Performing a Wilcoxon Test In Exercises 3–8,

d. find the test statistic.
[APPLET] Calcium Supplements and Blood Pressure In a study testing the effects of calcium supplements on blood pressure in men, 12 men were randomly chosen and given a calcium supplement for 12 weeks. The table shows the measurements for each subject’s diastolic blood pressure taken before and after the 12-week treatment period. At α = 0.01, can you reject the claim that there was no reduction in diastolic blood pressure? (Adapted from The Journal of the American Medical Association)

Verified step by step guidance

Step 1: Calculate the differences between the 'Before treatment' and 'After treatment' diastolic blood pressure values for each patient. For each patient, subtract the 'After treatment' value from the 'Before treatment' value.

Step 2: Assign ranks to the absolute values of the differences calculated in Step 1. Ignore the sign of the differences (positive or negative) when ranking.

Step 3: Restore the signs to the ranks based on the original differences. If the difference was negative, assign a negative sign to the rank; if positive, keep the rank positive.

Step 4: Sum the positive ranks and the negative ranks separately. These sums will be used to calculate the test statistic.

Step 5: Determine the test statistic (W) by taking the smaller of the two sums (positive ranks or negative ranks). Compare this test statistic to the critical value for the Wilcoxon signed-rank test at α = 0.01 to decide whether to reject the null hypothesis.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Wilcoxon Signed-Rank Test

The Wilcoxon Signed-Rank Test is a non-parametric statistical test used to compare two related samples, such as measurements taken before and after a treatment. 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.

Test Statistic

The test statistic in the Wilcoxon Signed-Rank Test is calculated based on the ranks of the differences between paired observations. It reflects the magnitude and direction of the differences, allowing researchers to determine whether the observed changes are statistically significant. The test statistic is then compared to critical values from the Wilcoxon distribution to make inferences about the null hypothesis.

Significance Level (α)

The significance level, denoted as α, is the threshold for determining whether to reject the null hypothesis in hypothesis testing. In this context, α = 0.01 indicates a 1% risk of concluding that a difference exists when there is none. A lower α value means a more stringent criterion for significance, reducing the likelihood of Type I errors, which occur when a true null hypothesis is incorrectly rejected.

Watch next

Master Introduction to Matched Pairs with a bite sized video explanation from Patrick

Start learning