My teacher said that I can't use t-test because the conditions of application aren't verified. I really don't know why he said that: my samples are independent and big (N=30). :\

Your teacher probably means the assumption of normality and equal variances. Test for those assumptions. The t-test is robust for non-normality with sample sizes > 30. If the variances are not equal, there is another version of the t-test that does not assume equal variances.

Last edited by Miner; 04-19-2013 at 06:47 AM.
Reason: correct typo

Then the data meet the assumptions for using the 2-sample t-test using equal variances. There is no need to use a non-parametric test. Since the non-parametric has only slightly less power for the normal distribution scenario you should get equivalent results using both unless it is a borderline situation.

But that's what I used and he said the conditions of application aren't verified. I found out that the MWW test is more widely applicable than independent samples Student's t-test...

"recommend MWW as the default test for comparing interval or ordinal measurements with similar distributions"
"MWW will give very similar results to performing an ordinary parametric two-sample t test on the rankings of the data."

When he said that, had you demonstrated that you have tested for normality and equal variances? He may have meant that you had not verified the assumptions prior to performing the test.

The MWW test also has assumptions of similar shape and equal variance, so you still have to verify the assumptions. Furthermore, you should try to use the most powerful test when it is appropriate. The MWW test is more powerful than the 2-sample t-test WHEN the distributions are non-normal. However, the 2-sample t-test is slightly more powerful when the distributions ARE normal.

It sounds like your teacher just has a bias toward the MWW test.

My conditions of application are in this Excel Sheet (it's in portuguese, but is easy to understand). I used KS to test normality and I concluded that the distribution can be approximated to a normal distribution (didn't reject H0). Then I used F-test to find out if the variances are equal and H0 isn't rejected. So... you said that t-test is more powerful in this situation. If I put this sheet in my project to explain the conditions of application, do you think my teacher will accept my analysis using 2-sample t-test?

Under the conditions of normality, the effectiveness of the MWW test is 0.95 compared to the 2-sample t-test. It is close, but the t-test does outperform.

I think that you have done all you need, but I am not your instructor. Instructors are not always reasonable. Boa sorte.

Just one more question: I send him an e-mail and he basically said that I needed to put the conditions of application before performing the test. So I can use the t-test. However, he also said that N=30 is in the limit for a sample be considered big, so I need further information to "justify" this single point.

The t-test does not have any restriction on the sample size.

The proper approach is to establish "a priori" the difference in means that you want to detect. That is, a difference that is of "practical" importance. Practical importance is that level that would convince the "powers that be" to provide funding for further research or to make changes. It is that level that would convince someone to change their behavior. Then determine the alpha and power that you desire and calculate the required sample size. That sample size might be 5 or it might be 200.

The only reason that 30 is ever mentioned is that at n >= 30, the t-test becomes more robust to deviations in normality. However, in your case, the data are normal, so a sample size of 30 is a moot point.