A sample of 15 patients suffer
A sample of 15 patients suffering from asthma participated in anexperiment to study the effect of a new treatment on pulmonaryfunction. Among the various measurements recorded were those areforced expiratory volume (liters) in 1 second (FEV1) before andafter application of the treatment. Suppose the researcher wouldlike to test if the treatment is effective in increasing the FEV1.Please clearly state the hypotheses, carry out the test and stateyour 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 thehypothesis.
(d) Please explain which test is the most powerfulnon-parametric test
Answer:
PartA:
The output of Paired Sample T Test is given below:
Hypothesis:
H0: µ1 = µ2 (“Thepaired population means are equal”)H1: µ1 ≠ µ2 (“The pairedpopulation means are not equal”)
As the 2 Tail P value (0.00031) is less than 0.05, so the nullhypothesis is not accepted… In this case, the paired sample meansare not equal…
Part2:
As the 2 Tail P value (0.00031) is less than 0.05, so the nullhypothesis is not accepted… In this case, the paired sample meansare not equal…
But, from the sign test, a box plot is done which shows that thedata is normally distributed and there are no outliers.
Part3:
Part4:
If your data is normally distributed — you can analyze a numberof 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 thedata it is best to use the non-parametric Wilcoxon Signed Ranktest.
End of the Solution…
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