In general, my feeling is that the real issue in the choice of null concerns risk. The null should be the alternative which is less costly--for you, for society, whatever--to accept.

Nulls are not chosen on the basis of 'what's most dangerous' or 'costly'.

You have entirely the wrong idea of the function of a null hypothesis.

http://en.wikipedia.org/wiki/Null_hypothesis

In all cases the p-values were greater than .05, so I do not have good evidence the distributions are the same in each case.

You will never have evidence that 'they are the same'. Only a lack of evidence against it.

If you feel that you are too easily failing to reject the null, consider the possibility that your sample sizes are simply too small. Perhaps a power analysis is in order!

I find some of the traditional ways of talking about choice of null in terms of "what you want to reject"

Well, is it actually statisticians that tend to say that?

I've never seen one say it myself.

I've seen people who aren't statisticians say nonsensical things like that all the time, but that's as to the point as what the guy that mows my lawn says about tax law.

I ask my tax accountant about tax law, and listen to the lawn mowing guy about stuff to do with mowing lawns. Even though he happens to have picked up a bit of knowledge of tax law along the way from running his own business, I don't regard his tax-law knowledge as anything but that of an interested amateur who happens to use it now and then. I expect him to make elementary mistakes, because that's not his thing.

I'd love to see an example from someone that wasn't actually just someone that uses stats as part of some other thing.

In general, my feeling is that the real issue in the choice of null concerns risk. The null should be the alternative which is less costly--for you, for society, whatever--to accept.

Nulls are not chosen on the basis of 'what's most dangerous' or 'costly'.

You have entirely the wrong idea of the function of a null hypothesis.

http://en.wikipedia.org/wiki/Null_hypothesis

In all cases the p-values were greater than .05, so I do not have good evidence the distributions are the same in each case.

You will never have evidence that 'they are the same'. Only a lack of evidence against it.

If you feel that you are too easily failing to reject the null, consider the possibility that your sample sizes are simply too small. Perhaps a power analysis is in order!

I find some of the traditional ways of talking about choice of null in terms of "what you want to reject"

Well, is it actually statisticians that tend to say that?

I've seen people who aren't statisticians say things like that.