Question 1

The Friedman test statistic is approximately chi-squared distributed with (k - 1) degrees of freedom, provided that either the number of blocks b or the number of treatments k is greater than or equal to 5.

Accepted Answer

This is a true statement. The Friedman test is a nonparametric test used to compare three or more related samples. The test statistic is calculated by ranking each observation within each block, then calculating the sum of ranks for each treatment. The test is based on the assumption that the differences between treatments are symmetrically distributed across all blocks, and the null hypothesis is that there is no difference between treatments. The test statistic is approximately chi-squared distributed with (k - 1) degrees of freedom, but only if either the number of blocks b, or the number of treatments k, is greater than or equal to 5. If both b and k are less than 5, the distribution of the test statistic cannot be assumed to be chi-squared.

Question 2

The z-test approximation to the Wilcoxon rank sum test for two independent samples requires that at least one of the two sample sizes exceed 10.

Accepted Answer

The z-test approximation to the Wilcoxon rank sum test can only be used when the sample sizes are sufficiently large. Generally, it is recommended that at least one of the sample sizes be greater than 10 for the z-test approximation to be valid.

Question 3

The Wilcoxon signed rank sum test is applied to compare two populations when the samples are matched pairs and the data are interval but not normally distributed.

Accepted Answer

The Wilcoxon signed rank sum test is specifically designed for comparing two populations with matched pairs and non-normal distribution of data. Therefore, the statement is true.

Question 4

A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 5 and 8. The alternative hypothesis is that the location of population 1 is different from the location of population 2. Using the 0.10 significance level, the appropriate critical values are 21 and 49.

Accepted Answer

The critical values for a Wilcoxon rank sum test depend on the sample sizes and the significance level. For sample sizes of 5 and 8 at a 0.10 significance level, the critical values would not be 21 and 49. These values need to be looked up in a Wilcoxon rank sum test table or calculated using statistical software.

Question 5

The Wilcoxon signed rank sum test is the nonparametric counterpart of the t-test of µ_D.

Accepted Answer

The Wilcoxon signed rank sum test is a nonparametric test used to compare two related samples, similar to the paired t-test, but it does not assume normal distribution of differences.

Question 6

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.

Accepted Answer

The answer of The Kruskal-Wallis test can be used to...

Question 7

The sign test and the Wilcoxon signed rank sum test require matched pairs.

Accepted Answer

Both the sign test and the Wilcoxon signed rank sum test are non-parametric tests that require matched pairs of observations, meaning that each value in one group is paired with a corresponding value in the other group.

Question 8

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 the 0.05 significance level, the appropriate critical values are 31 and 65.

Accepted Answer

The critical values for a Wilcoxon rank sum test depend on the sample sizes and the significance level. For sample sizes of 6 and 9 at a 0.05 significance level, the critical values would be different from 31 and 65.

Question 9

The Kruskal-Wallis test requires independent sample.

Accepted Answer

The Kruskal-Wallis test requires independent samples as it is a nonparametric test used for comparing three or more independent groups.

Question 10

The Friedman test is the non-parametric counterpart of the randomised block experimental design of the analysis of variance.

Accepted Answer

This statement is true. The Friedman test is a non-parametric test used to analyze the differences between three or more groups that are related. It is commonly used in randomized block designs, where each block represents a subject or group and each treatment is assigned to a block. The Friedman test is used to determine whether the differences between the groups are statistically significant.

Question 11

In a normal approximation to the sign test, the standardised test statistic is calculated as z = 2.07. If the alternative hypothesis states that the location of population 1 is to the right of the location of population 2, then the p-value of the test is 0.0192.

Accepted Answer

A p-value of 0.0192 indicates that we reject the null hypothesis at a significance level of 0.05, which supports the alternative hypothesis that population 1 is to the right of population 2. Therefore, the statement "the p-value of the test is 0.0192" is true.

Question 12

The Kruskal-Wallis test uses the Chi-squared distribution.

Accepted Answer

The Kruskal-Wallis test is a non-parametric method for testing whether samples originate from the same distribution, and it uses the Chi-squared distribution to determine the significance of the test statistic.

Question 13

The critical value is taken from the t-distribution whenever the test is a Kruskal-Wallis test.

Accepted Answer

The Kruskal-Wallis test is a non-parametric test and uses the chi-square distribution to determine the critical value, not the t-distribution.

Question 14

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

Accepted Answer

A two-independent-sample t-test is used for comparing the means of two independent groups, while a Wilcoxon signed rank sum test is used for comparing the medians of two paired groups. These two tests are not equivalent and should not be used interchangeably.

Question 15

The Wilcoxon rank sum test for independent samples actually tests whether the population distributions are identical.

Accepted Answer

The Wilcoxon rank sum test compares the rank sums of two independent samples to determine if they come from the same population distribution. Therefore, the statement is true.

Question 16

A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20. The value of the unstandardised test statistic is T = 225. The value of the standardised test statistic is z = -1.50.

Accepted Answer

The Wilcoxon rank sum test involves ranking all observations from both samples together and then summing the ranks for one of the samples. The standardised test statistic z is calculated based on the rank sum, sample sizes, and expected mean and variance under the null hypothesis. Given the unstandardised test statistic T and sample sizes, a z value of -1.50 is plausible.

Question 17

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

Accepted Answer

A one-sample t-test is not related to the Friedman test, which is used for non-parametric analysis of variance with repeated measures.

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 two-tailed and the level of significance is 0.05, then the null hypothesis will be rejected.

Accepted Answer

The critical value for a two-tailed test with sample sizes 4 and 6 at a 0.05 significance level is higher than 25, so the null hypothesis is not rejected.

Question 19

In a normal approximation to the Wilcoxon rank sum test, the standardised test statistic is calculated as z = 1.96. For a two-tailed test, the p-value 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 20

The Kruskal-Wallis test is applied to compare two or more populations when the samples are independent and the data are ordinal or numerical and non-normal.

Accepted Answer

The Kruskal-Wallis test is indeed applied to compare two or more populations when the samples are independent and the data are ordinal or numerical and non-normal.

Quiz 21: Nonparametric Techniques