Patients who suffered from moderate to severe migraine headache took part in a d
ID: 3205614 • Letter: P
Question
Patients who suffered from moderate to severe migraine headache took part in a double-blind clinical trial to assess an experimental surgery. A group of 75 patients were randomly assigned to receive either the real surgery on migraine trigger sites (n = 49) or a sham surgery (n = 26) in which an incision was made but no further procedure was performed. The surgeons hoped that patients would experience "a substantial reduction in migraine headaches, " which we will label as "success." The following table shows the result of the experiment. "Substantial reduction" means at least a 50 percent in reduction of migraine headache frequency, intensity, or duration when compared with baseline (presurgery) values. Conduct a chi-square test to see if the proportion of patients who demonstrate successful reductions in migraines under the real surgery group is better than for the patients in the sham group Practice using the table, but get the exact value of the P-value using Matlab Repeat the analysis in part (a), but this time use a z-test instead of a chi-square test. Practice using the table, but get the exact value of the P-value using Matlab Compare your answers in part (a) and (b).Explanation / Answer
a) chi square test:
below is the analysis
from above Chi square test stat X2=6.062
degree of freedom =(row-1)*(column-1) =(2-1)*(2-1) =1
hence p value for above chi stat and 1 degree of freedom from matab and table =0.0138
as p value is less then 0.05 we can conclude that proportion of patients who demonstrate successful reductions in migraines under the real surgery group is better.
b) for z test
p1 = 41/49=0.837 , n1 =49
and p2 =15/26 =0.577 ; n2=26
hence std error =(p1(1-p1)/n1 +p2(1-p2)/n2)1/2 =0.1103
therefore zstat=(p1-p2)/std error =2.3546
for above p value =0.0093
as p value is less then 0.05 we can conclude that proportion of patients who demonstrate successful reductions in migraines under the real surgery group is better.
c) p value in z test is lower then p value in chi square due to change in approach in both distribution towards samples.
Observed O real Sham Total success 41 15 56 no success 8 11 19 Total 49 26 75 Expected E=rowtotal*column total/grand total real Sham Total success 36.587 19.413 56 no success 12.413 6.587 19 Total 49 26 75 0.098 0.052 chi square =(O-E)^2/E real Sham Total success 0.532 1.003 1.536 no success 1.569 2.957 4.526 Total 2.101 3.960 6.062