Exam 21: Nonparametric Techniques

Radio advertising is big business, second only to television advertising. The objective for radio advertisements is to get listeners to remember as much as possible about the product/service being advertised. The advertising executive of a large company must decide between two pitched radio advertisements for their company. In order to ascertain the general public's perception, 12 randomly chosen people are selected to listen to both potential advertisements and are then asked a series of 5 questions regarding the radio advertisement's content. The number of correct responses are recorded and listed below. Assume that responses are non-normal. Number of correct responses from 10 questions Respondent Radio advertisement 1 Radio advertisement 2 1 3 1 2 5 5 3 5 4 4 4 3 5 3 2 6 2 1 7 1 3 8 4 2 9 5 1 10 3 4 11 4 3 12 3 1 a. Which test is appropriate for this situation? b. Do these data provide enough evidence at the 5% significance level to conclude that the two radio advertisements differ?

The Kruskal-Wallis test can be used to determine whether a difference exists between two populations. However, to determine whether one population location is larger than another, we must apply the Wilcoxon rank sum test.

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. $T _ { A } = 42$ , $n _ { A } = 6$ , $T _ { B } = \mathbf { 3 6 }$ , $n _ { B } = 9$ .

We can use the Friedman test to determine whether two populations differ. The conclusion will be the same as that produced by the sign test.

Which of the following is the correct sample size requirement for the Wilcoxon signed rank sum test statistic to be approximately normally distributed?

A supermarket chain has its own house brand of ice cream. The general manager claims that her ice cream is better than the ice cream sold by a well-known ice cream parlour chain. To test the claim, 40 individuals are randomly selected to participate in the following experiment. Each respondent is given the two brands of ice cream to taste (without any identification) and asked to judge which one is better. Suppose that 25 people judge the ice cream parlour brand better, four say that the brands taste the same, and the rest claim that the supermarket brand is better. Can we conclude at the 1% significance level that the general managers' claim is false?

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 Friedman test statistic is approximately chi-squared distributed with (k - 1) degrees of freedom, provided that either the number of blocks b or the number of treatments k is greater than or equal to 5.

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 Which test is appropriate if you want to compare the quality of service of the four airlines?

The Kruskal-Wallis test requires independent sample.

In a Wilcoxon signed rank sum test, the test statistic is calculated as T = 45. The alternative hypothesis is stated as: The location of population 1 is different from the location of population 2. If there are n = 15 observations for which $D \neq 0$ , and the 5% significance level is used, then:

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

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

In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly reviewed by university lecturers. Suppose that Cengage Australia publishing company has recently received two manuscripts for statistics books. To help them decide which one to publish, both are sent to 50 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 20 lecturers rate manuscript A as better and 30 rate manuscript B as better. What is the p-value of this test, if we were testing that manuscript B is more highly rated than manuscript A?

Because of the cost of producing television shows and the profits associated with successful shows, television network executives are keenly interested in public opinion. A network has recently developed three comedy series. The pilot of each series is shown to 10 randomly selected people, who evaluate each show on a 9-point scale where 1 = terrible and 9 = excellent. The results are shown below. $\quad$ $\quad$ $\quad$$\text { Assessments of Television Shows }$ Person Show 1 Show 2 Show 3 1 6 4 7 2 5 4 5 3 7 6 8 4 7 7 8 5 9 9 9 6 5 7 6 7 4 4 5 8 6 3 7 9 5 6 6 10 7 7 8 Using the appropriate statistical table, what statement can be made about the p-value for this test?

A supermarket chain has its own house brand of ice cream. The general manager claims that her ice cream is better than the ice cream sold by a well-known ice cream parlour chain. To test the claim, 40 individuals are randomly selected to participate in the following experiment. Each respondent is given the two brands of ice cream to taste (without any identification) and asked to judge which one is better. Suppose that 25 people judge the ice cream parlour brand better, four say that the brands taste the same, and the rest claim that the supermarket brand is better. What is the p-value of this test?

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 critical value is taken from the t-distribution whenever the test is a Kruskal-Wallis test.

Compared to parametric tests, non-parametric tests use the information contained in the data:

In testing the hypotheses: $H _ { 0 } :$ The two population locations are the same $H _ { 1 } :$ The two population locations are different, with data drawn from two independent samples, the following statistics are calculated: $n _ { A } = 5$ , $T _ { A } = 22$ , $n _ { B } = 9$ , $T _ { B } = 83$ . a. Which test is used for testing the hypotheses above? b. What is the p-value of this test?