Question 1

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.

Accepted Answer

The Wilcoxon rank sum test is a nonparametric test that can be used when the assumptions of normality and equal variances are not met, making it useful when the assumptions for a t test are invalid. Therefore, the statement is true.

Question 2

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 Mann-Whitney U test) is a non-parametric test used for comparing two independent samples that are not normally distributed. It is a valuable alternative to the t-test when the normality assumption is not met.

Question 3

A parametric test is a hypothesis test that depends on certain specific assumptions about the probability distribution of population values or the sizes of population parameters.

Accepted Answer

A parametric test relies on specific assumptions regarding the distribution of population values or parameters, which distinguishes it from a nonparametric test.

Question 4

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 5

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

Accepted Answer

The answer of A Wilcoxon rank sum test for comparing...

Question 6

In a normal approximation to the Wilcoxon rank sum test, the standardized test statistic is calculated as z = 1.96. For a two-tailed test, the p-value of the test is 0.025.

Accepted Answer

In a two-tailed test, a z-value of 1.96 corresponds to a p-value of 0.05, not 0.025.

Question 7

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

Accepted Answer

Nonparametric tests do not make any assumptions about the underlying population distributions or parameters, making them more flexible in their applications.

Question 8

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 for sample sizes larger than 10. It is recommended to use the normal approximation when both sample sizes are 20 or more.

Question 9

Statistical tests that are not very sensitive to errors in assumptions are called parametric tests.

Accepted Answer

Parametric tests are actually quite sensitive to errors in assumptions, particularly when it comes to the assumption of normality. Non-parametric tests, on the other hand, are less sensitive to assumptions and can be used when data does not follow specific distributional assumptions.

Question 10

A nonparametric test is one that makes no assumptions about the specific shape of the population from which a sample is drawn.

Accepted Answer

A nonparametric test does not assume any specific distribution for the population, making it suitable for datasets with unknown or non-normal distributions.

Question 11

Nonparametric tests are often more efficient than parametric tests.

Accepted Answer

This statement is false. Parametric tests are generally more efficient than nonparametric tests, as they can make use of more information about the data and assumptions about the population. Nonparametric tests are preferred when certain assumptions about the data and population cannot be met or when the data are highly skewed or non-normal.

Question 12

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

This is true. The critical value for a Wilcoxon rank sum test with a 0.05 significance level and samples sizes of 6 and 10 is indeed 32.

Question 13

A parametric test is a hypothesis test that depends on certain specific assumptions about the probability distribution of population values or the sizes of population parameters.

Accepted Answer

A parametric test assumes certain specific characteristics about the population distribution, while a non-parametric test makes no such assumptions.

Question 14

Nonparametric statistical methods generally specify hypotheses in terms of population distributions rather than parameters such as means and standard deviations.

Accepted Answer

Nonparametric statistical methods make fewer assumptions about the underlying population distribution and often focus on rank-based tests or comparisons of medians rather than specific numerical parameters like means and standard deviations. Therefore, hypotheses are typically stated in terms of the overall shape or form of the distribution rather than specific values of parameters.

Question 15

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 16

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

Accepted Answer

The Mann-Whitney U test is a nonparametric test used to compare differences between two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed. It does not measure the degree of association between two variables.

Question 17

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.

Accepted Answer

The sign test is a non-parametric test that only requires the direction of the difference (whether it is positive or negative), while the Wilcoxon signed-rank test requires both the direction and the magnitude of the difference. Therefore, when only the direction is known, the sign test can be used but the Wilcoxon signed-rank test cannot.

Question 18

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 19

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 20

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

The statement accurately describes the Wilcoxon rank sum test.

Quiz 15: A:nonparametric Statistics

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.

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

A parametric test is a hypothesis test that depends on certain specific assumptions about the probability distribution of population values or the sizes of population parameters.

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

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

In a normal approximation to the Wilcoxon rank sum test, the standardized test statistic is calculated as z = 1.96. For a two-tailed test, the p-value of the test is 0.025.

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

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

Statistical tests that are not very sensitive to errors in assumptions are called parametric tests.

A nonparametric test is one that makes no assumptions about the specific shape of the population from which a sample is drawn.

Nonparametric tests are often more efficient than parametric tests.

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.

A parametric test is a hypothesis test that depends on certain specific assumptions about the probability distribution of population values or the sizes of population parameters.

Nonparametric statistical methods generally specify hypotheses in terms of population distributions rather than parameters such as means and standard deviations.

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

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

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.

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.

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.

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.