The most common application for chi-square is in comparing observed counts of particular cases to the expected counts. For example, a random sample of people would contain m males and f females but usually we would not find exactly m=½N and f=½N. We could use the chi-squared test to determine if the difference were significant enough to rule out the 50/50 hypothesis.
The Chi Square Test determines whether the probabilities observed from data in a RxC contingency table are the same or different. The null hypothesis is that probabilities observed are the same. Output is a p-value which when compared to the user’s threshold, determines whether the null hypothesis should be rejected.