Statistics and Research Methods

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Questions and Answers

When should the Mann-Whitney U test be used instead of the t-test?

When the data is ordinal but not interval scaled (correct)
When the data is normally distributed
When the data is categorical
When the data is interval scaled but not normally distributed

What is the main advantage of the Wilcoxon Signed-Rank Test?

It can only be used for large samples
It is more powerful than the paired samples t-test
It does not depend on the form of the parent distribution nor its parameters (correct)
It assumes normal distribution of the data

What is the main difference between the Kruskal-Wallis test and one-way ANOVA?

The Kruskal-Wallis test does not assume normal distribution, while one-way ANOVA does (correct)
The Kruskal-Wallis test assumes normal distribution, while one-way ANOVA does not
The Kruskal-Wallis test is used for two groups, while one-way ANOVA is used for more than two groups
The Kruskal-Wallis test is used for continuous variables, while one-way ANOVA is used for categorical variables

What type of test is the Mann-Whitney U test?

Non-parametric test (B) Signup and view all the answers

What is the purpose of the Kruskal-Wallis test?

To assess for significant differences on a continuous dependent variable by a categorical independent variable (B) Signup and view all the answers

What is a disadvantage of the Kruskal-Wallis test compared to one-way ANOVA?

It is less powerful than one-way ANOVA (A) Signup and view all the answers

What is the Wilcoxon Signed-Rank Test used for?

To compare the median of a set of numbers against a hypothetical median (D) Signup and view all the answers

What is the Mann-Whitney U test an alternative to?

Independent t-test (D) Signup and view all the answers

What is a necessary condition for using parametric tests?

Prior knowledge of the population distribution, typically normal or a close approximation of it (B) Signup and view all the answers

What is the purpose of using the Central Limit Theorem in parametric tests?

To aid in using the normal distribution effectively (A) Signup and view all the answers

What is an advantage of using non-parametric tests?

No need to make assumptions about the population (C) Signup and view all the answers

What is the main reason for the growing popularity of non-parametric tests?

No need to make assumptions about the population (C) Signup and view all the answers

What is the purpose of finding the confidence interval for the population variance?

To estimate the population variance (A) Signup and view all the answers

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

Man-Whitney U Test (B) Signup and view all the answers

What is the characteristic of non-parametric tests?

They are also referred to as distribution-free tests (B) Signup and view all the answers

What is the purpose of finding the confidence interval for the difference of two means?

To estimate the difference between two population means (C) Signup and view all the answers

What is the primary purpose of a Pearson's chi-square test?

To determine whether the frequency distribution of a categorical variable is different from expected (B) Signup and view all the answers

Which test is used to examine differences between two independent groups with ordinal or continuous data that is not normally distributed?

Mann-Whitney U test (A) Signup and view all the answers

What is the main advantage of using a chi-square test of independence?

It is a non-parametric test that can be used with categorical data (B) Signup and view all the answers

When should you use linear regression?

When your variables are related linearly (A) Signup and view all the answers

What is the primary purpose of simple random sampling?

To randomly select a subset of participants from a population (A) Signup and view all the answers

What is the main limitation of linear regression?

It is susceptible to outliers (D) Signup and view all the answers

What is the chi-square test of goodness of fit used for?

To test whether the frequency distribution of a categorical variable is different from expected (A) Signup and view all the answers

What is regression analysis used for?

To answer questions like 'How does one variable affect another?' or 'Can we predict one variable based on the values of others?' (B) Signup and view all the answers

Study Notes

Sampling

Simple random sampling is a type of probability sampling where each member of the population has an equal chance of being selected.

Chi-Square Test

A Pearson's chi-square test is a statistical test used to determine if data is significantly different from expected results.
There are two types of chi-square tests: the chi-square goodness of fit test and the chi-square test of independence.
Chi-square is often written as Χ2 and pronounced as "kai-square".

Regression Analysis

Regression analysis is used to examine the relationship between variables and predict one variable based on others.
Linear regression is used when variables are related linearly, but it is susceptible to outliers and should not be used with big data sets.
Data collection, data preprocessing, and regression model selection are crucial phases in regression analysis.

Mann-Whitney U Test

The Mann-Whitney U test is used to examine differences between two independent groups with ordinal or continuous data that is not normally distributed.
It is used to test whether two samples are likely to derive from the same population.
The Mann-Whitney U test is preferable to the t-test when data is ordinal but not interval scaled.

Kruskal-Wallis Test

The Kruskal-Wallis test is a non-parametric test used when the assumptions of one-way ANOVA are not met.
It is used to assess significant differences on a continuous dependent variable by a categorical independent variable.
The Kruskal-Wallis test does not assume normal distribution or equal variance, making it suitable for both continuous and ordinal-level dependent variables.

Wilcoxon Signed-Rank Test

The Wilcoxon signed-rank test is a non-parametric test that compares the median of a set of numbers against a hypothetical median.
It does not require any assumptions about the shape of the distribution and is used to compare the median of a set of numbers against a hypothetical median.

Parametric and Non-Parametric Tests

Parametric tests assume prior knowledge of the population distribution, typically normal or approximately normal.
Parametric tests include tests that find the confidence interval for population means, variances, and differences of two means.
Non-parametric tests do not assume any knowledge of the population and are also referred to as distribution-free tests.
Non-parametric tests are easy to apply and understand, and do not require assumptions about the population.

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Description

This quiz covers concepts in statistics and research methods, including simple random sampling and the Pearson's chi-square test.