chi squared test or Z test?

Question

I have an outcome from a biological experiment, where I have counted the number of dead cells upon a mutation. For example, in once case - out of 120 cells we saw 16% of the dead cells, but our expectations were around 10%. So to check the difference is significant I have performed 'z-test for changes in proportions'.

But my question is, whether is it possible to do ch-squared test on a single experiment like the above? I have Googled a lot, but all examples I see use a contingency table or involve multiple variables.

Answer 1

Yes, it's possible to do a chi-square test on this.

Specifically, this is the chi-square goodness of fit test. To do it correctly you set up two cells (one for dead, one for not dead), like so:

       Dead   NotDead  Total
Obs     19      101     120
Exp     12      108     120

The chi-square is $\sum_i (O_i-E_i)^2/E_i$ and has $k-1$ df, where $k$ is the number of categories (k=2 in this case, meaning 1 df).

If you use the same information/approximations in both (including the same continuity corrections), the chi-square statistic will be the square of the two-tailed one-sample proportions Z statistic and will reject exactly the same cases. (Sometimes the p-values differ a little because different approximations/statistics are used.)