Exam 15: Nonparametric Statistics

A two-independent sample t-test corresponds to a Wilcoxon signed rank test for paired samples.

If the Friedman test is applied to a data set that are generated from a randomized block experiment with 5 treatments and 7 blocks, then the rejection region at the 5% significance level is .

In an investigation of the visual scanning behavior of deaf children, measurements of eye movement rates were taken on nine deaf and nine hearing children as shown in the table below. Does it appear that the distributions of eye-movement rates for deaf children and hearing children differ? Test at = 0.05 using the Wilcoxon rank sum test. The null and alternate hypotheses are: : The distributions of eye-movement rates for hearing impaired children and hearing children are identical. : The distributions of eye-movement rates for hearing impaired children and hearing children are different. What is the test statistic? T: ______________ What is the critical value for the test statistic? ______________ Thus: ______________ Conclude: We conclude that the hearing impaired children ______________ from the hearing children in eye-movement rate.

Nonparametric tests are methods of inference that make no assumptions whatsoever about the nature of underlying population distributions or their parameters.

Two aptitude tests are currently being used to screen applicants for a certain position within a company. The question arose as to whether the two tests are comparable, i.e., whether they yield the same results. Six applicants were selected at random to take both tests (in a random order). The following scores were recorded: Use the Wilcoxon signed-rank test to determine whether there is a difference in scores between the two tests. Use = 0.10. What is the test statistic? ______________ What is the critical value for the test statistic? ______________ Conclude: ______________ We ______________ conclude there is a difference in the frequency distributions of scores for the two aptitude tests.

The nonparametric counterpart of the parametric t-test of for matched pairs is the:

You are performing the Wilcoxon rank-sum test. The 14^th through 16^th values in an ordered array of pooled sample data all equal $160 (while the 13^th value is less and the 17^th value is more). The appropriate ranks for the three $160 values are:

A car dealer was interested in comparing two brands of tires to see if they yielded different wear length (in thousands of miles). The dealer selected eight cars at random and used each of the brands of tires on each car. The wear length was recorded as follows: Use the sign test to see if the distribution of wear length is the same for both brands of tires. Use = 0.05. The null and alternate hypotheses are: : The distributions of wear length are identical for the two brands of tires, and p = 0.50. : The distributions of wear length are not identical for the two brands of tires, and p 0.50. What is the test statistic? x = ______________ What is the p-value for the test statistic? ______________ Conclusion ______________ Conclude that the distributions of wear length for the two brands of tires are ______________.

If the Friedman test is applied to a data set that are generated from a randomized block experiment with 3 treatments and 5 blocks, then the rejection region at the 2.5% significance level is > 12.8325.

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

The nonparametric counterpart of the parametric one-way analysis of variance F-test is the:

The first step in a Wilcoxon rank sum test is to combine the data values in the two samples and assign a rank of 1 to the:

The Wilcoxon signed rank 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 Wilcoxon Rank Sum Test is a nonparametric test that can be used to compare two independent samples when the assumptions for a t-test are invalid.

Inferential procedures that are free from restrictive assumptions about the sampled populations are known as:

The general manager of a frozen TV dinner maker must decide which one of four new dinners to introduce to the market. He decides to perform an experiment to help make a decision. Each dinner is sampled by ten people who then rate the product on a 7-point scale, where 1 = poor, and 7 = excellent. The results are shown below. Which statistical technique the general manager can use to help him make a decision? ______________ Can the general manager infer at the 5% significance level that there are differences in the taste ratings of the four dinners? Test Statistic: ______________ Reject Region: Reject if test statistic > ______________ Conclude: ______________ The general manager ______________ infer at the 5% significance level that there are differences in the taste ratings of the four dinners. Using the appropriate statistical table, what statement can be made about the p-value for this test? ______________

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

When the direction (and not the magnitude) of the difference within each matched paired in a paired experiment is known, the sign test can be used while the Wilcoxon Signed-Rank test cannot be used.

In a Friedman test for comparing four populations, provided that there as eight blocks, the test statistic is calculated as = 10.98. If the test is conducted at the 5% significance level, the conclusion and p-value will be:

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.