Non-Parametric Tests: Learn Statistical Tests for Non-Normal Data

Question 1

Describe the main distinction between the Mann-Whitney U test and the Kruskal-Wallis test.

Accepted Answer

The Mann-Whitney U test is for two independent groups, while the Kruskal-Wallis test is for more than two independent groups.

Answer

The Mann-Whitney U test requires normally distributed data while the Kruskal-Wallis test does not.

Answer

The Kruskal-Wallis test is more powerful than the Mann-Whitney U test.

Answer

There is no difference between the two tests.

Question 2

In a Mann-Whitney U test, a test statistic of 200 is obtained, and the critical value for a two-tailed test with a significance level of 0.05 is 196. What is the researcher's conclusion?

Accepted Answer

Reject the null hypothesis.

Answer

Fail to reject the null hypothesis.

Answer

Cannot be determined without the sample size.

Answer

Cannot be determined without the data distribution.

Question 3

The Chi-square test is used specifically to:

Accepted Answer

Analyze the relationship between categorical variables

Answer

Test the equality of two proportions

Answer

Compare the means of two independent groups

Answer

Compare the variances of two independent groups

Question 4

Which of the following is an appropriate measure of effect size for non-parametric tests?

Accepted Answer

Cramer's V

Answer

Cohen's d

Answer

r-squared

Answer

Omega-squared

Question 5

When should the Mann-Whitney U test be utilized?

Accepted Answer

When comparing two independent groups with ordinal or continuous data that is not normally distributed

Answer

When comparing two independent groups with interval or ratio data that is normally distributed

Answer

When comparing two related groups with ordinal or continuous data that is not normally distributed

Answer

When comparing two related groups with interval or ratio data that is normally distributed

Question 6

The Kruskal-Wallis test is the non-parametric equivalent of which parametric test?

Accepted Answer

ANOVA

Answer

t-test

Answer

Chi-square test

Answer

Wilcoxon signed-rank test

Question 7

A key advantage of non-parametric tests is that:

Accepted Answer

They do not require the assumption of normal distribution

Answer

They can be used with small sample sizes

Answer

They are more powerful than parametric tests

Answer

They can be used to analyze both parametric and non-parametric data

Question 8

A potential limitation of non-parametric tests is that:

Accepted Answer

They can be less powerful than parametric tests

Answer

They cannot be used to make inferences about the population

Answer

They are not widely used in research

Answer

They can only be used for ordinal or categorical data

Question 9

What is the null hypothesis of the Chi-square test?

Accepted Answer

There is no relationship between the two variables.

Answer

There is a relationship between the two variables.

Answer

The two variables are normally distributed.

Answer

The variances of the two groups are equal.

Question 10

What is the purpose of the Kruskal-Wallis test?

Accepted Answer

To compare three or more independent groups.

Answer

To compare two independent groups.

Answer

To test the relationship between two variables.

Answer

To test the difference between two means.

Question 11

Which of the following is a measure of effect size for the Mann-Whitney U test?

Accepted Answer

Kendall's tau

Answer

Cohen's d

Answer

Pearson's r

Answer

Eta squared

Question 12

What is the difference between a one-tailed and a two-tailed test?

Accepted Answer

A one-tailed test tests a hypothesis in one direction, while a two-tailed test tests it in both directions.

Answer

A two-tailed test tests a hypothesis in one direction, while a one-tailed test tests it in both directions.

Answer

A one-tailed test is more powerful than a two-tailed test.

Answer

A two-tailed test is more powerful than a one-tailed test.

Question 13

Which of the following is a common misconception about non-parametric tests?

Accepted Answer

They are always less powerful than parametric tests.

Answer

They can only be used with small sample sizes.

Answer

They are more difficult to interpret than parametric tests.

Answer

They are not as reliable as parametric tests.

Question 14

Which of the following is NOT an assumption of the Chi-square test?

Accepted Answer

Normally distributed data

Answer

Independent observations

Answer

Equal sample sizes

Answer

Categorical data

Question 15

The Mann-Whitney U test is used to compare:

Accepted Answer

Two independent groups on an ordinal or continuous variable

Answer

Two dependent groups on a continuous variable

Answer

Multiple independent groups on a categorical variable

Answer

Two dependent groups on a categorical variable

Question 16

What is the null hypothesis for the Kruskal-Wallis test?

Accepted Answer

The median scores are equal across all groups

Answer

The median scores are not equal across all groups

Answer

The means are not equal across all groups

Answer

The variances are not equal across all groups

Question 17

A researcher wants to test whether there is a difference in happiness between three different age groups. Which non-parametric test would be most appropriate?

Accepted Answer

Kruskal-Wallis test

Answer

Chi-square test

Answer

Mann-Whitney U test

Answer

t-test

Question 18

Which of the following is an advantage of using non-parametric tests?

Accepted Answer

Fewer assumptions required

Answer

More powerful than parametric tests

Answer

Easier to interpret

Answer

Can only be used with small sample sizes

Question 19

What is the interpretation of a non-significant Kruskal-Wallis test result?

Accepted Answer

There is not a significant difference in medians across all groups

Answer

There is a significant difference in medians across all groups

Answer

The sample size was too small

Answer

The data is not normally distributed

Question 20

The Chi-square test is used to test the:

Accepted Answer

Independence between categorical variables

Answer

Difference between means of two independent groups

Answer

Difference between medians of two independent groups

Answer

Variance of a single sample

Question 21

In the Mann-Whitney U test, the U statistic represents:

Accepted Answer

The sum of ranks for one group minus the sum of ranks for the other group

Answer

The mean difference between ranks for the two groups

Answer

The variance of the difference between ranks for the two groups

Answer

The probability of observing the obtained difference in ranks by chance

Question 22

Which of the following is a limitation of the Kruskal-Wallis test?

Accepted Answer

Not sensitive to differences in the shape of distributions

Answer

Requires a large sample size

Answer

Can only be used with two independent groups

Answer

Assumes equal sample sizes across all groups

Question 23

Which of the following is a benefit of using non-parametric tests?

Accepted Answer

Fewer assumptions about the data

Answer

More powerful than parametric tests

Answer

Easier to interpret

Answer

Can only be used with small sample sizes

Question 24

Which of the following is a disadvantage of non-parametric tests?

Accepted Answer

Less powerful than parametric tests

Answer

Assumptions about the data are too strict

Answer

Can only be used with large sample sizes

Answer

Difficult to interpret

Question 25

Which of the following is an example of a research question that could be answered using a Chi-square test?

Accepted Answer

Is there a difference in the proportion of males and females in a population?

Answer

Is the average height of children in a particular school district significantly different from the national average?

Answer

Is there a relationship between the type of music people listen to and their personality traits?

Answer

Is the mean weight of newborn babies in a particular hospital significantly different from the national average?

Question 26

Which non-parametric test compares the medians of two independent groups?

Accepted Answer

Mann-Whitney U test

Answer

Chi-square test

Answer

Kruskal-Wallis test

Answer

Wilcoxon signed-rank test

Question 27

In a Chi-square test of independence, what is the null hypothesis?

Accepted Answer

Variables are independent.

Answer

Variables are not independent.

Answer

Groups are of equal size.

Answer

Data follows a normal distribution.

Question 28

Which data type is best suited for a Kruskal-Wallis test?

Accepted Answer

Ordinal

Answer

Nominal

Answer

Interval

Answer

Ratio

Question 29

True or False: Non-parametric tests are universally less powerful than parametric tests.

Accepted Answer

False

Answer

True

Question 30

Which research question can be best answered using a Kruskal-Wallis test?

Accepted Answer

Is the median age of students different across different majors?

Answer

Is the mean height of men different from that of women?

Answer

Is there a relationship between gender and political affiliation?

Answer

Is the distribution of income in the population normal?

Question 31

Which step is NOT part of conducting a non-parametric test?

Accepted Answer

Plotting a histogram

Answer

Defining the research question

Answer

Collecting data

Answer

Selecting an appropriate test

Question 32

What is the main purpose of the Mann-Whitney U test?

Accepted Answer

To compare the medians of two independent groups.

Answer

To compare the means of two independent groups.

Answer

To compare the variances of two independent groups.

Answer

To compare the proportions of two independent groups.

Question 33

Which of the following is a potential disadvantage of using non-parametric tests?

Accepted Answer

They are less powerful than parametric tests.

Answer

They can only be used with small sample sizes.

Answer

They require more complex calculations.

Answer

They are not as versatile as parametric tests.

Question 34

What is the null hypothesis for the Kruskal-Wallis test?

Accepted Answer

The medians of all groups are equal.

Answer

The means of all groups are equal.

Answer

The variances of all groups are equal.

Answer

The proportions of all groups are equal.

Question 35

Which of the following is a real-world example of an application of the Chi-square test?

Accepted Answer

Determining whether there is a relationship between two categorical variables.

Answer

Testing the effectiveness of a new advertising campaign.

Answer

Comparing the mean scores of two groups on a standardized test.

Answer

Predicting the future value of a stock.

Question 36

What is the key difference between a parametric test and a non-parametric test?

Accepted Answer

Parametric tests assume that the data are normally distributed, while non-parametric tests do not.

Answer

Non-parametric tests are more powerful than parametric tests.

Answer

Parametric tests require larger sample sizes than non-parametric tests.

Answer

Non-parametric tests are more versatile than parametric tests.

Question 37

Which of the following is NOT a type of non-parametric test?

Accepted Answer

t-test

Answer

Chi-square test

Answer

Mann-Whitney U test

Answer

Kruskal-Wallis test

Question 38

What is a potential advantage of using a non-parametric test over a parametric test?

Accepted Answer

Non-parametric tests are less sensitive to outliers.

Answer

Non-parametric tests are more accurate.

Answer

Non-parametric tests are more powerful.

Answer

Non-parametric tests are easier to interpret.

Question 39

Which of the following is the null hypothesis of the Chi-square test?

Accepted Answer

The two variables are independent.

Answer

The two variables are related.

Answer

The expected frequencies are equal to the observed frequencies.

Answer

The observed frequencies are equal to the expected frequencies.

Question 40

Which of the following is the purpose of the Kruskal-Wallis test?

Accepted Answer

To compare the means of three or more independent groups.

Answer

To compare the medians of two independent groups.

Answer

To compare the variances of two independent groups.

Answer

To compare the proportions of two independent groups.

Question 41

Which of the following is a limitation of non-parametric tests?

Accepted Answer

They are less powerful than parametric tests in large samples.

Answer

They can only be used with small sample sizes.

Answer

They are not as versatile as parametric tests.

Answer

They are more difficult to conduct than parametric tests.

Question 42

A researcher wants to compare the mean scores of two independent groups on a Likert scale. Which non-parametric test should they use?

Accepted Answer

Mann-Whitney U test

Answer

Chi-square test

Answer

Kruskal-Wallis test

Answer

Wilcoxon signed-rank test

Question 43

Which of the following is NOT a type of non-parametric correlation?

Accepted Answer

Pearson's correlation coefficient

Answer

Spearman's rho

Answer

Kendall's tau

Answer

Gamma