Exam 15: Nonparametric Statistics

The significance level for a Wilcoxon signed rank sum test is 0.05. The alternative hypothesis is stated as: The location of population 1 is different from the location of population 2. The appropriate critical value for a sample of size 20 (that is the number of nonzero differences is 20) is:

A computer laboratory manager was interested in whether there was a difference in functioning time before needing to be recharged for three battery packs for laptop computers. The manager took a random sample of six battery packs of each brand and tested them. The results, in hours of functioning before needing to be recharged, were recorded as The manager, unsure that the assumptions for the usual parametric analysis of variance were valid, decided to employ nonparametric methods. Use the appropriate nonparametric procedure to determine whether the distribution of functioning time before needing to be recharged is the same for the three brands of battery packs. Use = 0.05. Test Statistic: H = ______________ What is the critical value for the test statistic? Reject if the test statistic > ______________. Conclude: ______________ There ______________ sufficient evidence at = 0.05 to say that at least two of the distributions of functioning times before battery needing to be recharged differ in location.

The Kruskal-Wallis test statistic can be approximated by a chi-squared distribution with k - 1 degrees of freedom (where k is the number of populations) whenever the sample sizes are all greater than or equal to:

Given the statistics: T+ = 520, T- = 700, and n = 50 from a matched pairs experiment, perform the Wilcoxon signed rank test to determine whether we can infer at the 5% significance level that the two population locations differ. Test statistic: z-statistic = ______________ Rejection region: Reject if |z| > ______________ Conclusion: ______________ We ______________ infer at the 5% significance level that the two population locations differ.

The Wilcoxon Signed-Rank test:

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.

The Mann-Whitney U test is a nonparametric test that measures the degree of association between two variables for which only rank-order data are available.

In a Kruskal-Wallis test to determine whether differences exist among three different advertisements, the following statistics were obtained: Conduct the test at the 5% significance level. Test statistic: H = ______________ Reject if H > ______________ Conclude: ______________ There ______________ enough evidence to conclude that differences exist among three different advertisements. What is the most accurate statement that can be made about the p-value of this test? ______________

In testing the hypotheses : The two population locations are the same. : The location of population A is to the right of the location of population B. The statistics T+ = 271, T- = 107, and n = 27 are calculated with data drawn from a matched pairs experiment. Test statistic: z-statistic = ______________ p-value = ______________ Conclusion: ______________ We ______________ infer at the 1% significance level that the location of population A is to the right of the location of population B.

In a normal approximation to the Wilcoxon rank sum test, the standardized test statistic is calculated as z = 1.96. For a two-tail test, the p-value of the test is 0.025.

The Friedman test is the nonparametric counterpart of the randomized block experimental design of the analysis of variance.

The Wilcoxon Signed-Rank test may be more appropriate than the paired-difference t-test if:

Nonparametric tests can be appropriate for quantitative data when:

A nonparametric method to compare two populations, when the samples are independent and where the normality requirement necessary to perform the parametric test is not satisfied, is the:

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

In all applications of the Kruskal-Wallis test, the alternative hypothesis to be tested is always stated as:

The Friedman test is a nonparametric test that can be used to compare more than two dependent samples when the assumptions for an analysis of variance are invalid.

Suppose you want to use the Wilcoxon rank sum test to detect a shift in distribution 1 to the right of distribution 2, based on samples of sizes = 7 and = 9. Should you use T₁ or T₁* as the test statistic? ______________ What is the rejection region for the test if = 0.05? Reject if the test statistic ______________. What is the rejection region for the test if = 0.01? Reject if the test statistic ______________.

The Spearman rank-correlation is a nonparametric test that 1) uses the directions of differences observed in a matched-pairs sample to determine whether the relative frequency distributions of two statistical populations are identical to or different from one another and 2) determines whether a sample comes from a population with a specified median.

Another school district also planned to evaluate two different workbooks and two distinct teaching machines to assess their effectiveness in teaching the concept of multiplication. However, the administrators in this school district consulted a statistician about the design of their study. Because they were looking for a method effective on children of all abilities, the statistician suggested they check the children's past scholastic records and divide the children into groups according to their ability level. These ability groups represent relatively homogeneous experimental units within which the comparison of teaching methods may be made. She assigned one child from each ability level to each teaching method. Twenty students participated in the study. After receiving instruction, the children took a multiplication test and the number of errors they made were recorded. What experimental design did the statistician use? ________________________________________________________ The null and alternate hypotheses are as follows: : The three population distributions are identical. : At least two of the three population distributions differ in location. Describe what the test statistic is. ________________________________________________________ Test Statistic: = ______________ Reject Region: Reject if F > ______________ Conclude: ______________ The teaching methods ______________ equally effective. Estimate the observed significance level of this test. ______________