Question 1

Given that n = 37, and the value of sample Spearman rank correlation coefficient  = 0.35, then the value of the test statistic for testing  is z = 2.10.

Accepted Answer

This statement is true according to the standard procedure for testing the significance of a Spearman rank correlation coefficient. When n = 37, a sample Spearman rank correlation coefficient of 0.35, and a two-tailed test with a significance level of 0.05, the critical value for the test statistic is ±2.032. Since the calculated test statistic (z = 2.10) is greater than the critical value, we can reject the null hypothesis and conclude that there is a significant correlation between the two variables.

Question 2

In a Kruskal-Wallis test, there are four samples and the value of the test statistic is calculated as H = 13.21. Then the most accurate statement that can be made about the p-value of the test is that it is greater than 0.005 but smaller than 0.01.

Accepted Answer

The Kruskal-Wallis test statistic H = 13.21 does not directly indicate a specific p-value without additional context, such as the degrees of freedom (based on the number of groups) and the use of statistical tables or software to determine the exact p-value. The statement provided lacks the necessary information to accurately determine the p-value range.

Question 3

In a Kruskal-Wallis test, there are three samples and the value of the test statistic is calculated as H = 7.378. Then the p-value of the test is 0.025.

Accepted Answer

If the value of the test statistic is 7.378 and the p-value is 0.025, then the null hypothesis (that there is no difference among the populations) can be rejected at a significance level of 0.025, which is less than the commonly used level of 0.05. Therefore, there is evidence to suggest that at least one of the populations is different from the others.

Question 4

The Friedman test statistic is approximately chi-square 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 statement is true. The Friedman test is a non-parametric alternative to the repeated measures ANOVA, used when the data is not normally distributed. The test statistic used in Friedman's test is the Friedman test statistic. The Friedman test statistic is approximately chi-square 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.

Question 5

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

Accepted Answer

The answer of If the Friedman test is applied to...

Question 6

In a Kruskal-Wallis test, there are five samples and the value of the test statistic is calculated as H = 12.32. Then the most accurate statement that can be made about the p-value of the test is that it is greater than 0.025 but smaller than 0.05.

Accepted Answer

The Kruskal-Wallis test statistic H does not directly determine the p-value without considering the degrees of freedom and consulting the chi-square distribution table or using statistical software. The p-value depends on the degrees of freedom (number of groups - 1) and the distribution, not just the H value alone.

Question 7

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

Accepted Answer

The Kruskal-Wallis test is a non-parametric alternative to the one-way ANOVA test for comparing the median of more than two independent groups. It can also be used for two groups, and in that case, it is equivalent to the Wilcoxon rank sum test. However, the Wilcoxon rank sum test is a specific test for two groups only, while the Kruskal-Wallis test can be used for multiple groups.

Question 8

The Friedman test is the nonparametric counterpart to the randomized block design of the analysis of variance.

Accepted Answer

The Friedman test is indeed the nonparametric equivalent of the randomized block design ANOVA.

Question 9

The Spearman rank correlation coefficient is calculated by first ranking the data values, and then calculating the Pearson correlation coefficient of the ranks.

Accepted Answer

This is the correct explanation of how to calculate the Spearman rank correlation coefficient.

Question 10

The Friedman test is employed to compare two or more populations when the data are generated from a matched pairs experiment and are either ordinal or interval, but not normally distributed.

Accepted Answer

The Friedman test is specifically designed for comparing two or more populations with matched data that are not normally distributed but are either ordinal or interval.

Question 11

The Friedman test is a nonparametric test that can be used to compare more than two dependent samples when the assumptions for an analysis of variance are invalid.

Accepted Answer

The Friedman test is indeed a nonparametric test used to compare more than two dependent samples when the assumptions for an analysis of variance are not met, making it a useful alternative to ANOVA.

Question 12

We can use the Friedman test to determine whether a difference exists between two populations. However, if we want to determine whether one population location is larger than another, we must use the sign test.

Accepted Answer

The answer of We can use the Friedman test to...

Question 13

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 14

The Spearman rank correlation 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.

Accepted Answer

The Spearman rank-correlation test measures the strength and direction of association between two ranked variables, rather than comparing relative frequency distributions of two populations.

Question 15

To determine if a relationship exists between two variables, the hypotheses to be tested are  , where  is the Spearman rank correlation coefficient.

Accepted Answer

The answer of To determine if a relationship exists between...

Question 16

The Spearman rank correlation test is a nonparametric test that (1) 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, and (2) determines whether a sample comes from a population with a specified median.

Accepted Answer

The Spearman rank correlation test is a nonparametric test that assesses how well the relationship between two variables can be described using a monotonic function, not for comparing distributions or medians.

Question 17

The population Spearman correlation coefficient is labelled  , and the sample statistic used to estimate its value is labelled  .

Accepted Answer

This statement is true. The population Spearman correlation coefficient can be labelled as mentioned and its sample statistic is used to estimate its value.

Question 18

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

Accepted Answer

The answer of If the Friedman test is applied to...

Question 19

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

Accepted Answer

A one-sample t test and the Friedman test are not directly comparable as they are used for different types of data. A one-sample t test is used to compare a sample mean to a known population mean, while the Friedman test is used to compare multiple treatments across multiple blocks.

Quiz 15: A:nonparametric Statistics

Given that n = 37, and the value of sample Spearman rank correlation coefficient = 0.35, then the value of the test statistic for testing is z = 2.10.