Some Theory Behind Chisquare Tests
Chisquare tests are perhaps the most common nonparametric analysis. A chisquare test looks at frequencies and addresses the question of whether or not those frequencies are what you would expect to find in a population. To illustrate this concept, we'll look at a simple (singlevariable) example, then an example with two variables.
For a singlevariable chisquare, also known as a chisquare for goodness of fit, you can evaluate one of two types of hypotheses:

Questions of differences across groups.
Example: Redgreen colorblindness and gender. You could use a chisquare to conclude that colorblindness in our population, by gender, is not what one would expect due to chance. (Chance suggests an equal number of colorblind males and females.) This could be the initial observation that ultimately leads to discovering sexlinked colorblindness.

Questions of categorical changes and population differences.
Example: I have a percentage makeup of what political parties people identified with twenty years ago, as well as data on current party identification. I could compare past makeup to a current makeup and hypothesize about whether or not people identify with different political parties than they once did.
To determine if these differences are significant, a chisquare value is calculated. This is done by looking at the difference between the observed (O) and expected values (E) (literally subtracting OE), squaring it, dividing by E and summing the resulting values. This value is then compared to a chisquare distribution which is mostly influenced by sample size (sample size determines the degrees of freedom for the test).
The multiple variable chisquare, also known as a chisquare for independence, looks at whether variables are independent of one another. The simplest example would be a twobytwo grid with frequencies for each cell. Perhaps I have a theory that men, with their higher metabolism, wear tshirts more often in all seasons than women. I pick a nice location, like a downtown street and in each season, make a count of men and women in tshirts versus not. Since the count is not continuous (no one can be counted as wearing 1.5 tshirts) this chisquare analysis is looking in each season category, if more men or more women wore tshirts. A nonsignificant chisquare for independence would imply that gender and season did not influence sleeve length.
Unlike the chisquare for goodness of fit, which takes theoretical distribution from a comparison population or from the idea that things ought to be equally distributed, a chisquare test for independence uses the observed values to calculate what is expected.
For a more indepth explanation of a chisquare analysis, you can follow up with the online Handbook of Biological Statistics.
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