Question 1

A two-sample t-test with independent samples corresponds to:

Accepted Answer

A two-sample t-test with independent samples is used to compare the means of two independent groups, which is equivalent to a Wilcoxon rank sum test. Option A is incorrect because the Wilcoxon signed rank test is used for paired samples, where the same subjects are measured twice. Option C is incorrect because the Wilcoxon signed rank test for one sample is used to compare the median of a single group to a hypothesized value. Option D is incorrect because the Friedman test is used for blocked or repeated measures designs with three or more groups. Option E is incorrect because a chi-square test is used for categorical data, not continuous data.

Question 2

The procedure for the Wilcoxon rank sum test requires that we rank each group separately rather than together.

Accepted Answer

In the Wilcoxon rank sum test, all observations from both groups are ranked together, not separately.

Question 3

You are performing the Wilcoxon rank-sum test. The 10^th through 12^th values in an ordered array of pooled sample data all equal $100, while the 9^th value is less than $100 and the 13^th value is more than $100. The appropriate ranks for the three $100 values are:

Accepted Answer

In the Wilcoxon rank-sum test, when there are ties (identical values), the ranks assigned to these values are the average of the ranks that would have been assigned if the values were slightly different. Since the three $100 values are the 10th, 11th, and 12th in the ordered array, their ranks should be averaged: (10+11+12)/3 = 11. Therefore, each of the three $100 values should be assigned the rank of 11.

Question 4

The Wilcoxon rank sum test is used to compare two populations when the samples are independent but not normally distributed.

Accepted Answer

The Wilcoxon rank sum test, also known as the Mann-Whitney U test, is a nonparametric test that can be used to compare the medians of two independent populations that do not follow a normal distribution. Therefore, option A is correct.

Question 5

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.

Accepted Answer

The Wilcoxon rank sum test uses critical values from a table depending on the sample sizes and level of significance. In this case, with sample sizes of 6 and 10 and a significance level of 0.05, the appropriate critical value from the table is 32. Therefore, the statement is true.

Question 6

A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 6 and 9. The alternative hypothesis is that the location of population 1 is to the left of the location of population 2. Using a 0.05 significance level, the appropriate critical values are 31 and 65.

Accepted Answer

The given critical values are incorrect. For a Wilcoxon rank sum test with sample sizes 6 and 9 at a 0.05 significance level and a left-tailed test, the appropriate critical values are 18 and 50.

Question 7

Which of the following statements is false?

Accepted Answer

Given sample size and specified significance level, the probability of a Type II error is larger for a parametric test.

Question 8

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.

Accepted Answer

This is true. The standardized test statistic for a Wilcoxon rank sum test can be calculated using the formula z = (T - μT) / σT, where T is the un-standardized test statistic, μT is its expected value (which is equal to n1 * (n1 + n2 + 1) / 2), and σT is the standard deviation of T (which is equal to sqrt(n1 * n2 * (n1 + n2 + 1) / 12)). Plugging in the given values, we get:

z = (225 - 150) / sqrt(15 * 20 * (15 + 20 + 1) / 12) = -1.50

Therefore, the given value of z is correct.

Question 9

Nonparametric procedures are often, and perhaps more accurately, called free-agent statistics.

Accepted Answer

Nonparametric procedures are often, and perhaps more accurately, called distribution-free statistics because they do not assume a specific distribution for the data.

Question 10

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:

Accepted Answer

The Wilcoxon rank-sum test is appropriate for comparing two independent samples, such as the outputs from plots using fertilizer A and those using fertilizer B.

Question 11

Which one of the following statements correctly states the difference between parametric and nonparametric statistical methods?

Accepted Answer

The main difference is that parametric tests make assumptions about the distribution of the population, while nonparametric tests do not. Nonparametric tests do not rely on population parameters or assumptions about the distribution of the populations from which the samples are drawn, making them more flexible in application. Choice A is not entirely accurate as some nonparametric tests do make distributional assumptions at certain points in the process. Choice C is incorrect as both parametric and nonparametric tests can involve a range of data types. Choice D is incorrect as all populations have parameters, though not all parameters may be known or relevant for a particular analysis.

Question 12

Consider the following data set: 14, 14, 15, 16, 18, 19, 19, 20, 21, 22, 23, 25, 25, 25, 25, and 28. The rank assigned to the four observations of value 25 is:

Accepted Answer

The rank of the first observation of value 25 is 11. The rank of the second observation of value 25 is 12. The rank of the third observation of value 25 is 13. Therefore, the rank assigned to the fourth observation of value 25 is 13.5.

Question 13

Which of the following statements about nonparametric tests is false?

Accepted Answer

The statement "We can only conduct nonparametric tests with data of a higher order than nominal or ordinal" is false. Nonparametric tests can be conducted with nominal and ordinal data as well.

Question 14

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.

Accepted Answer

The statement correctly describes nonparametric techniques as tests for population characteristics without specific parameters.

Question 15

The Wilcoxon rank-sum test is a nonparametric test that uses two independent simple random samples to determine whether the relative frequency distributions of two statistical populations of continuous values are identical to or different from one another.

Accepted Answer

This is an accurate description of the Wilcoxon rank-sum test. It does not require any assumptions about the underlying distributions of the two populations being compared.

Question 16

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.

Accepted Answer

The p-value associated with a z-score of 1.96 in a two-tailed test is approximately 0.05, not 0.025.

Question 17

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

Accepted Answer

The z-test approximation to the Wilcoxon rank sum test can be used when both sample sizes are larger than 10. For smaller sample sizes, the exact Wilcoxon rank sum test should be used instead.

Question 18

In a Wilcoxon rank sum test for independent samples, the two sample sizes are 4 and 6, and the value of the Wilcoxon test statistic is T = 25. If the test is a two-tail and the level of significance is 0.05, then the null hypothesis will be rejected.

Accepted Answer

Given the sample sizes (4 and 6), the critical value for a two-tailed test at the 0.05 significance level from Wilcoxon rank sum tables does not match the provided test statistic (T = 25) for rejecting the null hypothesis. The exact critical values depend on tables or software, but typically, for such small sample sizes, a test statistic of 25 would not be extreme enough to reject the null hypothesis at the 0.05 level.

Question 19

Nonparametric tests can be appropriate for quantitative data when:

Accepted Answer

Nonparametric tests are often used when the assumptions required for parametric tests are not met, such as non-normal distributions or unequal variances.

Question 20

Which of the following statements is true?

Accepted Answer

Nonparametric methods have less rigid requirements than parametric methods, allowing them to be applied to a wider variety of problems. Nonparametric methods can also be applied to nominal data that lack numeric values. Therefore, options A, C, and D are incorrect.

Quiz 15: Nonparametric Statistics