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Non-parametric Statistics

Description: This quiz covers the fundamental concepts and methods of non-parametric statistics, a branch of statistics that makes no assumptions about the underlying distribution of data.
Number of Questions: 15
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Tags: non-parametric statistics hypothesis testing rank-based methods distribution-free tests
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Which of the following is a non-parametric statistical test?

  1. t-test

  2. ANOVA

  3. Chi-square test

  4. Linear regression

Show answer
Correct Option: C
Explanation:

The Chi-square test is a non-parametric test that is used to test the independence of two categorical variables.

What is the main advantage of using non-parametric tests?

  1. They are more powerful than parametric tests.

  2. They are less sensitive to outliers.

  3. They do not require the data to be normally distributed.

  4. They are easier to interpret.

Show answer
Correct Option: C
Explanation:

Non-parametric tests do not make any assumptions about the underlying distribution of the data, making them suitable for data that does not follow a normal distribution.

Which of the following is a rank-based non-parametric test?

  1. Mann-Whitney U test

  2. Kruskal-Wallis test

  3. Wilcoxon signed-rank test

  4. All of the above

Show answer
Correct Option: D
Explanation:

The Mann-Whitney U test, Kruskal-Wallis test, and Wilcoxon signed-rank test are all rank-based non-parametric tests that are used to compare the medians of two or more groups.

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

  1. The data is normally distributed.

  2. The medians of the two groups are equal.

  3. The two groups are independent.

  4. The data is randomly distributed.

Show answer
Correct Option: B
Explanation:

In a non-parametric test, the null hypothesis typically states that there is no difference between the medians of the two groups being compared.

Which of the following is a distribution-free test?

  1. t-test

  2. ANOVA

  3. Chi-square test

  4. F-test

Show answer
Correct Option: C
Explanation:

The Chi-square test is a distribution-free test, meaning that it does not require the data to follow a specific distribution.

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

  1. The probability of obtaining the observed results, assuming the null hypothesis is true.

  2. The probability of obtaining the observed results, assuming the alternative hypothesis is true.

  3. The probability of obtaining the observed results, assuming the data is normally distributed.

  4. The probability of obtaining the observed results, assuming the data is randomly distributed.

Show answer
Correct Option: A
Explanation:

The p-value in a non-parametric test is the probability of obtaining the observed results, assuming that the null hypothesis is true.

What is the critical value in a non-parametric test?

  1. The value of the test statistic that corresponds to the desired level of significance.

  2. The value of the test statistic that corresponds to the null hypothesis.

  3. The value of the test statistic that corresponds to the alternative hypothesis.

  4. The value of the test statistic that corresponds to the p-value.

Show answer
Correct Option: A
Explanation:

The critical value in a non-parametric test is the value of the test statistic that corresponds to the desired level of significance.

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

  1. Parametric tests make assumptions about the underlying distribution of the data, while non-parametric tests do not.

  2. Parametric tests are more powerful than non-parametric tests.

  3. Non-parametric tests are easier to interpret than parametric tests.

  4. All of the above

Show answer
Correct Option: D
Explanation:

Parametric tests make assumptions about the underlying distribution of the data, while non-parametric tests do not. Parametric tests are generally more powerful than non-parametric tests, but non-parametric tests are easier to interpret and can be used with data that does not follow a normal distribution.

Which of the following is an example of a non-parametric measure of central tendency?

  1. Mean

  2. Median

  3. Mode

  4. Standard deviation

Show answer
Correct Option: B
Explanation:

The median is a non-parametric measure of central tendency that is not affected by outliers.

Which of the following is an example of a non-parametric measure of variability?

  1. Range

  2. Variance

  3. Standard deviation

  4. Coefficient of variation

Show answer
Correct Option: A
Explanation:

The range is a non-parametric measure of variability that is calculated by subtracting the smallest value from the largest value in a dataset.

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

  1. t-test

  2. ANOVA

  3. Mann-Whitney U test

  4. Kruskal-Wallis test

Show answer
Correct Option: C
Explanation:

The Mann-Whitney U test is a non-parametric test for comparing two independent groups that is based on the ranks of the data.

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

  1. t-test

  2. ANOVA

  3. Wilcoxon signed-rank test

  4. Friedman test

Show answer
Correct Option: C
Explanation:

The Wilcoxon signed-rank test is a non-parametric test for comparing two related groups that is based on the differences between the paired observations.

Which of the following is an example of a non-parametric test for comparing three or more independent groups?

  1. t-test

  2. ANOVA

  3. Kruskal-Wallis test

  4. Friedman test

Show answer
Correct Option: C
Explanation:

The Kruskal-Wallis test is a non-parametric test for comparing three or more independent groups that is based on the ranks of the data.

Which of the following is an example of a non-parametric test for comparing three or more related groups?

  1. t-test

  2. ANOVA

  3. Friedman test

  4. Kendall's coefficient of concordance

Show answer
Correct Option: C
Explanation:

The Friedman test is a non-parametric test for comparing three or more related groups that is based on the ranks of the data.

Which of the following is an example of a non-parametric test for testing the independence of two categorical variables?

  1. t-test

  2. ANOVA

  3. Chi-square test

  4. Fisher's exact test

Show answer
Correct Option: C
Explanation:

The Chi-square test is a non-parametric test for testing the independence of two categorical variables.

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