Non-Parametric Statistics: Interactive Learning Quizzes for PhD Data Analysis

Question 1

Which of the following is a crucial assumption of non-parametric statistical tests?

Accepted Answer

The data points must be independent.

Answer

The data must follow a normal distribution.

Answer

The data must be measured at the interval or ratio level.

Answer

The sample size must be large.

Question 2

Which assumption is unique to parametric tests?

Accepted Answer

The data are normally distributed.

Answer

The data are independent.

Answer

The variances of the groups are equal.

Answer

The sample size is large.

Question 3

Which non-parametric test is used to determine if two independent samples originate from the same continuous distribution?

Accepted Answer

Kolmogorov-Smirnov test

Answer

Chi-squared test

Answer

Mann-Whitney U test

Answer

Kruskal-Wallis test

Question 4

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

Accepted Answer

Mann-Whitney U test

Answer

Chi-squared test

Answer

Kolmogorov-Smirnov test

Answer

Kruskal-Wallis test

Question 5

Which assumption is essential for the validity of a non-parametric statistical test?

Accepted Answer

Data is independent.

Answer

Data is normally distributed.

Answer

Sample size is large.

Answer

Variables are continuous.

Question 6

What is a key difference between parametric and non-parametric tests?

Accepted Answer

Parametric tests assume normal data distribution, while non-parametric tests do not.

Answer

Parametric tests are more powerful.

Answer

Non-parametric tests are always more conservative.

Answer

Parametric tests are always suitable for large sample sizes.

Question 7

In non-parametric statistical testing, which fundamental assumption is essential?

Accepted Answer

Samples are independent, and observations are identically distributed.

Answer

Data follows a normal distribution.

Answer

Sample size is sufficiently large.

Answer

Data is continuous.

Question 8

What is a primary benefit of using non-parametric tests over parametric tests?

Accepted Answer

Non-parametric tests are less sensitive to outliers.

Answer

Non-parametric tests are more powerful than parametric tests.

Answer

Non-parametric tests can be used with data that meet the assumptions of parametric tests.

Answer

Non-parametric tests are easier to compute than parametric tests.

Question 9

Which assumption is crucial for the Kruskal-Wallis test to be valid?

Accepted Answer

Data points are independent.

Answer

Data follows a normal distribution.

Answer

Data is measured on an interval or ratio scale.

Answer

Variances between groups are equal.

Question 10

In bootstrapping, a statistical technique for approximating the distribution of a sample statistic, what is the primary resampling method?

Accepted Answer

Resampling with replacement

Answer

Sampling without replacement

Answer

Exhaustive enumeration of all possible samples

Question 11

Which assumption is **exclusive** to non-parametric tests?

Accepted Answer

The data does not need to follow any specific distribution.

Answer

The data must follow a normal distribution.

Answer

The data must be independent and identically distributed.

Question 12

Which assumption is essential for the validity of non-parametric statistical tests?

Accepted Answer

Data must be independent.

Answer

Data must follow a normal distribution.

Question 13

Which assumptions are required for parametric statistical tests, but not for non-parametric statistical tests?

Accepted Answer

The data follows a normal distribution.

Accepted Answer

The variances of the groups being compared are equal.

Answer

The sample size is large.

Question 14

What's the core difference between parametric and non-parametric statistical tests?

Accepted Answer

Parametric tests assume a specific distribution (e.g., normal), while non-parametric tests don't.

Answer

Sample size doesn't determine test type.

Answer

Parametric tests aren't necessarily more powerful.

Answer

Non-parametric tests aren't always more conservative.

Question 15

Which assumption is essential for the validity of a non-parametric test?

Accepted Answer

The data points are independent.

Answer

The data follows a normal distribution.

Answer

The data has an equal number of observations in each category.

Question 16

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

Accepted Answer

Non-parametric tests do not require the data to be normally distributed.

Answer

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

Answer

Non-parametric tests are more complex to calculate than parametric tests.

Question 17

In non-parametric statistical analyses, what is the main reason for using Monte Carlo simulation?

Accepted Answer

To approximate sampling distributions and estimate population parameters through repeated random sampling

Answer

To randomly sample from a known probability distribution

Answer

To test hypotheses about differences between populations

Question 18

In Monte Carlo simulations, why is random sampling with replacement used?

Accepted Answer

To approximate the distribution of a statistic by generating numerous random samples.

Answer

To decrease the time needed for statistical calculations.

Answer

To address missing or incomplete data in the dataset.

Answer

To evaluate the stability and robustness of a statistical model.

Question 19

In bootstrapping, what is a key characteristic of the resampling process?

Accepted Answer

Drawing observations with replacement from the original sample

Answer

Including more observations in the pseudo-samples than in the original sample

Answer

Utilizing a different statistical test for each pseudo-sample

Answer

Calculating the median of each pseudo-sample

Question 20

In non-parametric statistical analysis, how can simulation be effectively employed? Analyze its benefits and drawbacks.

Accepted Answer

Simulation in non-parametric statistics allows for evaluating the power of a test and determining the optimal sample size for a desired power level.

Answer

Simulation in non-parametric statistics is mainly useful for visualizing data but not for hypothesis testing.

Answer

Simulation in non-parametric statistics always provides accurate results, regardless of sample size.

Answer

Simulation in non-parametric statistics is computationally demanding and impractical for large datasets.

Question 21

What is the primary purpose of the chi-squared test?

Accepted Answer

Testing for independence of categorical variables

Answer

Comparing the means of two or more groups

Answer

Determining if data are normally distributed

Answer

Comparing the variances of two or more groups

Question 22

What is the fundamental difference between parametric and non-parametric statistical tests?

Accepted Answer

Parametric tests make distributional assumptions about the data, while non-parametric tests do not

Answer

Non-parametric tests are more powerful than parametric tests

Answer

Parametric tests are easier to compute than non-parametric tests

Answer

Non-parametric tests can be used with any data type, while parametric tests cannot

Question 23

The Kruskal-Wallis test is used primarily to:

Accepted Answer

Compare medians between three or more independent groups

Answer

Compare medians between two independent groups

Answer

Test for independence between categorical variables

Answer

Determine if data are drawn from a specified distribution

Question 24

Which non-parametric test is used to compare two independent groups when the data is ordinal?

Accepted Answer

Mann-Whitney U test

Answer

Kruskal-Wallis H test

Answer

Wilcoxon signed-rank test

Answer

Friedman test

Question 25

What is the purpose of the chi-square goodness-of-fit test?

Accepted Answer

To compare the observed frequencies of a categorical variable to the expected frequencies

Answer

To test the independence of two categorical variables

Answer

To determine the correlation between two quantitative variables

Answer

To compare the means of two independent groups

Question 26

Which of the following would be the most appropriate non-parametric test to use for the following data: ordinal data on the level of satisfaction with a new customer service initiative?

Accepted Answer

Kruskal-Wallis H test

Answer

Mann-Whitney U test

Answer

Wilcoxon signed-rank test

Answer

Friedman test

Question 27

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

Accepted Answer

They can be less powerful than parametric tests

Answer

They can be more difficult to interpret

Answer

They are not suitable for large sample sizes

Answer

They are not widely used in practice

Question 28

In interpreting non-parametric statistical analyses, how does effect size enhance our understanding of the results?

Accepted Answer

Effect size provides context for the strength of the relationship, helping us interpret the practical significance of the findings.

Answer

Statistical significance alone is sufficient for making research decisions, making effect size redundant.

Answer

Effect size is only relevant for parametric tests and not applicable in non-parametric analyses.

Answer

When the p-value is statistically significant, considering effect size is unnecessary.

Question 29

Which of the following accurately distinguishes the Mann-Whitney U test from the t-test?

Accepted Answer

The Mann-Whitney U test is non-parametric, while the t-test is parametric.

Answer

The t-test is suitable for comparing paired groups, whereas the Mann-Whitney U test can only compare independent groups.

Answer

The critical values for the Mann-Whitney U test are constant, regardless of the sample size.

Answer

The Mann-Whitney U test is more powerful than the t-test when data is normally distributed.

Question 30

Identify the assumption that is NOT required for conducting a parametric test:

Accepted Answer

Outliers do not significantly impact results

Answer

Data follows a normal distribution

Answer

Groups have equal variances

Answer

Data points are independent

Question 31

Identify a limitation associated with non-parametric tests:

Accepted Answer

Lower power compared to parametric tests

Answer

Requirement for larger sample sizes

Answer

Inability to test hypotheses about means

Answer

Limited use compared to parametric tests

Question 32

What is the primary purpose of the median absolute deviation (MAD)?

Accepted Answer

Measuring the spread of a distribution

Answer

Calculating event probabilities

Answer

Testing variable independence

Answer

Transforming non-normal distributions into normal ones

Question 33

Provide the formula for calculating the interquartile range (IQR):

Accepted Answer

Q3 - Q1

Answer

Q1 - Q3

Answer

(Q3 - Q1) / 2

Answer

Q1 / Q3

Question 34

Provide an example of a practical application for non-parametric statistics:

Accepted Answer

Analyzing survey results

Answer

Evaluating the effectiveness of a new drug

Answer

Determining intelligence differences between two groups

Answer

Predicting weather conditions

Question 35

Which of the following non-parametric tests is used to test the association between two independent categorical variables?

Accepted Answer

Chi-square test

Answer

Fisher's exact test

Answer

Kendall's tau

Answer

Spearman's rho

Question 36

Which non-parametric test is used to test the homogeneity of variances?

Accepted Answer

Levene's test

Answer

Bartlett's test

Answer

Cochran's test

Answer

Fligner-Killeen test

Question 37

Which non-parametric test is used to test the symmetry of a distribution?

Accepted Answer

Sign test

Answer

Wilcoxon signed-rank test

Answer

Kolmogorov-Smirnov test

Answer

Anderson-Darling test

Question 38

How should the p-value be interpreted in a non-parametric test?

Accepted Answer

The p-value represents the probability of observing the results by chance

Answer

The p-value represents the level of significance of the test

Answer

The p-value represents the effect size of the test

Answer

The p-value represents the power of the test

Question 39

What is the null hypothesis in a non-parametric test?

Accepted Answer

There is no significant difference between the groups

Answer

There is a significant difference between the groups

Answer

The median of the data is equal to a specific value

Answer

The data is normally distributed

Question 40

In which real-world scenario would a non-parametric test be appropriate?

Accepted Answer

Comparing the happiness levels of two groups of people

Answer

Testing the effectiveness of a new drug

Answer

Predicting the future stock price based on historical data

Answer

Analyzing the relationship between height and weight

Question 41

Which non-parametric test is used to compare medians between two independent groups?

Accepted Answer

Mann-Whitney U test

Answer

Kruskal-Wallis test

Answer

Friedman test

Answer

Wilcoxon signed-rank test

Question 42

What is the purpose of a permutation test?

Accepted Answer

To determine the probability of obtaining a given test statistic under the null hypothesis.

Answer

To compare the distribution of two samples.

Answer

To test for normality.

Answer

To determine the effect size of a treatment.

Question 43

A researcher wants to test for a trend in ordinal data. Which non-parametric test should they use?

Accepted Answer

Cochran-Armitage test for trend

Answer

Spearman's rank correlation coefficient

Answer

Kendall's tau-b

Answer

Lin's concordance coefficient

Question 44

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

Accepted Answer

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

Answer

Non-parametric tests are more powerful than parametric tests.

Answer

Parametric tests can only be used with continuous data.

Answer

Non-parametric tests do not require any assumptions about the data.

Question 45

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

Accepted Answer

The medians of the groups being compared are equal.

Answer

The variances of the groups being compared are equal.

Answer

The data is normally distributed.

Answer

The sample size is large enough.

Question 46

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

Accepted Answer

A one-tailed test tests for a difference in one direction, while a two-tailed test tests for a difference in either direction.

Answer

A two-tailed test tests for a difference in one direction, while a one-tailed test tests for a difference in either direction.

Answer

One-tailed tests are more powerful than two-tailed tests.

Answer

Two-tailed tests are more powerful than one-tailed tests.

Question 47

Which is not a type of non-parametric correlation?

Accepted Answer

Pearson's correlation coefficient

Answer

Spearman's rank correlation

Answer

Kendall's tau correlation

Answer

Gamma correlation

Question 48

How do you calculate Spearman's rank correlation?

Accepted Answer

By ranking the data and then calculating the correlation between the ranks.

Answer

By calculating the difference between the ranks of the data points.

Answer

By calculating the mean of the ranks of the data points.

Answer

By calculating the standard deviation of the ranks of the data points.

Question 49

Which of the following is a non-parametric test used to compare the medians of two independent groups?

Accepted Answer

Mann-Whitney U test

Answer

Two-sample t-test

Answer

Wilcoxon signed-rank test

Answer

Kruskal-Wallis test

Question 50

Which of the following is a common application of the Kruskal-Wallis test?

Accepted Answer

Comparing the medians of three or more independent groups.

Answer

Comparing the means of two independent groups.

Answer

Testing for the independence of two categorical variables.

Answer

Testing for the normality of a distribution.

Question 51

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

Accepted Answer

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

Answer

Non-parametric tests are more powerful than parametric tests.

Answer

Parametric tests are more widely accepted than non-parametric tests.

Answer

Non-parametric tests require a larger sample size than parametric tests.

Question 52

Which of the following is a defining characteristic of non-parametric tests?

Accepted Answer

They do not assume a normal distribution of the data.

Answer

They require specialized software.

Answer

They are more powerful than parametric tests.

Answer

They are always less sensitive to violations of assumptions than parametric tests.

Question 53

Which of the following is a commonly used non-parametric test for comparing two related groups?

Accepted Answer

Wilcoxon signed-rank test

Answer

ANOVA

Answer

Independent t-test

Answer

Chi-square test

Question 54

What is the purpose of a Spearman's rank correlation coefficient?

Accepted Answer

To measure the monotonic relationship between two variables.

Answer

To test the difference between two means.

Answer

To compare three or more independent groups.

Answer

To determine the distribution of a variable.

Question 55

What is the primary advantage of using a non-parametric test when the assumptions of a parametric test are not met?

Accepted Answer

It provides a robust test that is less sensitive to violations of assumptions.

Answer

It is easier to calculate than a parametric test.

Answer

It is more powerful than a parametric test.

Question 56

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

Accepted Answer

They can be less powerful than parametric tests, especially when the sample size is large.

Answer

They require specialized software.

Answer

They are more difficult to interpret than parametric tests.

Answer

They can only be used on small sample sizes.

Question 57

When should a non-parametric test be selected over a parametric test?

Accepted Answer

When the assumptions of a parametric test are not met or when the data distribution is non-normal.

Answer

When the sample size is too small.

Answer

When the data is categorical.

Question 58

Which of the following is a non-parametric equivalent to the chi-square test for homogeneity of proportions?

Accepted Answer

Fisher's exact test

Answer

Lilliefors test

Answer

Shapiro-Wilk test

Answer

Jarque-Bera test

Question 59

What is the purpose of bootstrapping in non-parametric statistics?

Accepted Answer

To estimate the sampling distribution and reduce bias in parameter estimation.

Answer

To generate random samples.

Answer

To test for significance.

Question 60

Which of the following statements about effect size in non-parametric statistics is true?

Accepted Answer

It can be difficult to interpret due to the lack of an underlying normal distribution.

Answer

It is always smaller than effect size in parametric statistics.

Answer

It is only meaningful for ordinal data.

Question 61

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

Accepted Answer

**Data are not normally distributed**

Answer

**Homogeneity of variances**

Answer

**Sample size is large enough**

Answer

**Independent observations**

Question 62

**Which of the following is a non-parametric test used for comparing two independent groups?**

Accepted Answer

**Mann-Whitney U test**

Answer

**T-test**

Answer

**Chi-square test**

Answer

**Analysis of variance (ANOVA)**

Question 63

**Which of the following is a non-parametric test used for comparing two related groups?**

Accepted Answer

**Wilcoxon signed-rank test**

Answer

**T-test**

Answer

**Chi-square test**

Answer

**Analysis of variance (ANOVA)**

Question 64

**Which of the following is a non-parametric test used for testing the goodness of fit of a distribution?**

Accepted Answer

**Chi-square goodness-of-fit test**

Answer

**T-test**

Answer

**Mann-Whitney U test**