I'd like to understand the use of Monte Carlo simulation in the
chisq.test() function in R.
I have a qualitative variable which has 128 levels / classes. My sample size is 26 (I was not able to sample more "individuals"). So obviously, I will have some levels with 0 "individuals". But the fact is that I have only a very small number of classes represented out of the 127 possible. As I have heard that to apply chi-squared test we should have at least 5 individuals in each level (I do not completely understand the reason for that), I thought I had to use the
simulate.p.value option to use Monte Carlo simulation to estimate the distribution and compute a p-value. Without Monte Carlo simulation, R gives me a p-value
< 1e-16. With Monte Carlo simulation, it gives me a p-value at
I tried to compute the p-value with a vector of 26 ones and 101 zeros, and with Monte-Carlo simulation, I get a p-value at 1.
Is it OK to state that, even if my sample size is small compared with the number of possible classes, the observed distribution is such that it is very unlikely that all possible classes exist at the same probability (1/127) in the real population?