Question

A sample of 15 patients suffering from asthma participated in an experiment to study the effect of a new treatment on pulmonary function. Among the various measurements recorded were those are forced expiratory volume (liters) in 1 second (FEV1) before and after application of the treatment. Suppose the researcher would like to test if the treatment is effective in increasing the FEV1. Please clearly state the hypotheses, carry out the test and state your conclusion for the tests listed below.

Subject Before After

(1) 1.69, 1.69

(2) 2.77, 2.22

(3) 1, 3.07

(4) 1.66, 3.35

(5) 3, 3

(6) .85, 2.74

(7) 1.42, 3.61

(8) 2.82, 5.14

(9) 2.58, 2.44

(10) 1.84, 4.17

(11) 1.89, 2.42

(12) 1.91, 2.94

(13) 1.75, 3.04

(14) 2.46, 4.62

(15) 2.35, 4.42

(a) Use the matched pairs t-test to test the hypothesis.

(b) Use the sign test to test the hypothesis.

(c) Use the Wilcoxon signed rank test to test the hypothesis.

(d) Please explain which test is the most powerful non-parametric test

Answer 1

Part A:

The output of Paired Sample T Test is given below:

Hypothesis:

H₀: µ₁ = µ₂ ("The paired population means are equal")
H₁: µ₁ ≠ µ₂ ("The paired population means are not equal")

As the 2 Tail P value (0.00031) is less than 0.05, so the null hypothesis is not accepted... In this case, the paired sample means are not equal...

Part 2:

As the 2 Tail P value (0.00031) is less than 0.05, so the null hypothesis is not accepted... In this case, the paired sample means are not equal...

But, from the sign test, a box plot is done which shows that the data is normally distributed and there are no outliers.

Part 3:

Part 4:

If your data is normally distributed -- you can analyze a number of ways, including a QQ Plot, then it is fine to run a t-test.

But, in order to make the least number of assumptions about the data it is best to use the non-parametric Wilcoxon Signed Rank test.

End of the Solution...