Exam 15: A:nonparametric Statistics

In a Wilcoxon rank sum test, the two sample sizes are 4 and 6, and the value of the Wilcoxon test statistic is T = 20. The test is two-tailed and the level of significance is . What may be deduced from the given information?

The Friedman test statistic is approximately chi-square 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.

If the Friedman test is applied to a data set that are generated from a randomized block experiment with five treatments and seven blocks, then the rejection region at the 5% significance level is

A one-sample t test is the parametric counterpart of the Wilcoxon signed-rank test for matched pairs.

A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 5 and 7. The alternative hypothesis is stated as: The location of population 1 is different from the location of population 2. In this case, what is the appropriate critical value at the 5% significance level?

Suppose we want to compare the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B in order to make a general assessment of relative fertilizer effectiveness. Which of the following tests might we use?

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.

The sign test is employed to compare two populations when the experimental design is matched pairs, and the data are ordinal but not normally distributed.

The procedure for the Wilcoxon rank sum test requires that we rank each group separately rather than together.

Suppose there is interest in comparing the median response time for three independent groups learning a new specific task. In this case, what is the appropriate nonparametric procedure to use?

In a Kruskal-Wallis test, there are four samples and the value of the test statistic is calculated as H = 13.21. Then the most accurate statement that can be made about the p-value of the test is that it is greater than 0.005 but smaller than 0.01.

The Wilcoxon signed-rank test is applied to compare two populations when the samples are matched pairs and the data are interval but not normally distributed.

In the sign test applications, the normal approximation to the binomial distribution works very well even when the number of non-zero differences is as small as which of the following values?

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

The Wilcoxon rank sum test (like most of the nonparametric tests presented in your text) is used to determine whether the population distributions have certain identical characteristics. Which of these properties would be included in that list of characteristics?

Which of the following is the nonparametric counterpart of the parametric one-way analysis of variance F-test?

A Friedman test is applied to a data set that is generated from a randomized block experiment with four treatments and eith blocks. What is the rejection region at the 5% significance level?

Statistical tests that are not very sensitive to errors in assumptions are called parametric tests.

Consider the following two independent samples: In this case, what is the value of the test statistic for a right-tailed Wilcoxon rank sum test?

You are performing the Wilcoxon rank sum test. The 10th through 12th values in an ordered array of pooled sample data all equal $100, while the 9th value is less than $100 and the 13th value is more than $100. What are the appropriate ranks for the three $100 values?