Question 1

Apply the Friedman test to the accompany table of ordinal data to determine whether we can infer at the 10% significance level that at least two population locations differ.  Test Statistic:  = ______________
Reject Region:
Reject  if  > ______________
Conclude: ______________
We ______________ infer at the 10% significance level that at least two population locations differ.

Accepted Answer

The answer of Apply the Friedman test to the accompany...

Question 2

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 Kruskal-Wallis test is used for comparing more than two groups, while the Wilcoxon rank sum test is specifically for comparing two groups to determine if one is larger than the other.

Question 3

A one-sample t-test corresponds to a Kruskal-Wallis test.

Accepted Answer

A one-sample t-test is used to test if a sample mean is different from a known population mean, while a Kruskal-Wallis test is used to test if there are differences between multiple groups in a non-parametric setting. These two tests are not equivalent and are used for different purposes.

Question 4

The Kruskal-Wallis test can be conducted as one or two-tail test.

Accepted Answer

The Kruskal-Wallis test is a non-parametric method for comparing three or more independent samples. It assesses whether the populations from which the samples originate have identical distributions. It does not test for specific directional alternatives (i.e., it does not distinguish between "greater than" or "less than"), making it inherently a one-tailed test.

Question 5

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.

Accepted Answer

The Kruskal-Wallis test is a non-parametric test that can be used to test for differences between two or more populations. It compares the medians of the populations, using a rank-based approach. The two-tail Wilcoxon rank sum test is also a non-parametric test that can be used to test for differences between two populations, based on their ranks. The Kruskal-Wallis test and the Wilcoxon rank sum test will produce the same outcome if used to compare only two populations. Therefore, the statement is true.

Question 6

In all applications of the Kruskal-Wallis test, the alternative hypothesis to be tested is always stated as:
A) the locations of all k populations are the same
B) at least two population locations differ
C) the locations of all w populations differ
D) the locations of all k populations differ
E) at least two population locations are the same

Accepted Answer

The Kruskal-Wallis test is a non-parametric test used to determine whether there is a statistically significant difference between the medians of two or more independent groups. The null hypothesis is that all populations have the same median, while the alternative hypothesis is that at least two populations have different medians. Therefore, the correct answer is B: at least two population locations differ.

Question 7

In a Kruskal-Wallis test for comparing three populations, the test statistic is calculated as H = 2.80. If the test is conducted at the 5% significance level, then:
A) the null hypothesis will be rejected
B) the null hypothesis will not be rejected
C) the alternative hypothesis will not be rejected
D) the test results are inconclusive
E) the t-test for matched pairs must be used

Accepted Answer

The Kruskal-Wallis test is a non-parametric method for comparing three or more independent samples. It is used to determine if there are statistically significant differences between the groups' medians. The decision to reject or not reject the null hypothesis is based on the comparison of the calculated H value with the critical value from the Chi-square distribution (since the test statistic of the Kruskal-Wallis test follows a Chi-square distribution) at the given degrees of freedom (number of groups - 1) and the significance level (alpha). Without the critical value provided or the degrees of freedom, we cannot directly determine the outcome based on the H value alone. However, typically, an H value of 2.80 is considered low for rejecting the null hypothesis at a 5% significance level for most practical sample sizes and group numbers, implying that there is not enough evidence to suggest a significant difference between the groups. Therefore, the null hypothesis will not be rejected.

Question 8

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 9

The normal approximation to the Wilcoxon signed rank sum test is used whenever the number of none zero differences is 50 or more.

Accepted Answer

The correct name of the test is Wilcoxon signed rank test or Wilcoxon signed rank sum test (depending on the context), but there is no normal approximation to this test. The Wilcoxon signed rank test is a non-parametric test that does not assume a normal distribution of the data, so it can be used regardless of the sample size or the number of none zero differences. However, for small sample sizes (i.e. less than 20), the exact distribution of the test statistic should be used instead of the normal approximation.

Question 10

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

Accepted Answer

The critical value is not taken from the F-distribution for the Kruskal-Wallis test, but rather from a chi-squared distribution based on the degrees of freedom of the test.

Question 11

The Kruskal-Wallis test is applied to compare two or more populations, when the samples are independent and the data are either ordinal or interval but not normal.

Accepted Answer

The Kruskal-Wallis test is a non-parametric test for comparing two or more samples when the data are ordinal or continuous but not assumed to be normally distributed. It is used when the samples are independent of one another.

Question 12

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

Accepted Answer

A one-sample t-test is a test for comparing a sample mean to a known population mean, while the Kruskal-Wallis test is a nonparametric test for comparing three or more independent samples. They are not directly related or counterparts of each other.

Question 13

Kruskal-Wallis test is a nonparametric test that can be used to compare more than two independent samples when the assumptions for an analysis of variance are invalid.

Accepted Answer

Kruskal-Wallis test is indeed a nonparametric alternative to ANOVA and can be used when the assumptions for ANOVA are not met.

Question 14

The nonparametric counterpart of the parametric one-way analysis of variance F-test is the:
A) Kruskal-Wallis test
B) Friedman test
C) Wilcoxon rank sum test
D) Wilcoxon signed rank sum test
E) two-tailed t-test

Accepted Answer

The Kruskal-Wallis test is the nonparametric equivalent of the parametric one-way analysis of variance F-test. It is used to compare the medians of three or more groups to determine if there is a significant difference between them. The Friedman and Wilcoxon tests are nonparametric tests for dependent samples, while the Wilcoxon signed rank test is a nonparametric test for independent samples. The two-tailed t-test is a parametric test for comparing the means of two groups.

Question 15

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 16

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

A Kruskal-Wallis test is a non-parametric test used to compare three or more independent samples. The test statistic is denoted as H and its value represents the degree of difference between the medians of the samples. The p-value is then calculated to determine the significance of the results. In this case, the p-value is 0.025, which means that there is a 2.5% chance of observing these results by chance alone. Therefore, we reject the null hypothesis and conclude that there is a significant difference between the groups.

Question 17

The Kruskal-Wallis test is always:
A) one-tail
B) two-tail
C) used with one sample
D) used with only two samples
E) used when the populations are normally distributed

Accepted Answer

The answer of The Kruskal-Wallis test is always:
A) one-tail
B) two-tail
C)...

Question 18

The Kruskal-Wallis Test for Differences in more than 2 Medians is a nonparametric alternative to:
A) ANOVA F test for completely randomized experiments
B) Student's t-test for related samples
C) Student's t-test for independent samples
D) Wilcoxon's Rank Sum Test for differences in two medians
E) Student's t-test for related samples and Student's t-test for independent samples

Accepted Answer

The Kruskal-Wallis test is a nonparametric alternative to the ANOVA F test for completely randomized experiments that compares the medians of three or more groups, assuming the populations have the same shape but potentially different central tendencies. Therefore, the best choice is A. The other options refer to tests that compare two groups or sets of paired data, and are not suitable for comparing multiple groups.

Question 19

The Kruskal-Wallis H test is an extension of the Wilcoxon rank-sum test from two to more than two statistical populations.

Accepted Answer

The Kruskal-Wallis H test is indeed an extension of the Wilcoxon rank-sum test for more than two populations.

Question 20

The Kruskal-Wallis test is an extension of the Wilcoxon rank-sum test from two to more than two statistical populations.

Accepted Answer

The Kruskal-Wallis test is indeed an extension of the Wilcoxon rank-sum test for more than two populations.

Quiz 15: Nonparametric Statistics