I would be grateful for general guidance/advice about data analysis with some data that is problematic for me because of the small sample size, and the large number of categorical data. I realize this question is a bit vague, but that's because I'm not sure what to do. I'd like to come up with some good descripive characterization of the data, and see if ther's any way to make any meaningful inferences.
Sample size = 13, number of variables 93 (81 categorical, only 12 numerical). In the past I've worked with mostly numeric data with large sample sizes so I'm not sure how to proceed.
Given the small sample, I don't feel I can make any assumptions about normality.
Other than generating basic descriptive statistics (mean, std dev for the numeric data, and tables for the categorical data) what else can I do to meaningfully summarize this data?
Is it possible to generate some reliable confidence intervals for the means via some nonparametric tests with such limited data?
In addition to descriptive statistics, I am also wondering about simple linear regression. From what I have read, automatic selection of relevant variables, say via stepwise regression, is questionable to start with, and especially with such a mall sample won't be reliable. Also, I'm not so much interested in prediction, as to exploration of the relationships between a numeric response variable and the rest of the data.
I also worry about detecting collinearity.
With numeric data I could generate a correlation matrix, not sure this makes sense with this small sample, nor am I certain how to do the equivalent for the large set of categorical data. So not sure if there is a any automatic or semi-automatic way for stats to guide me to the relevant variables as a start and then take it from there. I.e., other than manually considering various combinations of independent variables, is there another way?
I'm using R.