Exam 15: Nonparametric Statistics

A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 6 and 10. The alternative hypothesis is that the location of population 1 is different from the location of population 2. Using a 0.05 significance level, the appropriate critical value is 32.

Comparing 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, may well call for a:

To apply the Friedman test to determine whether the locations of two or more populations are the same, the samples must be:

The Kruskal-Wallis test can be used to test for a difference between two populations. It will produce the same outcome as the two-tail Wilcoxon rank sum test.

Which of the following correctly describes the Wilcoxon rank-sum test?

A matched pairs experiment yielded the following results: Number of positive differences = 20, Number of negative differences = 8 Number of zero differences = 2 Can we infer at the 5% significance level that the location of population 1 is to the right of the location of population 2? Test statistic: z-statistic = ______________ Rejection region: Reject if the z-statistic ______________. Conclusion: ______________ We ______________ infer at the 5% significance level that the location of population 1 is to the right of the location of population 2.

A paired sample, two-sample t-test, corresponds to:

A one-sample t-test is the parametric counterpart of the Friedman test for randomized block experimental design.

In the sign test applications, the normal approximation to the binomial distribution works very well even when the number of nonzero differences is as small as:

The Sign test or Wilcoxon Signed-Rank test are nonparametric tests that can be used to compare two dependent samples when the assumptions for a t-test are invalid.

A three independent samples one-way analysis of variance test corresponds to:

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

A one-sample t-test is the parametric counterpart of the Kruskal-Wallis test.

Three treatments were compared using a completely randomized design. The data are shown in the table. Do the data provide sufficient evidence to indicate a difference in location for at least two of the population distributions? Test using the Kruskal-Wallis H statistic with = 0.05. Test statistic: H = ______________ What is the critical value for the test statistic? Reject if the test statistic > ______________. Conclude: ______________ There ______________ a difference in location among the three treatments.

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. If the test is a two-tailed and the level of significance is , then:

The reaction times to three stimuli were recorded for each of 8 subjects. The data, recorded in seconds, are shown below. This problem uses Friedman's test to determine if there is a difference among the population distributions of reaction times. What experimental design is being used in this problem? ____________________________ 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: = ______________ Rejection region for =0.05: Reject if > ______________ Conclusion: ______________ There is ______________ evidence to conclude that the reaction times for the three stimuli are different. Estimate the p-value for this problem? ______________

In a normal approximation to the Wilcoxon signed rank test, the test statistic is calculated as z = 1.36. For a two-tail test, the p-value is:

Which of the following correctly describes the Wilcoxon rank-sum test?

Which of the following tests employs matched-pairs sampling?

A paired-difference experiment was conducted to compare two populations. The data are shown in the table. Use a sign test to determine whether the population distributions are different. The null and alternate hypotheses are as follows: Determine an appropriate rejection region with 0.01. Critical Values: ______________ Enter n1, n2 Calculate the observed value of the test statistic. ______________ Conclude: ______________ The data present ______________ evidence to indicate that populations 1 and 2 are different.