An experiment is conducted to determine if an experimental birth control pill ha

Question

An experiment is conducted to determine if an experimental birth control pill has the side effect of changing blood pressure. Ten women are randomly sampled from the city in which you live. Five of them are given a placebo for a month and then their diastolic blood pressure is measured. Then they are switched to the birth control pill for a month and again blood pressure is measured. The other five women are given the birth control pill first for a month, followed by the placebo for a month. The blood pressure readings are shown here.

Assume the data are so far from normally distributed as to invalidate use of the t test for correlated groups. Analyze the data with the Wilcoxon signed ranks test. What do you conclude, using = 0.012 tail?

Diastolic Blood Pressure Subject
No. Birth control
pill Placebo 1 109 103 2 76 70 3 68 68 4 77 69 5 73 78 6 87 80 7 79 83 8 78 81 9 80 80 10 80 86

Explanation / Answer

Solution:-

The following table is obtained:

Now that the absolute differences are in ascending order, we assign ranks to them, taking care of assigning the average rank to values with rank ties (same absolute value difference)

The sum of positive ranks is:

W+ = 5 + 5 + 7 + 8 = 25

and the sum of negative ranks is:

W- = 1 + 2 + 3 + 5 = 11

Hence, the test statistic is T = min{W+, W- } = min{ 25, 11} = 11

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0: Median (Difference) = 0

Ha: Median (Difference) 0

(2) Rejection Region

The critical value for the signficance level alpha = 0.012 provided, and the type of tail specified is Tc = 0, and the null hypothesis is rejected if T < 0.

(3) Decision

Since in this case T = 11 > 0, there is not enough evidence to claim that the population median of differences is different than 0, at the = 0.012 significance level.

Pair Sample 1 Sample 2 Difference Abs. Difference Sign 1 109 103 6 6 +1 2 76 70 6 6 +1 3 68 68 0 0 0 4 77 69 8 8 +1 5 73 78 -5 5 -1 6 87 80 7 7 +1 7 79 83 -4 4 -1 8 78 81 -3 3 -1 9 80 80 0 0 0 10 80 86 -6 6 -1

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