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11 COMPARISON - 2 GROUPS
Note
It is necessary to select the appropriate area (data without headings) before the analysis begins, because
usually there are more informa on in a datasheet. You should also select the op on indica ng the
content of the variable (frequency (numerator) or proportion). The difference between propor ons
dis nguished in the sample is 30.56%, a 95% and the confidence interval for it (15.90%, 43.35%) does
not contain 0.
Based on the Z test without the con nuity correc on as well as on the Z test with the con nuity
correc on (p value = 0.000053 and p value = 0.0001), on the significance level α=0.05, the alterna ve
hypothesis can be accepted (similarly to the Fisher exact test, its the mid-p correc ons, the χ2 test and
the χ2 test with the Yate's correc on). So, the propor on of men, who passed the exam is different than
the propor on of women, who passed the exam in the analysed popula on. Significantly, the exam was
50
passed more o en by women ( 90
= 55.56% out of all the women in the sample who passed the exam)
20
than by men ( 80 = 25.00% out of all the men in the sample who passed the exam).
E
11.8.
Let us assume that the mortality rate of a disease is 100% without treatment and that therapy lowers
the mortality rate to 50% − that is the result of 20 years of study. We want to know how many people
have to be treated to prevent 1 death in 20 years. To answer that ques on, two samples of 100 people
were taken from the popula on of the diseased. In the sample without treatment there are 100 pa ents
of whom we know they will all die without the therapy. In the sample with therapy we also have 100
pa ents of whom 50 will survive.
Pa ents − not undergoing therapy
sample numerator sample (denominator)
100
100
Pa ents − undergoing therapy
sample numerator sample (denominator)
50
100
We will calculate the NNT.
The difference between propor ons is sta s cally significant (p < 0.000001) but we are interested in
the NNT − its value is 2, so the treatment of 2 pa ents for 20 years will prevent 1 death. The calculated
confidence interval value of 95% should be rounded off to a whole number, wherefore the NNT is 2 to
3 pa ents.
11.2.9 The McNemar test, the Bowker test of internal symmetry
Basic assump ons:
− measurement on a nominal scale,
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