Exam 14: Nonparametric Methods

Apartments Residents of two different high rise apartment units may or may not have the same consumer indebtedness.A sample from each results in the following outstanding debt amounts: East West 14340 12832 13160 5038 9746 10146 16042 10651 17566 15394 7986 -The test question is: Do residents of the two apartment units have similar debt medians? What is the calculated test statistic W?

The z-test approximation to the Wilcoxon rank sum test for comparing two independent samples is used whenever both sample sizes are at least ____________________.

Which of the following tests would be an example of a nonparametric method?

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 Camen 90 90 David 68 62 Edward 87 89 Fraris 73 75 Gill 81 78 Heidi 92 98 Use the Wilcoxon signed rank test to determine at the 5% significance level whether the extra help sessions have been effective.

The Spearman coefficient of rank correlation measures both the strength and direction of paired observations that are at least a nominal measurement scale.

What is the parametric counterpart to the Wilcoxon signed rank test for paired samples? Compare the assumptions involved in using the respective tests.

The following data are drawn from four independent samples: Sample 13 15 18 9 9 10 15 10 16 15 17 6 12 14 18 6 15 13 8 Test at the 1% significance level to determine whether the population medians differ. H₀: __________________________ H₁: __________________________ Test statistic = ____________________ Critical Value = ____________________ Conclusion: _____________________________ Interpretation: ______________________________________________________

Differentiate between the Kruskal-Wallis test and the one-way analysis of variance in terms of their assumptions and the circumstances under which each should be applied.

Diet programs A consumer research organization will evaluate the results of two diet programs,Take-It-Off and Melt-Away.Persons are randomly sampled from each of the programs and their weight loss results follow. Take-It- Off Melt-Away 150 130 75 68 40 20 68 54 30 27 98 -Use the Wilcoxon rank sum test on the data below to determine at the 10% significance level whether the two population medians differ. Sample 1: 32 22 19 29 20 34 25 9 28 17 Sample 2: 29 20 18 27 19 23 19 12 22 10 H₀: ____________________ H₁: ____________________ Test statistic = ____________________ Rejection region = ____________________ If necessary,separate your answers with commas,for example x,y,z,etc. Conclusion: _____________________________ Interpretation: _______________________________________________________

Seven Dwarfs Several years ago a television station interviewed individuals and asked them to name the "Seven Dwarfs" from the story of "Snow White." The amount of time (in seconds)to name the dwarfs was recorded by age group.The data were: Under 12 12 to 25 Over 25 60 120 75 45 65 45 38 60 75 30 48 55 35 150 100 -The test question is: Do the different age groups require the same median time to name the Dwarfs? State the null and alternative hypotheses. H₀: _______________________ H₁: ________________________

Treatments Treatments Blocks 1 2 3 1 12 20 16 2 13 18 14 3 13 20 12 4 15 16 18 5 8 10 10 6 10 17 16 No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? -State the appropriate conclusion employing a 0.025 significance level.

What key feature distinguishes nonparametric from parametric tests?

Writers Eight professional food writers have been asked to rate the taste characteristics of a meat dish prepared first by flame grilling and then by charcoal grilling. After each of the dishes is prepared it is rated on a scale from 1 to 5 with 1 being best and 5 being worst. The results of the rating were: Writer Flame Charcoal A 5 1 4 4 B 4 2 2 2 C 1 2 -1 1 D 4 3 1 1 E 3 1 2 2 F 4 4 0 0 G 4 5 -1 1 H 2 3 -1 1 -The Wilcoxon signed rank test for paired samples is used to test the hypotheses $H _ { 0 } : m _ { d } = 0 \text { vs. } H _ { 1 } : m _ { d } \neq 0$ State the appropriate conclusion,using the 0.05 significance level.

Writers Eight professional food writers have been asked to rate the taste characteristics of a meat dish prepared first by flame grilling and then by charcoal grilling. After each of the dishes is prepared it is rated on a scale from 1 to 5 with 1 being best and 5 being worst. The results of the rating were: Writer Flame Charcoal A 5 1 4 4 B 4 2 2 2 C 1 2 -1 1 D 4 3 1 1 E 3 1 2 2 F 4 4 0 0 G 4 5 -1 1 H 2 3 -1 1 -In testing the hypotheses H₀: m_d = 0,H₁: m_d ≠ 0,data are drawn from a matched pairs experiment,and the following statistics are calculated: n = number of nonzero differences = 40; R+ = 238; R- = 582.Assume that the 5% level of significance is used.What is the p-value of this test?

Wilcoxon In a Wilcoxon signed rank test the following information describes the results: Number of nonzero differences = 12; R+ = 22; R- = 56.The hypothesis set is: H₀: m ≤ 33 H₁: m > 33 -Assume the population is symmetrically distributed.State the conclusion. Test statistic = ____________________ Critical Value = ____________________ Conclusion: ____________________________

Treatments Treatments Blocks 1 2 3 1 12 20 16 2 13 18 14 3 13 20 12 4 15 16 18 5 8 10 10 6 10 17 16 No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? -On a multiple-choice exam consisting of ten questions with A through D as choices,the correct answers were: C D C B C B D A C D.Use these data to test the hypothesis that the answer sequence is random.What is the expected number of runs?

Airline Ten business people who fly frequently were asked to rank four airlines in terms of the quality of service.The people assigned scores using a 5-point 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 1 3 5 2 2 5 4 2 1 3 2 5 3 2 4 4 2 4 1 5 3 3 1 5 6 4 4 5 3 7 3 4 1 4 8 2 5 2 1 9 5 3 4 2 10 5 5 4 3 -Can we conclude at the 5% significance level that there are differences in service quality among the four airlines? H₀: __________________________ H₁: __________________________ Test statistic = ____________________ Critical Value = ____________________ Conclusion: ________________________________ Interpretation: ________________________________________________________

The sign test for comparing paired samples assumes that the measurement scale of the sample data is:

The Wilcoxon signed rank test assumes sample data to be

In a normal approximation to the Wilcoxon rank sum test,the standardized test statistic value is calculated as z = 1.80.For a two- tail test,the p-value is: