# Test of two distributions/functions

1. Jan 24, 2012

### phonic

Dear All,

I have two functions that are defined on a table, i.e. $f1(x,y), f2(x,y)$, where x and y are bin indices, and $1\leq f1(x,y) \leq 1$, $1\leq f2(x,y) \leq 1$.

I would like to perform some test to show whether $f1(x,y)$ and $f2(x,y)$ are significantly different. Is there some way to do this? I thought of using chi square test for $f1(x,y)+n$ and $f2(x,y)+n$, where n>1 is a constant added to make $f1(x,y)$ and $f2(x,y)$ interpretable as frequencies.

Thanks a lot!

2. Jan 26, 2012

### Stephen Tashi

Statistical signficance is not a meaningful concept unless you are dealing with a phenomena that involves probability. To do the usual type of "hypothesis testing" , you must assume the two functions are generated by the same probabalistic process. Until you state exactly what that process is, it isn't possible to say what sort of statistical test is appropriate.

For example if we assume each table is generated by one realization of the uniform [0,1] random variable u according to the formula $f(i,j) = (-0.5)(i) - (0.5)(j) + u$ then it wouldn't make sense to do a chi square test.