Exam 14: Nonparametric Methods

What is a nonparametric test?

FAA The FAA recorded the number of complaints per month for three airlines.The data were: Airline Airline Airline 3248 2462 1544 2876 2838 2381 2943 3042 2279 3486 3211 2163 2777 1968 1459 -The test question is: Do the three airlines have the same median number of complaints? State the appropriate conclusion employing a 0.025 significance level.

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? -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? What is the rank of the value in the second treatment and third block?

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? State the null and alternative hypotheses. H₀: ____________________ H₁: ____________________

Quiz scores It is important to sponsors of television shows that viewers remember as much as possible about the commercials.The advertising executive of a large company is trying to decide which of two commercials to use on a weekly half-hour comedy.To help make a decision she decides to have 12 individuals watch both commercials.After each viewing,each respondent is given a quiz consisting of 10 questions.The number of correct responses is recorded and listed below.Assume that the quiz results are not normally distributed. Quiz Scores Respondent Commercial 1 Commercial 2 1 7 9 2 8 9 3 6 6 4 10 10 5 5 4 6 7 9 7 5 7 8 4 5 9 6 8 10 7 9 11 5 6 12 8 10 -Do these data provide enough evidence at the 5% significance level to conclude that the two commercials differ? Hypotheses: _________________________ Test statistic = ____________________ Critical Value = ____________________ Conclusion: ______________________

The nonparametric counterpart to the one-sample t-test is the

FAA The FAA recorded the number of complaints per month for three airlines.The data were: Airline Airline Airline 3248 2462 1544 2876 2838 2381 2943 3042 2279 3486 3211 2163 2777 1968 1459 -The test question is: Do the three airlines have the same median number of complaints? What is the calculated test statistic H?

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.Which test is used for testing the hypotheses above?

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 test statistic?

In applying the Friedman test,either the number of blocks or the number of treatments should be at least ____________________.

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? What is the appropriate conclusion employing a 0.05 significance level?

The Wilcoxon signed rank test for comparing paired samples assumes the data are continuous and are of the interval or ratio scale of measurement.

The nonparametric ____________________ test is used for the same purposes as the Wilcoxon signed rank test,but data need only be of the ordinal scale of measurement.

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 conclusion?

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

The critical value of the Kruskal-Wallis test for comparing more than two independent samples is obtained from the ____________________ distribution whenever each sample size is at least ____________________.

The significance level for a Wilcoxon signed rank test for one sample is 0.025.The alternative hypothesis is m < m₀,and the sample size is 14.What is the appropriate critical value?

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 -Explain how to use the p-value to reach a conclusion when testing at the 0.025 level of significance.

A three independent samples one-way analysis of variance test corresponds to a:

A Wilcoxon rank sum test for comparing two independent samples involves two sample sizes: 8 and 6.The alternate hypothesis is m₁ ≠ m₂.Use a 0.05 significance level.What are the appropriate table values? Separate your answers with commas,for example x,y,z,etc.