I have just recently been learning how to do chi square tests. And here is the summary that I came up with. This is how I understand it. Let me know if I am correct or not.
Chi square test is often applied when we deal with categorical data involving proportions.
There are two types of Chi square tests: Goodness-of-fit chi square test, and the Chi square test for independence.
Goodness-of-fit Chi square test:
This test involves investigating the distribution of population among different categories of a single variable. Thus, it can be thought of as checking whether the “expected” bar graph of a variable for the overall population agrees with the results of our particular sample. Hence, we are checking whether the expected model for the population distribution of a variable will be a good "fit" for the distribution of that same variable observed in our sample. Or, putting it a different way, how "close" are the observed...
Here is a procedure that I wrote up a few years ago (and edited it a few times since then) when I saw that Testing Null Hypothesis was a rather difficult topic for students to understand. In fact, when I was learning statistics, it took me a while to get it as well. So, here it is. Let me know if it is helpful.
Testing null hypothesis:
1. Determine Ho (null hypothesis) and Ha (alternative hypothesis). Ho always claims that µ = something; Ha always claims that either µ ? something, µ < something,
or µ > something.
2. Determine if this is a one-tailed or two-tailed test.
If Ha claims that µ ? something, than it is a two-tailed test.
If Ha claims that either µ < something or µ > something, then it is a one-tailed test.
3. Draw the normal sampling distribution curve. The central mean of the curve is that claimed by Ho (which we initially assume to be true).
4. If it is a 1-tailed test, determine on which side of the curve should a (alpha)...