Hi Priya,

Kamil is right and has pointed you to two useful webpages. Let me just add a couple of things...

You have paired, binary data so McNemar's test is the correct choice. However, since your data are binary, you could still use Wilcoxon's signed-rank test. If you have only two categories, you can arbitrarily assign one category a higher rank than the other... the result should be same regardless of which category you denote as the "higher" value. However, if you had more than two categories you wouldn't be able to reasonably decide which category fell into the "middle".

So although you can use either test, the caveat is that for both of these tests most software provide only approximate p-values. When your sample size is small or when one of the cells has a small number of observations, these approximations do not work well. In these cases, you should calculate the exact p-value. The binomial method mentioned on Wikipedia and on the other web page Kamil pointed you to does exactly this... it provides a way to calculate the exact p-value.

Hi Priya,

It depends on which cells are 0.  If cells a or d are 0, then you should be able to run the McNemar's test.  If you have a small sample, there is an exact McNemar's test, which is available in Stata.  Agresti (2013) shows that the McNemar's exact test is equivalent to a binomial test of the b and c cells agains an expected proportion of .5, e.g., Ho: b/(b+c) = .50, where n = b + c.   In his example, a sample of 12 paired observations (i.e., 12 switched party votes -- 8 one way, 4 the other).  In Stata, you can use either -mcci- to get the exact p-value, or use -bitest-, the binomial probablity test.  The code for -bitesti- is:    bitesti 12 8 .5

The two-sided p-value is 0.3877, which is his answer

-Paul

McNemar's Chi-square is exactly the same thing as a Chi-square goodness-of-fit test on the two discordant cells, with a null hypothesis specifying equal expected frequencies.  If the expected counts in the two discordant cells (not the observed counts) are too low for use of the Chi-square approximation (i.e., expected counts < 5, or < 10 according to some more conservative authors), you can use a binomial test on the two discordant cells instead.  For your binomial test, the null hypothesis specifies that pi = 1-pi = 0.5.  (The SPSS procedure for computing McNemar's Chi-square automatically performs the binomial test instead when the expected counts fall below some threshold, for example.)

HTH.

I think you can use the exact function while calculating McNemar for small samples in SPSS. Better calculate the mid-p for McNemar which is shown in the file I am attaching for many statistical softwares. Good luck.

This was suggested to me by an RG member just yesterday :)

Yes McNemar test cannot be done when one of the cell frequency is 0.  You have to do Fisher exact test.

Priya, McNemar's test can be computed when one cell frequency = 0.  Try it using the following 2x2 table (apologies if things do not align properly):

                Ctl-Yes Ctl-No Total

Case-Yes 200        0        200

Case-No  100     100       200

Total         300     100       400

McNemar's test is exactly the same thing as a Chi-square goodness of fit test on the two off-diagonal cells with a null hypothesis 50% of the discordant observations falling in each cell.  The observed counts are 0 and 100, but both expected counts are 50.  So there is absolutely no problem with computing McNemar's test here.  (There would be a problem if one of the expected counts was 0.)  The Chi-square value = 100, with p < .0001.  (You can use the online calculator linked below to check.)

HTH.

http://scistatcalc.blogspot.ca/2013/11/mcnemars-test-calculator.html

Bruce - I tried your suggestion and it works.  Okay then when do you choose to do Fisher exact or McNemar exact test?  I always thought that the latter two tests are used when the cell frequency is less than 5 especially cells b or c.

Hi Priya.  Many people use Fisher's exact test (aka., the Fisher-Irwin test) in place of a Chi-square test of independence, not in place of McNemar's Chi-square.*  As Paul Visintainer and I both mentioned in earlier posts, the exact test one would use in place of McNemar's Chi-square is a binomial test, with a null hypothesis stating that 50% of the observations fall in each off-diagonal cell.  And again, rules of thumb involving low frequencies are always about low expected frequencies (given a true H0), not about low observed frequencies. 

* But unless you have the rare situation where all of the marginal totals are fixed in advance, the N-1 Chi-square test is generally a better choice than the Fisher-Irwin test.  See Ian Campbell's website (link below) for more information, including the reference to his nice simulation study in Statistics in Medicine.  HTH.

http://www.iancampbell.co.uk/twobytwo/twobytwo.htm

Priya, in my last post, I didn't respond to the question about when one can safely use the McNemar Chi-square test rather than the exact binomial test.  Bearing in mind the McNemar's Chi-square is identical to a Chi-square Goodness of Fit test on the off-diagonal cells, with the expected frequencies being equal in the two cells, this info I found in some of my notes is relevant.

Q. When can one safely use the Chi-square Goodness of Fit (GOF) test in place of a binomial test?

A. One rule of thumb is that n × Pi_0 and n × (1-Pi_0) both must be equal to or greater than 5 (or 10 according to some more cautious statisticians).

But of course, such rules of thumb were developed at a time when folks did not have the computation power we have now.  Nowadays, one could use the binomial test routinely, except perhaps in the case of really large samples. 

HTH.

It depends on where your zero cells lie in the table. McNemar's test may be unreliable if the discordant cells (yes/no or no/yes) add up to less than 5 or 10 or 25, according to different authors. If the zero cells lie in your concordant cells, McNemar's test will work fine. If the discordant cells do not add up to 5-25, then a binomial test should be used.

http://rcompanion.org/handbook/H_05.html