Wilcoxon Tests What is the difference between the Wilcoxon signed-ranks test and the Wilcoxon rank-sum test?
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 22m
- 11. Correlation1h 6m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
Problem 13.CRE.5
Textbook Question
In Exercises 1–10, use the following weights (g) of Hershey’s Kisses from Data Set 38 “Candies” in Appendix B.

Wilcoxon Signed-Ranks Test Repeat Exercise 3 using the Wilcoxon signed-ranks test to test the claim that the sample of weights is from a population with a median of 4.5333 g.

1
Step 1: Understand the Wilcoxon Signed-Ranks Test. This test is a non-parametric statistical test used to compare the median of a sample to a hypothesized median. It is particularly useful when the data does not follow a normal distribution.
Step 2: Calculate the differences between each sample weight and the hypothesized median (4.5333 g). For each weight, subtract 4.5333 g to find the difference.
Step 3: Rank the absolute values of the differences from smallest to largest, ignoring the sign of the differences. Assign ranks to these absolute differences.
Step 4: Apply the signs of the original differences (positive or negative) to the ranks. This creates signed ranks for each data point.
Step 5: Compute the test statistic by summing the positive signed ranks and the negative signed ranks separately. Use the smaller of these sums as the test statistic. Compare this test statistic to the critical value from the Wilcoxon Signed-Ranks Test table to determine whether to reject or fail to reject the null hypothesis.

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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 data that do not meet the assumptions of normality required for parametric tests. This test is particularly useful when dealing with small sample sizes or ordinal data.
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Median
The median is a measure of central tendency that represents the middle value in a data set when it is ordered from least to greatest. Unlike the mean, the median is less affected by outliers and skewed data, making it a robust indicator of the data's central location. In the context of the Wilcoxon test, the hypothesis often involves testing whether the median of the sample differs from a specified value.
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Hypothesis Testing
Hypothesis testing is a statistical method used to make inferences about population parameters based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample data to determine whether to reject H0. The outcome is typically assessed using a p-value, which indicates the probability of observing the data if H0 is true, guiding the decision-making process.
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Step 1: Write Hypotheses
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