Describe the test statistic for the sign test when the sample size n is less than or equal to 25 and when n is greater than 25.
Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 53m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample2h 19m
- 10. Hypothesis Testing for Two Samples3h 26m
- 11. Correlation1h 6m
- 12. Regression1h 35m
- 13. Chi-Square Tests & Goodness of Fit1h 57m
- 14. ANOVA1h 0m
9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
Problem 11.3.1
Textbook Question
What are the conditions for using a Kruskal-Wallis test?

1
The Kruskal-Wallis test is a non-parametric statistical test used to compare three or more independent groups. The first condition is that the data should be ordinal, interval, or ratio in nature, but it does not need to follow a normal distribution.
The second condition is that the groups being compared must be independent of each other. This means that the observations in one group should not influence or be related to the observations in another group.
The third condition is that the dependent variable should be measured on at least an ordinal scale. This means the data should have a meaningful order or ranking.
The fourth condition is that the sample sizes across the groups do not need to be equal, but they should be reasonably large to ensure the test's robustness.
Finally, the Kruskal-Wallis test assumes that the distributions of the dependent variable are similar in shape across the groups, even though the medians may differ. This ensures that the test is comparing medians rather than other distributional characteristics.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Kruskal-Wallis Test
The Kruskal-Wallis test is a non-parametric statistical method used to compare three or more independent groups. It assesses whether the samples originate from the same distribution, making it suitable when the assumptions of ANOVA are not met, particularly regarding normality and homogeneity of variances.
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Independence of Samples
A key condition for the Kruskal-Wallis test is that the samples must be independent. This means that the observations in one group should not influence or be related to the observations in another group, ensuring that the test results are valid and unbiased.
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Ordinal or Continuous Data
The Kruskal-Wallis test requires that the data be at least ordinal, meaning that the values can be ranked. It can also be applied to continuous data that do not meet the assumptions of normality, allowing for a broader application in analyzing non-normally distributed datasets.
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