What hypothesis test to use for categorical variables?  Possibly in R? Edit: I think this is a better question,
Say, I have categorical characteristics such as gender, race.  How should I use Fisher's test and chi-square test?
I was looking at this: http://math.hws.edu/javamath/ryan/ChiSquare.html
end edit.
I want to do a hypothesis testing for cancer patients.
Everyone is admitted to the hospital, a small portion went developed cancer, while the rest didn't.  The dependent variable is categorical, not numerical, meaning  something like severe, mild, and unknown.
How should I give a hypothesis test?  Is it possible?  Thanks!
Edit: The data analyst used Fisher's Exact or Chi-squared test.  I don't know how I can do that, R asks the 2 test groups of equal length
 A: Sounds like you want ordinal logistic regression. The hypothesis would be something like:
Null: The IVS were not related to the severity of XXX
Alt: The IVS were related to the severity of XXX
You can do ordinal logistic regression in R, SAS or many other programs. I wrote a presentation on ordinal logistic using SAS, but some of it will apply more generally.
But "unknown" as a category worries me. That's not ordinal, that's missing data. Or do you mean that those people didn't get cancer?
A: The categorical responses have distributions (e.g. the percentage that answer severe, the percentage that answer mild and the percentage that answer unknown.  You can do a test of the null hypothesis that the distributions are the same for both groups vs the alternative that they differ.
To the revised question I would answer that you can construct the 3x2 contingency table with no restriction on the number of counts in each cell or column or row of cells and apply the Fisher test.  A good contingency table analysis program written in R should allow you to do that.
A: I am doing an experiment which is also all categorical, I think you need to run a Normality test to determine whether the data is normal or not normal. Then based on that you can choose to run a parametric(normal) or a non-parametric( not normal) chi-squared analysis.
By the way the tutorial provided is a journal or just a tabulation of information. Thanks, by the way, I think its true but could you state your IV and DV? If all are categorical then a Chi Square test is possible, but due to limitation of the test, when analysing  the data can be a bit tough due to restrictions of the Chi Square test.
