# What’s wrong with McNemar’s test?

A quick note from EACL: some papers related to LSDSem workshop (Bugert et al. 2017; Zhou et al. 2015) use McNemar’s test to establish statistical significance and I find it very odd.

McNemar’s test examine “marginal (probability) homogeneity” which in our case is whether two systems yield (statistically) the same performance. According to the source code I found on Github, the way it works is:

1. Obtain predictions of System 1 and System 2
2. Compare them to gold labels to fill this table:
Sys1 correct Sys1 wrong a b c d
3. Compute the test statistics: $\chi^2 = {(b-c)^2 \over b+c}$ and p-value
4. If p-value is less than a certain level (e.g. the magical 0.05), we reject the null hypothesis which is p(Sys1 correct) == p(Sys2 correct)

As it happens in the papers, the difference is statistically significant and therefore results are meaningful. Happy?