# Tests for Difference in Mean VERSUS Tests for Difference in Median

1. Dec 3, 2011

### number0

Sup everyone,

Assume I have two sample observations.

I am wondering when I should use a test for a difference in mean and when I should use a test for a difference in median.

Should I test for mean if both the distribution of both the samples are normal?
Should I test for median otherwise?

I am confused!

Any help would be greatly appreciated.

Last edited: Dec 4, 2011
2. Dec 4, 2011

### chiro

If you have sufficient evidence that your underlying distribution has a particular distribution of the Normal variety, it would probably be better to use a sampling distribution of the mean, which in your case is also a normal distribution.

There is no silver bullet answer for your problem because it depends on the assumptions you have and what you are trying to do: it's not completely a plug and chug mechanical process.

Also you have to realize that your sample size is not great no matter what test you are doing. When you have a low amount of samples like you have, its probably be better to use prior information techniques like those found in Bayesian statistics.

Also I think I have misunderstood you: when you say two 'samples' do you mean two distinct collections of observations or do you mean two observations only? If its the first answer, how many observations in each sample?

3. Dec 4, 2011

### number0

Oh, my apologies! I meant to say that I have two distinct collections of observations (16 observations total and 8 observation per each category). Other than that information (aside from the actual data), I am not given any conditions to work with.

4. Dec 4, 2011

### chiro

Well above you mentioned an assumption namely that your data is normally approximated.

If the data is (or is approximately) normally distributed with an unknown population variance, a good test would be to use a t-test.

Now again, more assumptions enter the equation. If the two variances are not statistically significant you would use a pooled variance. If not, you don't. Also if the different processes are linked (or are thought to be anyway) in a kind of "cause-effect" manner between pairs of observations, then you would consider a paired t-test.

All of the above tests also have distributional assumptions, and if these are not met, you may need to use tests that are lot more complicated.

If you want to test normal approximations, there are different tests for this but the main test is the Shapiro-Wilk test. Any decent statistical software package will do this very easily and quickly.

There are other tests, but I am a) not familiar with them and b) don't understand enough about their differences to give specific advice.

For this problem, I would check normality assumptions for both samples and then do a two-sample t-test. In saying this, if you want to draw conclusions that are statistically significant and useful, I would take a bit of time to either learn the statistics or to ask a statistician for advice.

If this is for some kind of research, I strongly recommend you get some advice. If this is a homework question, I would be interested in telling us what course this is in and what statistical background you have so that I can put your problem into the proper context.