Non-Parametric Tests: Master Statistical Analysis Without Assumptions

Question 1

Identify the assumption of parametric tests that is often violated in practical applications.

Accepted Answer

Data follows a normal distribution.

Answer

Data is measured on an ordinal scale.

Answer

Population variance is known.

Answer

Samples are randomly selected.

Question 2

Define the p-value in the context of non-parametric testing.

Accepted Answer

Probability of obtaining results assuming the null hypothesis is true.

Answer

Probability of obtaining results assuming the alternative hypothesis is true.

Answer

Probability of making a Type I error.

Answer

Probability of making a Type II error.

Question 3

In the context of the Kruskal-Wallis test, what is the purpose of the H statistic?

Accepted Answer

Calculating the p-value.

Answer

Determining the critical value.

Answer

Ranking data points.

Answer

Comparing group medians.

Question 4

Which non-parametric test is specifically designed to analyze trends?

Accepted Answer

Chi-square test for trend

Answer

Mann-Whitney U test

Answer

Kruskal-Wallis test

Answer

Spearman's rank correlation coefficient

Question 5

What is the primary purpose of the Chi-square test?

Accepted Answer

To test the relationship between two categorical variables

Answer

To compare the means of two independent groups

Answer

To compare the medians of two independent groups

Answer

To test if a sample comes from a specific population

Question 6

Which non-parametric test is most appropriate for comparing the means of two independent groups?

Accepted Answer

Mann-Whitney U test

Answer

Chi-square test

Answer

Kruskal-Wallis test

Answer

Fisher's exact test

Question 7

The Chi-square test is used to test for:

Accepted Answer

Differences in proportions

Answer

Rank differences between two groups

Answer

Differences in variance between multiple groups

Answer

Correlation between two variables

Question 8

The Kruskal-Wallis test is used to compare the:

Accepted Answer

Medians of multiple groups

Answer

Proportions in two groups

Answer

Variances of three groups

Answer

Ranks of two groups

Question 9

In a Chi-square test, the expected frequency for a cell is:

Accepted Answer

(Row total / Grand total) * (Column total / Grand total)

Answer

(Row total * Column total) / Grand total

Answer

(Row total + Column total) / Grand total

Answer

(Grand total / Row total) * (Grand total / Column total)

Question 10

The Mann-Whitney U statistic is calculated as:

Accepted Answer

The difference in the sum of the ranks between the two groups

Answer

The sum of the ranks in the first group

Answer

The sum of the ranks in the second group

Answer

The ratio of the sum of the ranks in the first group to the sum of the ranks in the second group

Question 11

When using non-parametric tests, it is important to:

Accepted Answer

Check the assumptions of the test

Answer

Transform the data to meet normality

Answer

Use a different parametric test instead

Answer

Ignore the possibility of non-normality

Question 12

Which defining characteristic sets non-parametric statistical tests apart from parametric tests?

Accepted Answer

Non-parametric tests make no assumptions about the underlying distribution of the data.

Answer

Non-parametric tests are always more powerful than parametric tests.

Answer

Non-parametric tests can only be used on categorical data.

Answer

Non-parametric tests are not suitable for real-world applications.

Question 13

What is the null hypothesis for the Mann-Whitney U test?

Accepted Answer

The medians of the two groups being compared are equal.

Answer

The means of the two groups being compared are equal.

Answer

The standard deviations of the two groups being compared are equal.

Answer

The variances of the two groups being compared are equal.

Question 14

What is the primary purpose of conducting a Kruskal-Wallis test?

Accepted Answer

To compare more than two independent groups on the basis of their medians.

Answer

To test whether a sample follows a normal distribution.

Answer

To determine the correlation between two variables.

Answer

To analyze the relationship between a categorical variable and a numerical variable.

Question 15

Which of the following is NOT an assumption that non-parametric tests require?

Accepted Answer

The data is normally distributed.

Answer

The data points are independent.

Answer

The variances of the groups being compared are equal.

Answer

The sample size is sufficiently large.

Question 16

What is the effect of applying the Bonferroni correction to p-values?

Accepted Answer

It makes p-values larger.

Answer

It makes p-values smaller.

Answer

It leaves p-values unchanged.

Answer

It removes the need for p-values.

Question 17

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

Accepted Answer

They can be less powerful than parametric tests, especially when the underlying distribution is normal.

Answer

They cannot be used to test complex hypotheses.

Answer

They require a lot of computation.

Answer

They cannot be applied to real-world data.

Question 18

In non-parametric tests, why is the median a crucial measure? Discuss its advantages and limitations.

Accepted Answer

The median is unaffected by outliers, making it a robust measure of central tendency in non-parametric tests.

Answer

The median is used in non-parametric tests as an alternative to the mean due to its ease of calculation.

Answer

The median is not a reliable measure in non-parametric tests as it can be influenced by sample size.

Answer

The median is exclusively used in non-parametric tests when the data is ordinal.

Question 19

Non-parametric tests are known for their flexibility. Which assumption do they *not* require, unlike their parametric counterparts?

Accepted Answer

Data follows a normal distribution

Answer

Observations are independent

Answer

Groups have equal variances

Question 20

The Kruskal-Wallis test yields a p-value of 0.025. What does this imply about the medians of the three independent groups under comparison?

Accepted Answer

The medians of the three groups are significantly different.

Answer

The medians of the three groups are not significantly different.

Answer

The data is not normally distributed.

Answer

The sample size is insufficient.

Question 21

Which of the following is NOT an assumption of parametric tests?

Accepted Answer

Continuous level of measurement

Answer

Independence of observations

Answer

Normally distributed population

Answer

Equal variances between groups

Question 22

What is the primary purpose of the Chi-square test?

Accepted Answer

To test the independence of two categorical variables

Answer

To compare the means of two independent groups

Answer

To compare the variances of two independent groups

Answer

To test the normality of a distribution

Question 23

Which non-parametric test is the equivalent of the t-test for independent samples?

Accepted Answer

Mann-Whitney U test

Answer

Wilcoxon signed-rank test

Answer

Kruskal-Wallis test

Answer

Friedman test

Question 24

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

Accepted Answer

The medians of all groups are equal

Answer

The distributions of all groups are normal

Answer

The variances of all groups are equal

Answer

The means of all groups are equal

Question 25

What is a potential limitation of non-parametric tests?

Accepted Answer

They can be less powerful than parametric tests

Answer

They cannot be used to test specific hypotheses

Answer

They require larger sample sizes than parametric tests

Answer

Not suitable for complex data structures

Question 26

Which assumption is NOT a requirement for parametric tests to be valid?

Accepted Answer

Ordinal data

Answer

Normality

Answer

Independence

Answer

Homogeneity of variance

Question 27

What is a defining characteristic of non-parametric tests?

Accepted Answer

They require fewer assumptions than parametric tests.

Answer

They assume a normal distribution of data.

Answer

They are always more powerful than parametric tests.

Answer

They can only be used in qualitative research.

Question 28

Which non-parametric test is used to compare two independent samples with ordinal data?

Accepted Answer

Mann-Whitney U test

Answer

Chi-square test

Answer

Kruskal-Wallis test

Answer

Friedman test

Question 29

When calculating the Chi-square test statistic, which of the following values is subtracted from the observed frequency?

Accepted Answer

Expected frequency

Answer

Theoretical frequency

Answer

Residual frequency

Answer

Raw frequency

Question 30

Which non-parametric test is used to compare k independent samples with ordinal data?

Accepted Answer

Kruskal-Wallis test

Answer

Chi-square test

Answer

Mann-Whitney U test

Answer

Wilcoxon signed-rank test

Question 31

Which of the following is NOT an advantage of using non-parametric tests?

Accepted Answer

Can be used with only ratio data

Answer

Less restrictive assumptions

Answer

More robust to outliers

Answer

Can handle missing data

Question 32

True or False: Non-parametric tests make no assumptions about the distribution of the data.

Accepted Answer

True

Answer

False

Question 33

Which non-parametric test is used to test the association between two nominal variables?

Accepted Answer

Chi-square test

Answer

Mann-Whitney U test

Answer

Kruskal-Wallis test

Answer

Fisher's exact test

Question 34

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

Accepted Answer

The medians of all groups are equal

Answer

The variances of all groups are equal

Answer

The means of all groups are equal

Answer

The proportions of all groups are equal

Question 35

What is the interpretation of a non-significant p-value in a non-parametric test?

Accepted Answer

Fail to reject the null hypothesis

Answer

Reject the null hypothesis

Answer

Accept the null hypothesis

Answer

Cannot be determined

Question 36

The Chi-square test is used to:

Accepted Answer

Test for independence between categorical variables

Answer

Compare means of two independent groups

Answer

Analyze the variance of multiple independent groups

Answer

Determine the correlation between two variables

Question 37

Which of the following assumptions must be met for the Mann-Whitney U test to be valid?

Accepted Answer

Independence of observations

Answer

Normality of data distribution

Answer

Equal variances between groups

Answer

Interval or ratio data

Question 38

What is the purpose of the Kruskal-Wallis test?

Accepted Answer

To test for differences in medians among three or more independent groups

Answer

To compare means of two dependent groups

Answer

To determine the correlation between two ordinal variables

Answer

To analyze the variance of a single independent group

Question 39

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

Accepted Answer

They are less powerful than parametric tests

Answer

They cannot be used to analyze continuous data

Answer

They require large sample sizes

Answer

They are sensitive to outliers

Question 40

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

Accepted Answer

The variables are independent

Answer

The variables are not independent

Answer

The variables are normally distributed

Answer

The variables have equal variances

Question 41

When is the Mann-Whitney U test used instead of the Kruskal-Wallis test?

Accepted Answer

When there are two independent groups

Answer

When there are three or more independent groups

Answer

When the data is continuous

Answer

When the data is ordinal and has more than two levels

Question 42

What is the interpretation of a significant p-value in a non-parametric test?

Accepted Answer

The null hypothesis is rejected

Answer

The null hypothesis is accepted

Answer

The test is not statistically significant

Answer

The data is not normally distributed

Question 43

Which of the following is the null hypothesis for the Mann-Whitney U test?

Accepted Answer

The medians of the two groups are equal

Answer

The medians of the two groups are different

Answer

The means of the two groups are equal

Answer

The variances of the two groups are equal

Question 44

The Kruskal-Wallis test is used to compare:

Accepted Answer

Multiple independent groups

Answer

Two independent groups

Answer

Two dependent groups

Answer

Multiple dependent groups

Question 45

When might it be more appropriate to use a non-parametric test instead of a parametric test?

Accepted Answer

Any of the above

Answer

When the data is not normally distributed

Answer

When the sample size is small

Answer

When the variances between groups are unequal

Question 46

The Mann-Whitney U test is a non-parametric alternative to which parametric test?

Accepted Answer

t-test

Answer

ANOVA

Answer

Pearson correlation coefficient

Answer

Regression analysis

Question 47

The Mann-Whitney U test is a non-parametric test used for comparing:

Accepted Answer

Two independent groups.

Answer

More than two independent groups.

Answer

Two dependent groups.

Answer

More than two dependent groups.

Question 48

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

Accepted Answer

The variables are independent.

Answer

The variables are dependent.

Answer

The difference between the observed and expected frequencies is statistically significant.

Question 49

Which step is NOT involved in conducting a non-parametric test?

Accepted Answer

Transform the data to meet parametric assumptions.

Answer

Select the appropriate test statistic.

Answer

Calculate the p-value.

Answer

Draw a conclusion.

Question 50

The Kruskal-Wallis test is used for comparing:

Accepted Answer

More than two independent groups.

Answer

Two independent groups.

Answer

Two dependent groups.

Answer

More than two dependent groups.

Question 51

Which of the following is a potential application of a non-parametric test?

Accepted Answer

Comparing the satisfaction levels of different customer groups.

Answer

Predicting the outcome of a sporting event.

Question 52

Which non-parametric test is used to compare the distributions of two independent samples?

Accepted Answer

Mann-Whitney U test

Answer

Chi-square test

Answer

Kruskal-Wallis test

Answer

Wilcoxon signed-rank test

Question 53

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

Accepted Answer

The variables are independent.

Answer

The variables are dependent.

Answer

The data is normally distributed.

Answer

The sample size is large.

Question 54

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

Accepted Answer

They can be less powerful than parametric tests when the data meets the assumptions of parametric tests.

Answer

They can only be used with ordinal data.

Answer

They require the data to be normally distributed.

Answer

They are difficult to interpret.

Question 55

In which scenario would it be appropriate to use the Mann-Whitney U test instead of the t-test?

Accepted Answer

When the data is not normally distributed.

Answer

When the sample size is very large.

Answer

When the variances of the groups are significantly different.

Answer

When the data is qualitative.

Question 56

Which of the following is NOT an assumption of the Kruskal-Wallis test?

Accepted Answer

Normally distributed data

Answer

Independent samples

Answer

Equal variances among groups

Answer

Equal sample sizes

Question 57

Which of the following is a primary assumption of parametric tests that is not required for non-parametric tests?

Accepted Answer

Data is normally distributed

Answer

Sample size is large

Answer

Variables are independent

Answer

Data is continuous

Question 58

Which non-parametric test is used to compare measurements from two independent samples?

Accepted Answer

Mann-Whitney U test

Answer

Chi-square test

Answer

Kruskal-Wallis test

Answer

Wilcoxon signed-rank test

Question 59

The Kruskal-Wallis test is an extension of the Mann-Whitney U test designed to compare:

Accepted Answer

Multiple independent samples

Answer

Two independent samples

Answer

Paired samples

Answer

The distribution of a variable over time

Question 60

When calculating the test statistic for the Chi-square test, which value is used as the expected frequency?

Accepted Answer

Mean frequency

Answer

Observed frequency

Answer

Median frequency

Answer

Mode frequency

Question 61

Which type of data is most suitable for analysis with the Mann-Whitney U test?

Accepted Answer

Ordinal data

Answer

Nominal data

Answer

Interval data

Answer

Ratio data

Question 62

The Kruskal-Wallis test statistic is based on the:

Accepted Answer

Sum of ranks

Answer

Median rank

Answer

Mean rank

Answer

Standard deviation of ranks

Question 63

When interpreting the results of a Chi-square test, a p-value less than 0.05 generally indicates:

Accepted Answer

There is a significant difference between the observed and expected frequencies

Answer

There is no significant difference between the observed and expected frequencies

Answer

The test is not statistically significant

Answer

The data is normally distributed

Question 64

The assumptions of non-parametric tests are less restrictive compared to parametric tests primarily because they:

Accepted Answer

Do not require normally distributed data

Answer

Do not require large sample sizes

Answer

Do not require independent variables

Answer

Are always more powerful