Exam 14: Nonparametric Methods

Consider the following two independent samples: Sample A: 14 15 17 20 45 Sample B: 25 29 32 35 38 -The value of the test statistic for a left-tail Wilcoxon rank sum test is:

A nonparametric method to compare two or more populations,when the samples are matched pairs and the data are either ranked or quantitative but not normal is the:

The following data are drawn from a matched pairs experiment: Matched Pairs 1 2 3 4 5 6 7 8 After 4 10 12 7 6 7 3 10 Before 6 9 12 10 12 10 5 8 Use the 5% significance level to test the hypotheses H₀: m_d ≥ 0,H₁: m_d < 0 Test statistic = ____________________ Critical Value = ____________________ Conclusion: ___________________________ Interpretation:__________________________________________________________

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 -Which test is appropriate for this situation?

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 -The test question is: Do the data indicate that the two programs are equally effective? What is the rank for observation 150?

To determine whether or not the median total expenditure by households was the same for three states,an economist took three samples of five counties from the states of New Mexico,Colorado,and Utah.The data were: New Me xico Colorado Utah 15207 16493 15276 13781 17599 12385 13884 13792 16237 13622 15151 12645 12657 13770 13627 Test the hypotheses: H₀: m₁ = m₂ = m₃ H₁: Not all medians are the same.Use $\alpha$ = 0.025. Test statistic = ____________________ Critical Value = ____________________ If necessary,separate your answers with commas,for example x,y,z,etc. Conclusion: _____________________________________ Interpretation: _____________________________________________________

Dataset Consider the following data set: 11 11 12 13 15 16 16 17 18 19 20 22 22 22 22 25 -What is the rank assigned to the four observations of value 22?

Whether testing a single sample or comparing paired samples,how should one go ahead deciding whether to use the sign test versus the Wilcoxon signed rank test?

What is the parametric counterpart to the Wilcoxon rank sum test? Compare the assumptions involved in using the respective tests.

The Wilcoxon signed rank test is applied to a single sample in testing whether the population proportion could be a hypothesized value.

Nonzero Number of nonzero differences = 14; R+ = 16; R- = 89. The hypothesis set is: H₀: m ≥ 22,H₁: m < 22 -Assume the population is symmetrically distributed.What is the conclusion? Test statistic = ____________________ Critical Value = ____________________ Conclusion: _______________________

Ten observations were drawn from a population whose distribution is unknown.They are: 33 55 87 68 93 73 61 82 91 85 Can we infer at the 5% significance level that the distribution is not normal? Hypotheses: ________________________________ Test statistic = ____________________ Critical Value = ____________________ Conclusion: _____________________________

The nonparametric counterpart to the two-sample t-test with independent samples is the:

Like the randomized block ANOVA,the Friedman test has the goal of comparing treatments,though it is concerned their medians rather than their means.

Compared to the chi-square method,the _________________________ does not require any minimum values for expected frequencies and can be used with relatively small samples.(Answer could be several words).

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 $H _ { 0 } : m _ { d } = 0 \text { vs. } H _ { 1 } : m _ { d }$ $\neq 0$ What will be the rank for writer A?

The Kruskal-Wallis test compares the medians of more than two independent samples.

The Wilcoxon rank sum test assumes that the measurement scale of the data be at least:

The chapter lists two major disadvantages to nonparametric testing.What are they?

A Nonparametric test is one that assumes that the population from which a sample is drawn is normally distributed or approximately so.