Exam 15: Nonparametric Statistics

In a Wilcoxon signed rank test for matched pairs with n = 32, the rank sums of the positive and negative differences are 367.5 and 160.5, respectively. The value of the standardized test statistic z is:

When assigning ranks during a Wilcoxon rank-sum test, tied values are each given the mean of the next ranks to be assigned. Which of the following statements about this averaging procedure is false?

We can use the Friedman test to determine whether a difference exists between two populations. However, if we want to determine whether one population location is larger than another, we must use the sign test.

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

A supermarket chain has its own house brand of ice cream. The general manager claims that her ice cream is better than the ice cream sold by a well-known ice cream parlor chain. To test the claim 40 individuals are randomly selected to participate in the following experiment. Each respondent is given the two brands of ice cream to taste (without any identification) and asked to judge which one is better. Suppose that 25 people judge the ice cream parlor brand better, four say that the brands taste the same, and the rest claim that the supermarket brand is better. Can we conclude at the 1% significance level that the general managers' claim is false? Test statistic: z-statistic = ______________ Rejection region: Reject if the z-statistic ______________. Conclusion: ______________ We ______________ conclude at the 1% significance level that the general managers' claim is false. What is the p-value for the above test? ______________

The Kruskal-Wallis test is applied to compare two or more populations, when the samples are independent and the data are either ordinal or interval but not normal.

In a Friedman test for comparing three populations, provided that there are five blocks, the test statistic is calculated as = 6.594. Then, the most accurate statement that can be made about the p-value is that:

The Wilcoxon rank sum test statistic T is approximately normally distributed whenever the sample sizes are larger than or equal to:

The following data were generated from a blocked experiment. Conduct a Friedman test at the 5% significance level to determine if at least two population locations differ. Test Statistic: = ______________ Reject Region: Reject if > ______________ Conclude: ______________ The locations of all four populations are ______________.

Ten secretaries were selected at random from among the secretaries of a large university. The typing speed (number of words per minute) was recorded for each secretary on two different brands of computer keyboards. Assume that the typing speeds are not normally distributed. The following results were obtained. Test to determine if these data provide enough evidence at the 5% significance level to infer that the brands differ with respect to typing speed. z-statistic = ______________ Reject if |z| > ______________ Conclusion: ______________ These data ______________ enough evidence at the 5% significance level to infer that the brands differ with respect to typing speed.

The Spearman rank-correlation test is a nonparametric test that 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.

The critical value is taken from the F-distribution whenever the Wilcoxon signed rank test is employed.

A nonparametric method to compare two populations, when the samples are matched pairs and the data are interval, and where the normality requirement necessary to perform the parametric test is unsatisfied, is the:

In testing the hypotheses: H₀: The two population locations are the same. H₁: The two population locations are different. The statistics n₁ = 5, n₂ = 9, T₁ = 22, and T₁* = 53 are calculated with data drawn from two independent samples. What is the value of the test statistic? Test statistic = ______________ What is the rejection region for this test at = 0.05? Critical Value = ______________ What is your conclusion at = 0.05? Conclusion: ______________ The two population locations are ______________.

A dog kennel manager was interested in determining whether there is a difference in the time it takes a dog to complete an obstacle course for two different courses. A random sample of 36 dogs was selected and the time it took each dog to complete each course was recorded. In twelve cases it took the dog longer to complete course #1. Use the normal approximation to the sign test to determine if there is a significant difference in the time it takes to complete the two obstacle courses. Use = 0.05. The null and alternate hypotheses are: : The distributions of completion time for an obstacle course are identical for the two different courses, and p = 0.50. : The distributions of completion time for an obstacle course are not identical for the two different courses, and p 0.50. What is the z-statistic? ______________ What is the critical value for the test statistic? Reject if |z| > ______________ ______________ Conclude that the distributions of completion time for an obstacle course are ______________ for the two different courses.

Suppose you wish to detect a difference in the locations of two population distributions based on a paired-difference experiment consisting of n = 35 pairs. Use the Wilcoxon Signed-Rank test. [NOTE: = n(n+ 1) / 2.] If = 339, what are your conclusions? Give the test statistic. T = ______________ Give the rejection region for the test for = 0.05. Reject if T ______________. Conclude: ______________ There is ______________ of a difference between the two distributions. Conduct the test using the large-sample z-test. Compute the z-statistic: ______________ Reject if the z-statistic ______________. Conclude: ______________ There is ______________ of a difference between the two distributions. Compare your results with the nonparametric test results above. ______________

Which of the following correctly describes the sign test?

In a Kruskal-Wallis test, there are five samples, and the value of the test statistic is calculated as H = 12.32. Then the most accurate statement that can be made about the p-value of the test is that it is greater than 0.025 but smaller than 0.05.

A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20. If the value of un-standardized test statistic is T = 225, then the value of the standardized test statistic is z = -1.50.

A professor was interested in the relationship between a student's rank on an oral exam and the student's rank on a written exam. The professor selected 8 students at random and ranked their scores for both the oral exam and the written exam. The following data was recorded: Find and interpret the rank correlation between a student's rank on the oral exam and the student's rank on the written exam. Compute : ______________ There is ______________ relationship between the student's rank on the oral exam and the student's rank on the written exam.