Performing a Wilcoxon Test In Exercises 3–8,

e. decide whether to reject or fail to reject the null hypothesis.
[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: Understand the Wilcoxon Signed-Rank Test. This test is used to compare paired data (before and after treatment) to determine if there is a significant difference between the two sets of measurements. It is a non-parametric test suitable for small sample sizes and does not assume normality.

Step 2: Calculate the differences between the 'Before treatment' and 'After treatment' values for each patient. For example, for Patient 1, the difference is 108 - 99 = 9. Repeat this for all 12 patients.

Step 3: Assign ranks to the absolute values of the differences calculated in Step 2. Ignore the sign of the differences during ranking, but keep track of whether each difference was positive or negative.

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

Step 5: Compare the smaller of the two rank sums (positive or negative) to the critical value for the Wilcoxon Signed-Rank Test at α = 0.01 for a sample size of 12. If the test statistic is less than the critical value, reject the null hypothesis; otherwise, 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-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 the median of the differences between paired observations is significantly different from zero. This test is particularly useful when the data does not meet the assumptions required for a paired t-test, such as normality.

Null Hypothesis (H0)

The null hypothesis (H0) is a statement that there is no effect or no difference, serving as a default position in hypothesis testing. In this context, the null hypothesis would assert that calcium supplements do not lead to a reduction in diastolic blood pressure. The goal of the statistical test is to determine whether there is enough evidence to reject this hypothesis in favor of an alternative hypothesis (H1), which posits that a reduction does occur.

Significance Level (α)

The significance level (α) is the threshold used to determine whether to reject the null hypothesis. It represents the probability of making a Type I error, which occurs when the null hypothesis is incorrectly rejected. In this case, a significance level of α = 0.01 indicates that there is a 1% risk of concluding that a reduction in blood pressure exists when it actually does not. This stringent level is often used in medical studies to minimize false positives.

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