Use Yates correction when a $3 \times 2$ table is collapsed to $2 \times 2$?

Question

I have this Chi Squared question I'm doing where I have had to combine two expected columns of a 3 by 2 table as I have a value <5, however, when I combine these two I get a 2 by 2 table, which as I have been taught needs Yates correction, would I still need to use Yates correction to do the question? Just that the mark scheme says otherwise.

Answer 1

Recommendations for use of the Yates correction differ depending on textbook and field of application. If you are supposed to do a Yates correction for $2 \times 2$ tables, then it does not matter whether that $2 \times 2$ table was 'derived' from a larger table. (Some people feel, I believe with good reason, that the Yates correction is too 'conservative'--sometimes not rejecting the null hypothesis when it should.)

Alternative analyses of $2 \times 2$ tables include 'Fisher's exact test' and a simulation to find the the exact distribution of the goodness-of-fit statistic under $H_0$ instead of relying on a chi-squared approximation. (The simulation method might also work with the original $2 \times 3$ table. The rule that all expected values should be more than 5, is a guideline to help ensure that the chi-squared approximation is valid.)

If this is a problem for a course, then you need to do what the textbook or instructor recommends. If this is a problem arising from your own research, you might want to consider one of the alternative analyses mentioned above.