Textbook Question
In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise.
Exercise 7 in Section 9-1 “Buttered Toast Drop”
9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
3:04 minutesProblem 13.CQQ.9
Textbook Question
Wilcoxon Tests What is the difference between the Wilcoxon signed-ranks test and the Wilcoxon rank-sum test?
Verified step by step guidance1
The Wilcoxon signed-ranks test is a non-parametric test used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ. It is an alternative to the paired t-test when the data does not meet the assumptions of normality.
The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, is a non-parametric test used to compare two independent samples to determine whether their population distributions differ. It is an alternative to the independent samples t-test when the data does not meet the assumptions of normality.
The key difference lies in the type of data being analyzed: the Wilcoxon signed-ranks test is for paired or dependent samples, while the Wilcoxon rank-sum test is for independent samples.
Both tests rank the data but differ in how the ranks are used. The Wilcoxon signed-ranks test considers the differences between paired observations and ranks their absolute values, while the Wilcoxon rank-sum test ranks all observations from both groups together and compares the sum of ranks between the groups.
Both tests are non-parametric, meaning they do not assume a specific distribution for the data, making them suitable for ordinal data or data that violates normality assumptions.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Wilcoxon Signed-Ranks Test
The Wilcoxon signed-ranks test is a non-parametric statistical test used to compare two related samples or matched observations. It assesses whether their population mean ranks differ, making it suitable for paired data, such as before-and-after measurements. This test is particularly useful when the data does not meet the assumptions of normality required for parametric tests like the paired t-test.
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Step 2: Calculate Test Statistic
Wilcoxon Rank-Sum Test
The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, is a non-parametric test used to compare two independent samples. It evaluates whether the distributions of the two groups differ by ranking all observations and comparing the sum of ranks between the groups. This test is appropriate when the data is ordinal or when the assumptions of normality for the independent t-test are not met.
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06:34Step 2: Calculate Test Statistic
Non-parametric Tests
Non-parametric tests are statistical methods that do not assume a specific distribution for the data, making them versatile for various types of data, especially ordinal or non-normally distributed interval data. These tests, including the Wilcoxon tests, are advantageous when sample sizes are small or when the data violates the assumptions of parametric tests. They focus on ranks rather than raw data values, providing a robust alternative for hypothesis testing.
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