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The MC Nemar

The document discusses Mc Nemar’s test for correlated proportions, a nonparametric chi-square test used for matched samples to determine significant changes between two related situations. An example is provided, analyzing seat belt use before and after automobile accidents, with a computed chi-square value of 6.76, which exceeds the critical value of 3.841 at a 0.05 significance level. Consequently, the null hypothesis is rejected, indicating a significant increase in seat belt use post-accident.

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Regine Gierz
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33 views2 pages

The MC Nemar

The document discusses Mc Nemar’s test for correlated proportions, a nonparametric chi-square test used for matched samples to determine significant changes between two related situations. An example is provided, analyzing seat belt use before and after automobile accidents, with a computed chi-square value of 6.76, which exceeds the critical value of 3.841 at a 0.05 significance level. Consequently, the null hypothesis is rejected, indicating a significant increase in seat belt use post-accident.

Uploaded by

Regine Gierz
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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THE MC NEMAR’S TEST FOR CORRELATED PROPORTIONS

This belongs to the nonparametric statistics. A chi-square test for the situations when samples are matched, that
is, they are not independent. This is before and after design which all are trying to test whether there is a significant
change between the before and after situations. The formula is:

(𝑏−𝑐)2
𝑥2 = 𝑏+𝑐

𝑥 2 = chi-square test
b = is the first cell of the 2nd
column in a 2x2 table
c = is the first cell of the 2nd
row in a 2x2 table

Example 1. Data on seat belt use before and after involvement in auto accidents for a sample of 100
accident victims.

Wore seat Wore seat belt regularly after the Total


belt regularly accident
before the Yes No
accident yes a= 60 b= 6 66
no c= 19 d= 15 36
Total 79 21 100

Problem: Is there a significant difference in the use of seat belt before and after involvement in an
automobile accident?
I. Hypotheses:
𝐻0 : There is no significant difference in the use of seat belt before and after involvement in an
automobile accident.

𝐻𝑎 : There is a significant difference in the use of seat belt before and after involvement in an involvement
in an automobile accident.

II. Level of Significance


α = .05
df = (c-1)(r-1)
= (2-1)(2-1)
= (1)(1)
=1
2
𝑥.05 = 3.84
III. Test Statistic: The Mc Nemar’s test for correlated proportion
Computation:

(𝑏−𝑐)2
𝑥2 = 𝑏+𝑐
(6−19)2
= 6+19
(−13)2
= 25
169
= 25
2
𝑥 = 6.76
Decision Rule: If the 𝑥 2 computed value is greater than the 𝑥 2 tabular value, reject 𝐻0 .
IV. Decision & Conclusion: Since the computed 𝑥 2 s 6.76 larger than the tabular value of 3.841 at
.05 level of significance with 1 degree of freedom, the null hypothesis is rejected in favor of the research
hypothesis that there is a significant difference in the use of seat belt before and after involvement in an
automobile accident. It implies that there is increase in seat belt use after involvement in an automobile
accident.

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