Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

a. Differences d

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Step 1: Understand the Wilcoxon signed-ranks test. This test is a non-parametric statistical test used to compare two related samples, matched pairs, or repeated measurements on a single sample to assess whether their population mean ranks differ. It is often used as an alternative to the paired t-test when the data does not meet the assumptions of normality.

Step 2: Identify the matched pairs from the problem. These pairs represent the two related samples or measurements that are being compared. For example, they could be 'before' and 'after' measurements for the same subjects.

Step 3: Calculate the differences (d) for each pair. For each matched pair, subtract one value from the other. The difference is typically calculated as d = x1 - x2, where x1 and x2 are the two values in the pair.

Step 4: Record the differences (d) for all pairs. Ensure that you keep track of the sign of each difference (positive or negative), as this will be important for the next steps in the Wilcoxon signed-ranks test.

Step 5: Verify the differences. Check that all differences have been calculated correctly and that no data points are missing. This step ensures the accuracy of the subsequent analysis.

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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 method used to compare two related samples or matched pairs. 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 in situations where the sample size is small or when the data are ordinal.

Differences (d)

In the context of the Wilcoxon signed-ranks test, 'differences (d)' refer to the calculated differences between paired observations. For each pair, the difference is computed by subtracting one value from the other. These differences are then ranked, and the test evaluates the sum of the ranks of the positive and negative differences to determine if there is a statistically significant difference between the two related groups.

Ranked Data

Ranked data is a method of organizing data points based on their order rather than their actual values. In the Wilcoxon signed-ranks test, the absolute values of the differences are ranked from smallest to largest, regardless of their sign. This ranking process allows the test to analyze the relative positions of the differences, which is essential for determining the significance of the results without relying on the assumptions of normal distribution.

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