculty management is trying to ascertain which keyboard administration staff will work faster with. The faculty randomly selected ten administration staff. The typing speed (number of words per minute, wpm) was recorded for each member in the sample on each of the two different brands of computer keyboards. The following results were obtained. $\quad$ $\quad$ $\quad$ $\quad$$\text { Computer Keyboard: wpm }$ Staff menber Brand A Brand B Amy 75 75 Brad 85 86 Lee 65 72 Donna 79 70 Mark 91 85 Faith 80 73 Amir 83 72 Heather 74 80 Tom 75 79 Jody 70 64 Assume that the typing speeds are not normally distributed. Perform the sign test to determine whether these data provide enough evidence at the 5% significance level to infer that the brands differ with respect to typing speed.

Which of the following best describes when to apply the Wilcoxon rank sum test to determine whether the location of population 1 is different from the location of population 2?

A non-parametric method to compare two or more populations, when the samples are matched pairs and the data are either ordinal or interval but not normal, is the:

A non-parametric method to compare two or more populations, when the samples are independent and the data are either ordinal or interval but not normal, is the:

In a Wilcoxon signed rank sum test, the test statistic is calculated as T = 75. If there are n = 15 observations for which $D \neq 0$ , and a two-tail test is performed at the 5% significance level, then:

Use the Wilcoxon rank sum test on the data below to determine at the 10% significance level whether the two population locations differ. Sample 1: 17 20 18 25 16 22 Sample 2: 17 25 33 38 15 26 21

A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20. The unstandardised test statistic (that is the rank sum) is T = 210. The value of the standardised test statistic z is:

Use the Wilcoxon rank sum test on the data below to determine at the 5% significance level whether the location of population A is to the left of the location of population B. Sample A: 75 60 67 54 69 Sample B: 80 84 100 74 90

Which of the following is the non-parametric equivalent to the parametric t-test of $\mu _ { D }$ for matched pairs?

The following data represent the test scores of eight students on a statistics test before and after attending extra help sessions for the test. Student Before After Abby 82 90 Brenda 75 86 Carmen 90 90 David 68 62 Edward 87 89 Frank 73 75 Gill 81 78 Heidi 92 98 Uses the Wilcoxon signed rank sum test to determine at the 5% significance level whether the extra help sessions have been effective.

The Wilcoxon signed rank sum test is the nonparametric counterpart of the t-test of µ_D.

In a normal approximation to the sign test, the standardised test statistic is calculated as z = -1.58. To test the alternative hypothesis that the location of population 1 is to left of the location of population 2, the p-value is:

The z-test approximation to the Wilcoxon rank sum test for two independent samples requires that at least one of the two sample sizes exceed 10.

The appropriate measure of central location of ordinal data is the:

The restaurant critic on a newspaper claims that the hamburgers one gets at the hamburger chain restaurants are all equally bad, and that people who claim to like one hamburger over others are victims of advertising. In fact, he claims that if there were no differences in appearance, then all hamburgers would be rated equally. To test the critic's assertion, ten teenagers are asked to taste hamburgers from three different fast-food chains. Each hamburger is dressed in the same way (mustard, relish, tomato and pickle) with the same type of bun. The teenagers taste each hamburger and rate it on a 9-point scale with 1 = bad and 9 = excellent. The data are listed below. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Ham burger Ratings }$ Teenager Chain 1 Chain 2 Chain 3 1 7 5 6 2 5 3 4 3 6 4 5 4 9 8 8 5 4 3 2 6 4 5 4 7 6 5 5 8 5 4 5 9 8 7 9 10 9 8 7 Using the appropriate statistical table, what statement can be made about the p-value for this test?

The F-test of the randomised block design of the analysis of variance requires that the random variable of interest must be normally distributed and the population variances must be equal. When the random variable is not normally distributed, we can use:

Which of the following best describes the hypotheses in the Kruskal-Wallis test and Friedman test?

The Wilcoxon rank sum test is used to compare two populations when the samples are independent and the data are either ordinal or interval but not normally distributed.