Exam 19: Further Non-Parametric Tests

Instruction 19-5 A perfume manufacturer is trying to choose between two magazine advertising layouts.An expensive layout would include a small package of the perfume.A cheaper layout would include a "scratch-and-sniff" sample of the product.The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate.The manufacturer presents both layouts to five groups and determines the approval rating from each group on both layouts.The data are given below.Use this to test whether the median difference in approval rating is different from zero in favour of the more expensive layout with a level of significance of 0.05. Package Scratch 52 37 68 43 43 53 48 39 56 47 -Referring to Instruction 19-5,what are the lower and upper critical values of the test?

One reason for using the Wilcoxon Rank Sum test rather than the t test is if you cannot assume that the populations from which the samples came are normally distributed.

Instruction 19-1 The director of transportation of a large company is interested in the usage of her van pool.She considers her routes to be divided into local and non-local.She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: Male Female Total Local 27 44 71 Non-Local 33 25 5 Total 60 69 129 She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05. -Referring to Instruction 19-1,the director now wants to know if the proportion of users who are male and the proportion of users who use the local routes are the same.What is the p-value of the test statistic using a 5% level of significance?

The Kruskal-Wallis Rank Test for Differences in more than two medians is a nonparametric alternative to

One disadvantage of the Wilcoxon rank sum test,as compared to the t test,is that Wilcoxon rank sum test is much less powerful.

Instruction 19-5 A perfume manufacturer is trying to choose between two magazine advertising layouts.An expensive layout would include a small package of the perfume.A cheaper layout would include a "scratch-and-sniff" sample of the product.The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate.The manufacturer presents both layouts to five groups and determines the approval rating from each group on both layouts.The data are given below.Use this to test whether the median difference in approval rating is different from zero in favour of the more expensive layout with a level of significance of 0.05. Package Scratch 52 37 68 43 43 53 48 39 56 47 -Referring to Instruction 19-5,what is the appropriate test to use?

Instruction 19-4 The director of the MBA program of a university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good.Given below is the result from 215 students' view of the program before and after the orientation. After the Orientation Before the Orientation Good Not Good Total Good 93 37 130 Not Good 71 14 85 Total 164 51 215 -Referring to Instruction 19-4,the director should reject the null hypothesis using a 1% level of significance.

Instruction 19-4 The director of the MBA program of a university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good.Given below is the result from 215 students' view of the program before and after the orientation. After the Orientation Before the Orientation Good Not Good Total Good 93 37 130 Not Good 71 14 85 Total 164 51 215 -Referring to Instruction 19-4,the null hypothesis for the Friedman rank test for the difference in the means should be rejected at a 0.01 level of significance.

The Kruskal-Wallis test is an extension of which of the following for two independent samples?

The McNemar test is used to determine whether there is evidence of a difference between the proportions of two related samples.

Instruction 19-4 The director of the MBA program of a university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good.Given below is the result from 215 students' view of the program before and after the orientation. After the Orientation Before the Orientation Good Not Good Total Good 93 37 130 Not Good 71 14 85 Total 164 51 215 -When the normality assumption is not met in a randomised block design,which of the following tests should be used?

The McNemar test is approximately distributed as a chi-square random variable.

If the sample sizes in each group are larger than 5,the Kruskal-Wallis rank test statistic can be approximated by a chi-square distribution.

If the sample sizes in each group are larger than 5,the Kruskal-Wallis rank test statistic can be approximated by a standardised normal distribution.

Instruction 19-6A As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She took three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below. -Referring to Instruction 19-6A,the calculated value of the Kruskal-Wallis test statistic H is ________.

If the number of blocks in the experiment is larger than 5,the Friedman rank test statistic can be approximated by a standardised normal distribution.

Instruction 19-6 An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants all three varieties of the seeds on each of five different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomised block design,the results are presented in the table that follows. Fields Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 Below is the Minitab output of the Friedman rank test: Friedman Test: Yield versus Varieties, Fields Friedman test for Yield by Varieties blocked by Fields $\mathrm { S } = 10.00 \mathrm { DF } = 2 \mathrm { P } = 0.007$ Varieties Est Median Sum of Ranks Smith 5 13.500 5.0 Trevor 5 15.667 10.0 Walsh 5 18.533 15.0 Grand median $= 15.900$ -Referring to Instruction 19-6,the null hypothesis for the Friedman rank test is

Instruction 19-7 An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants all three varieties of the seeds on each of five different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomised block design,the results are presented in the table that follows. 1elds Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 Below is the Minitab output of the Friedman rank test: Friedman Test: Yield versus Varieties, Fields Friedman test for Yield by Varieties blocked by Fields $\mathrm { S } = 10.00 \mathrm { DF } = 2 \mathrm { P } = 0.007$ Est Sum of Varieties Median Ranks Smith 5 13.500 5.0 Trevor 5 15.667 10.0 Walsh 5 18.533 15.0 Grand median = 15.900 -Referring to Instruction 19-7,what is the value of the test statistic for the Friedman rank test for the difference in the medians?

If the number of blocks in the experiment is larger than 5,the Friedman rank test statistic can be approximated by a chi-square distribution.

Suppose there is interest in comparing the median response time for three independent groups learning a specific task.The appropriate nonparametric procedure is