Exam 21: Nonparametric Techniques

Which of the following tests would be an example of a non-parametric method? A Wil coxon signed rank sum test. B Kruskal-Wallis test. C Friedman test. D All these choices are correct.

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. 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 Using the appropriate statistical table, what statement can be made about the p-value for the test?

We can use the Friedman test to determine whether a difference exists between two populations. However, if we want to determine whether one population location is larger than another, we must use the sign 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 left of the location of population B, given that the data below are drawn from a matched pairs experiment. Matched Pair 1 2 3 4 5 6 7 8 A 8 10 11 7 6 7 13 10 B 6 9 12 10 12 10 5 8

The significance level for a Wilcoxon signed rank sum test is 0.05. The alternative hypothesis is stated as: The location of population 1 is to the left of the location of population 2. The appropriate critical value for a sample of size 20 (that is, the number of nonzero differences) is: A. 158. B. 150. C. 60 D. 52

The Kruskal-Wallis test uses the Chi-squared distribution.

A movie critic wanted to determine whether or not moviegoers of different age groups evaluated a movie differently. With this objective, he commissioned a survey that asked people their ratings of their most recently watched movies. The rating categories were: 1 = terrible. 2 = fair. 3 = good. 4 = excellent. Each respondent was also asked to categorise his or her age as either: 1 = teenager. 2 = young adult (20-34). 3 = middle age (35-50). 4 = senior (over 50). The results are shown below. Movie Ratings Teenager Young Adult Middle Age Seni or 3 2 3 3 4 3 2 4 3 3 1 4 3 2 2 3 3 2 2 3 4 1 3 4 2 3 1 4 4 2 4 3 Which test the movie critic can use in this situation?

The marketing manager of a pizza chain is in the process of examining some of the demographic characteristics of her customers. In particular, she would like to investigate the belief that the ages of the customers of pizza parlours, hamburger emporiums and fast-food chicken restaurants are different. As an experiment, the ages of eight customers of each of the restaurants are recorded and listed below. From previous analysis we know that the ages are not normally distributed. Custoner Age Pizza Hamburger Chicken 23 26 25 19 20 28 25 18 36 17 35 23 36 33 39 25 25 27 28 19 38 31 17 31 Using the appropriate statistical table, what statement can be made about the p-value for the test?

The non-parametric counterpart of the randomised block model of the analysis of variance is the: A Kruskal-Wallis test. B Friedman test. C Wilcoxon rank sum test. D Wilcoxon signed rank sum test.

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. 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 significance level for a Wilcoxon signed rank sum test is 0.05. The alternative hypothesis is stated as: The location of population 1 is left to the location of population 2. The appropriate critical values for a sample of size 20 (that is the number of nonzero differences is 20) are: A. 60,150. B. 52,150. C. 60,158. D. 52,158.

Each year the personnel department in a large corporation assesses the performance of all of its employees. Each employee is rated for various aspects of his or her job on a 7-point scale where 1 = very unsatisfactory and 7 = satisfactory. The president of the company believes that the assessment scores this year are lower than last year's. To examine the validity of this belief, she draws a random sample of six employees' scores from last year and another six employees' scores this year. Do the data listed below allow the president to conclude at the 5% significance level that her belief is correct? Employees Ratings Scores This Year Last Year 5 5 6 5 4 3 5 3 5 4 4 3

In a normal approximation to the Wilcoxon rank sum test, the standardised test statistic is calculated as z = 1.96. For a two-tailed test, the p-value is 0.025.

The Wilcoxon rank sum test for independent samples actually tests whether the population distributions are identical.

A one-sample t-test is the parametric counterpart of the Friedman test for randomised block experimental design.

If in a matched pairs experiment we find 20 negative, 8 zero, and 10 positive differences, perform the sign test at the 10% significance level to determine whether the two population locations differ.

Consider the following two samples: A:: 14 15 37 40 35 B: 25 29 32 35 38 The value of the test statistic for a left-tailed Wilcoxon rank sum test is: A. 27.5. B. 27. C. 28. D. 28.5.

The Kruskal-Wallis test statistic can be approximated by a Chi-squared distribution with k - 1 degrees of freedom (where k is the number of populations) whenever the sample sizes are all greater than or equal to: A. 30 B. 20 C. 10 D. 5

A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20. The value of the unstandardised test statistic is T = 225. The value of the standardised test statistic is z = -1.50.

The marketing manager of a pizza chain is in the process of examining some of the demographic characteristics of her customers. In particular, she would like to investigate the belief that the ages of the customers of pizza parlours, hamburger emporiums and fast-food chicken restaurants are different. As an experiment, the ages of eight customers of each of the restaurants are recorded and listed below. From previous analysis we know that the ages are not normally distributed. Custoner Age Pizza Hamburger Chicken 23 26 25 19 20 28 25 18 36 17 35 23 36 33 39 25 25 27 28 19 38 31 17 31 Do these data provide enough evidence at the 10% significance level to infer that there are differences in age among the customers of the three restaurants?