24 Questions
When should the Mann-Whitney U test be used instead of the t-test?
When the data is ordinal but not interval scaled
What is the main advantage of the Wilcoxon Signed-Rank Test?
It does not depend on the form of the parent distribution nor its parameters
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
What type of test is the Mann-Whitney U test?
Non-parametric test
What is the purpose of the Kruskal-Wallis test?
To assess for significant differences on a continuous dependent variable by a categorical independent variable
What is a disadvantage of the Kruskal-Wallis test compared to one-way ANOVA?
It is less powerful than one-way ANOVA
What is the Wilcoxon Signed-Rank Test used for?
To compare the median of a set of numbers against a hypothetical median
What is the Mann-Whitney U test an alternative to?
Independent t-test
What is a necessary condition for using parametric tests?
Prior knowledge of the population distribution, typically normal or a close approximation of it
What is the purpose of using the Central Limit Theorem in parametric tests?
To aid in using the normal distribution effectively
What is an advantage of using non-parametric tests?
No need to make assumptions about the population
What is the main reason for the growing popularity of non-parametric tests?
No need to make assumptions about the population
What is the purpose of finding the confidence interval for the population variance?
To estimate the population variance
Which of the following is an example of a non-parametric test?
Man-Whitney U Test
What is the characteristic of non-parametric tests?
They are also referred to as distribution-free tests
What is the purpose of finding the confidence interval for the difference of two means?
To estimate the difference between two population means
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
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
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
When should you use linear regression?
When your variables are related linearly
What is the primary purpose of simple random sampling?
To randomly select a subset of participants from a population
What is the main limitation of linear regression?
It is susceptible to outliers
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
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?'
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.
This quiz covers concepts in statistics and research methods, including simple random sampling and the Pearson's chi-square test.
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