Non-Parametric Statistics: A Comprehensive Guide for Educational Research

Question 1

In the context of non-parametric statistical tests, define statistical power and explain its significance.

Accepted Answer

Statistical power is the likelihood of correctly rejecting the null hypothesis when it is false.

Answer

Statistical power is the likelihood of incorrectly rejecting the null hypothesis when it is true.

Answer

Statistical power is irrelevant in non-parametric tests.

Answer

Statistical power alone determines the sample size needed for a study.

Question 2

Which statistical test compares the medians of two independent groups of data?

Accepted Answer

Mann-Whitney U test

Answer

Wilcoxon rank-sum test

Answer

Kruskal-Wallis test

Answer

Friedman test

Question 3

A key difference between parametric and non-parametric tests relates to:

Accepted Answer

Assumptions about data distribution

Answer

Use of summary statistics

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Power of the test

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Type of data that can be analyzed

Question 4

A potential limitation of using non-parametric tests is their:

Accepted Answer

Loss of statistical power

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Difficulty in interpreting results

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Increased computational complexity

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Inability to handle missing data

Question 5

Considering non-normal data distributions in educational research is important because it:

Accepted Answer

Can lead to biased results in parametric tests

Answer

Requires the use of non-parametric tests

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Improves the generalizability of research findings

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Simplifies the process of data analysis

Question 6

Bootstrapping in non-parametric analysis involves:

Accepted Answer

Resampling to estimate sampling distributions

Answer

Generating random data

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Transforming data to meet parametric assumptions

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Comparing results from different non-parametric tests

Question 7

Which of the following is a fundamental assumption underlying parametric statistical tests?

Accepted Answer

Data distribution is normal

Answer

Data is non-parametric

Answer

Data is categorical

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Data is ordinal

Question 8

When is it appropriate to employ a non-parametric statistical test?

Accepted Answer

When data fails to meet the assumptions of parametric tests

Answer

When data exhibits a normal distribution

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When data sample size is small

Answer

When data is categorical

Question 9

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

Accepted Answer

Mann-Whitney U test

Answer

Wilcoxon signed-rank test

Answer

Kruskal-Wallis test

Answer

Friedman test

Question 10

What is the primary purpose of a contingency table in the context of non-parametric statistics?

Accepted Answer

To illustrate the frequency of observations across category combinations

Answer

To compute the mean and standard deviation of the data

Answer

To test for significant differences between groups

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To visualize data distribution

Question 11

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

Accepted Answer

There is no difference between the groups

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The data is normally distributed

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The population mean is equal to zero

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The correlation between the variables is zero

Question 12

What is a potential limitation of using non-parametric tests?

Accepted Answer

They can be less powerful than parametric tests

Answer

They require a larger sample size

Answer

They are more difficult to interpret

Answer

They cannot be used with ordinal data

Question 13

Which of the following assumptions is NOT necessary to use parametric statistical tests?

Accepted Answer

The data is continuous and has a known distribution.

Answer

The data is normally distributed.

Answer

The data is independent and randomly sampled.

Answer

The data has equal variances.

Question 14

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

Accepted Answer

The variables are independent.

Answer

The variables are positively correlated.

Answer

The variables are negatively correlated.

Answer

The variables have equal means.

Question 15

Which measure of central tendency is appropriate for ordinal data?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Interquartile range

Question 16

What is the purpose of a post-hoc test in non-parametric statistics?

Accepted Answer

To determine specific significant pairwise differences among groups.

Answer

To check the assumptions of the test.

Answer

To calculate the effect size of the test.

Answer

To interpret the results of the test.

Question 17

Which non-parametric test is used to compare variances?

Accepted Answer

Levene's test

Answer

Kruskal-Wallis test

Answer

Mann-Whitney U test

Answer

Chi-square test

Question 18

What is a potential limitation of using non-parametric statistical tests?

Accepted Answer

They have lower statistical power than parametric tests.

Answer

They require larger sample sizes than parametric tests.

Answer

They are challenging to interpret compared to parametric tests.

Answer

They cannot be used to test hypotheses about group means.

Question 19

What advantage do non-parametric bootstrap hypothesis tests provide over parametric tests?

Accepted Answer

They do not require assumptions about the data distribution.

Answer

They are always more powerful than parametric tests.

Answer

They are easier to interpret than parametric tests.

Answer

They allow for a broader range of hypothesis testing.

Question 20

Which of the following is a characteristic of non-parametric statistics?

Accepted Answer

Chi-square is an example of a non-parametric statistic.

Answer

They use data with a normal distribution.

Answer

They make assumptions about the data distribution.

Answer

Correlation coefficient is a non-parametric statistic.

Question 21

Which non-parametric test is specifically designed for comparing two independent groups?

Accepted Answer

Mann-Whitney U test

Answer

Kruskal-Wallis test

Answer

Friedman test

Answer

Wilcoxon signed-rank test

Question 22

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

Accepted Answer

Testing the independence of two categorical variables

Answer

Testing the difference between two means

Answer

Testing the significance of a correlation coefficient

Question 23

Which non-parametric test is suitable for comparing the medians of three or more **independent** groups?

Accepted Answer

Kruskal-Wallis test

Answer

Wilcoxon signed-rank test

Answer

Friedman test

Answer

Mann-Whitney U test

Question 24

What is the fundamental distinction between parametric and non-parametric tests?

Accepted Answer

Parametric tests assume specific data distribution, while non-parametric tests make no such assumptions

Answer

Parametric tests are always more powerful than non-parametric tests

Answer

Non-parametric tests are easier to interpret than parametric tests

Question 25

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

Accepted Answer

They are less sensitive to violations of normality assumptions

Answer

They are easier to interpret than parametric tests

Answer

They are always more powerful than parametric tests

Question 26

What is the null hypothesis tested by the Friedman test?

Accepted Answer

The medians of all groups are equal

Answer

The proportions of all groups are equal

Answer

The means of all groups are equal

Answer

The variances of all groups are equal

Question 27

Which non-parametric test is appropriate for analyzing the difference between two **related** groups?

Accepted Answer

Wilcoxon signed-rank test

Answer

Kruskal-Wallis test

Answer

Friedman test

Answer

Mann-Whitney U test

Question 28

What is the primary purpose of Kendall's tau correlation coefficient?

Accepted Answer

Measuring the strength and direction of association between two ordinal variables

Answer

Testing the difference between two means

Answer

Measuring the strength and direction of association between two interval variables

Question 29

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

Accepted Answer

They may have lower statistical power compared to parametric tests under certain conditions

Answer

They are more difficult to calculate than parametric tests

Answer

They are more difficult to interpret than parametric tests

Answer

They are always less accurate than parametric tests