Exam 21: Nonparametric Techniques

The sign test is employed to compare two populations when the experimental design is matched pairs, and the data are ordinal but not normally distributed.

Given the following statistics from a matched pairs experiment, perform the Wilcoxon signed rank sum test to determine whether we can infer at the 10% significance level that the two population locations differ. $T ^ { + } = 520$ $T ^ { - } = 700$ , n = 50

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: A. 14.0. B. 10.5. C. 6.0. D. -2.0.

A non-parametric method to compare two populations, when the samples are independent but the assumptions behind the independent samples t-test are violated, is the: A Wilcoxon rank sum test. B sign test. C matched pairs t -test. D Wilcoxon signed rank sum test.

The appropriate measure of central location of ordinal data is the: A mean. B median. C mode. D All these choices are correct.

Consider the following two samples: A: 12 14 15 B: 11 13 16 16 17 19 20 The value of the test statistic for a right-tailed Wilcoxon rank sum test is: A. 3. B. 7. C. 11. D. 44.

The Kruskal-Wallis test can be used to test for a difference between two populations. It will produce the same outcome as the two-tailed Wilcoxon rank sum test.

Use the 5% significance level to test the hypotheses $H _ { 0 } :$ The two population locations are the same $H _ { 1 } :$ The location of population A is to the right of the location of population B, given that the data below are drawn from two independent samples: Sample A: 9 11 9 10 12 8 5 Sample B: 8 7 5 7 9 5 6 8

A statistics course co-ordinator has decided to incorporate team based learning in tutorials. Each tutorial class of 30 students are grouped into 5 teams of 6 members each. The teams have one group project which is assessed out of 30 marks. There are three tutorial classes in this statistics course, with 5 teams each. Each tutorial class is taught by a different tutor. Each tutor marks their team's projects. The course coordinator wants to ascertain if marking is consistent by the three different tutors. The course coordinator has tabled each teams mark by tutor so as to conduct a Kruskal-Wallis test to determine whether there is enough evidence at the 10% significance level to infer that at least two of the populations represented by the samples below differ. That is, use this test to determine if at least two of the tutor's marks for team's projects differ. Sample Tutor A Tutor B Tutor C 23 28 20 22 27 22 25 27 19 20 19 21 18 20 20

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: A Kruskal-Wallis test. B Friedman test. C Wilcoxon rank sum test. D Wil coxon signed rank sum test.

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. Con puter Keyboard: wpm Staffmem ber 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.

In a Wilcoxon rank sum test, the two sample sizes are 6 and 6, and the value of the Wilcoxon test statistic is T = 20. If the test is two-tailed and the level of significance is $\alpha = 0.05$ , then: A the null hypothesis will be rejected. B the null hypothesis will not be rejected. C the alternative hypothesis will not be rejected. D not enough in formation has been given to answer this question.

In recent years, airlines have been subjected to various forms of criticism. An executive of Airline X has taken a quick poll of 16 regular airplane passengers. Each passenger is asked to rate the airline he or she last flew on. The ratings are on a 7-point Likert scale, where 1 = poor and 7 = very good. Of the 16 respondents, six last flew on Airline X and the remainder flew on other airlines. The ratings are shown below. Can the executive conclude from these data with 5% significance that Airline X is more highly rated than the other airlines? Ratings of Airlines Airline Other Airlines 6 5 4 3 5 3 6 2 5 3 3 4 3 5 3 1

Given the following statistics, use the Wilcoxon rank sum test to determine at the 5% significance whether the location of population A is to the right of the location of population B. $T _ { A } = 42$ , $n _ { A } = 6$ , $T _ { B } = 36$ , $n _ { B } = 9$ .

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. 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?

One of the required conditions of the sign test is that the number of nonzero differences n must be smaller than or equal to 10.

A matched pairs experiment yielded the following paired differences: 3 -2 2 2 2 -2 0 1 0 3 0 -1 2 -1 3 2 1 2 The value of the standardised sign test statistic z is: A. 1.807. B. 11.0. C. 3.873. D. -5.939.

The following data were generated from a randomised blocked experiment. Conduct a Friedman test at the 5% significance level to determine if at least two population locations differ. Treatment Block A Rank B C Rank D 1 70 80 50 65 2 50 87 52 81 3 69 97 75 83 4 65 72 62 73 5 58 87 52 62

In a normal approximation to the Wilcoxon rank sum test, the standardised test statistic is calculated as z = 1.80. For a two- tail test, the p-value is: A. 0.0359 B. 0.4641 C. 0.2321 D. 0.0718

A fitness centre employs 4 different fitness instructors. Management would like to investigate if the different fitness instructors are getting different results with their team members. The number of kilograms lost per member over the last twelve months is recorded and divided by fitness instructor they were using. A table of fitness instructors with kilograms lost by each individual member, is given below. Can you advise management if the fitness instructors are consistent, (ie: test that at least two populations differ), at the 5% level of significance. Fitness instructor 13 15 18 9 9 10 15 10 16 15 17 6 12 14 18 6 15 13 8