McNemar procedure demonstrated with an example
Simar to the contigency test, McNemar's test can be used to analyze categorical data in survey and questionnarie. But when the data are dependent, McNemar's test is more appropiate. For example, assume that each of several test subjects is afflickted with tinea pedis(athlete's foot) on each foot, and each subject is given a treatment X on one foot and Y on the other foot. Frequency count from matched pairs of foot is measured for both cured and not cured. Because left and right foot of the same subject are dependent, contingency test cannot be used and McNemar's test should be used. The table below demonstrates the frequency count.
2 X 2 Table with Frequency Counts from Mathed Pairs ___________________________________________________________________ Treatment X ___________________________________ Cured Not Cured ___________________________________________________________________ Cured a b Treatment Not cured c d ___________________________________________________________________
In summary, McNemar's test is appropiate if the following assumptions are met:
The clinical Trials for treatments for athelete's foot is in the file "athelete.csv".
The question is to test whether treatments X or Y matter to the results.
Open the data set from SAS. Or import with the following command. Note that the procedure "format" organize the lable from 'c' to 'cured' and 'nc' to 'not cured'.
proc format; value $result 'c'='cured' 'nc'='Not cured'; data athelete; infile "H:\sas\data\athelete.csv" dlm=',' firstobs=2; input subject treatX $ treatY $; format treatX treatY $result. ; run;
The McNemar's test can be run as follows. Note that the "agree" option on the tables statement produces a both McNemer's test statistics as well as a measure of agreement called Kapped, which is often used as a measure of interrater reliability.
proc freq data=athelete; title "McNemar's test for Paired Samples"; tables treatX*treatY /agree expected norow nocol nopercent; run;
The control option "agree" requests tests and measures of classification agreement for square tables. it provides McNemar's test for 2×2 tables and Bowker's test of symmetry for tables with more than two response categories.
The control option "expected" asks for expected value for assumption checking.
The other options such as "norow" eliminate unwanted outputs for clarity.
McNemar's test for Paired Samples The FREQ Procedure Table of treatX by treatY treatX treatY Frequency Expected cured Not cured Total ______________________________________________ cured 12 8 20 13 7 ______________________________________________ Not cured 40 20 60 39 21 ______________________________________________ Total 52 28 80 Statistics for Table of treatX by treatY McNemar's Test __________________________ Statistic (S) 21.3333 DF 1 Pr > S <.0001 Simple Kappa Coefficient ____________________________________ Kappa -0.0435 ASE 0.0821 95% Lower Conf Limit -0.2044 95% Upper Conf Limit 0.1174 Sample Size = 80
This output shows McNemar's test statistics is 21.33, with a corresponding p-value <0.0001. Thus we conclude that the treatment make a difference in the result.
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