Exam 15: Nonparametric Statistics

The statistical methods discussed in this chapter are used to test characteristics of populations without referring to specific parameters. For this reason, these techniques are called nonparametric techniques.

The Friedman test is employed to compare two or more populations when the data are generated from a matched pairs experiment, and are either ordinal or interval, but not normally distributed.

In a normal approximation to the Wilcoxon rank sum test, the standardized test statistic is calculated as z = 1.80. For a two-tail test, the p-value is:

Two gourmets, A and B, rated 22 meals on a scale of 1 to 10. The data are shown in the table. Do the data provide sufficient evidence to indicate that one of the gourmets tends to give higher ratings than the other? Test by using the sign test with a value of near 0.05. The null and alternate hypotheses are as follows: Critical Value approach: What is the test statistic? ______________ Use the binomial tables to find the exact rejection region for the test. Reject if x ______________ or x ______________ Conclude: ______________ There ______________ enough evidence to indicate a difference between the two gourmets. p-value approach: Test Statistic: ______________ p-value = ______________ Conclude: ______________ There is ______________ enough evidence to indicate a difference between the two gourmets. Use the large-sample z statistic for testing. (NOTE: Although the large-sample Approximation is suggested for 25, it works fairly well for values of n as small as 15.) The large sample z-statistic is: ______________ The two-tailed rejection region is |z| > ______________. Conclude: ______________ There is ______________ enough evidence to indicate a difference between the two gourmets. Compare the results of the two tests. The two tests give ______________ results.

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

In a Kruskal-Wallis test for comparing three populations, the test statistic is calculated as H = 2.80. If the test is conducted at the 5% significance level, then:

Which of the following statements about nonparametric tests is false?

The Spearman rank correlation coefficient allows us to measure and test to determine whether there is evidence of a linear relationship between two variables if:

Eight people were asked to perform a simple puzzle-assembly task under normal conditions and under stressful conditions. During the stressful time, a mild shock was delivered to subjects 3 minutes after the start of the experiment and every 30 seconds thereafter until the task was completed. Blood pressure readings were taken under both conditions. The data in the table are the highest readings during the experiment. Do the data present sufficient evidence to indicate higher blood pressure readings under stressful conditions? Analyze the data using the Wilcoxon signed-rank test for a paired experiment. Test statistic: T = ______________ What is the critical value for the test statistic? Reject if the test statistic < ______________. Conclude: ______________ We ______________ conclude that higher blood pressure readings occur during conditions of stress.

The normal approximation to the Wilcoxon signed rank sum test is used whenever the number of none zero differences is 50 or more.

To use the Wilcoxon Rank Sum Test as a test for location, we must assume that:

In a Kruskal-Wallis test, there are three samples, and the value of the test statistic is calculated as H = 7.378. Then the p-value of the test is 0.025.

To apply the Wilcoxon rank sum test to determine whether the location of population 1 is different from the location of population 2, the samples must be:

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. The appropriate critical value at the 5% significance level is:

Suppose there is interest in comparing the median response time for three independent groups learning a new specific task. The appropriate nonparametric procedure is:

The Friedman test are always:

In a Wilcoxon signed rank test, the test statistic is calculated as T = 75. If there are n = 15 observations for which the difference is not zero, and a two-tailed test is performed at the 5% significance level, then:

The z-test approximation to the Wilcoxon rank sum test for two independent samples requires that both sample sizes are smaller than 10.