# Comparing means

#### Vthompson

##### New Member
Hello,
I hope you can help. I am working with numerical data and I wish to compare means.
Data set 1 has N=30 (normally distributed)
Data set 2 has N=24 (not normal)
Data set 3 has N=24 (not normal)
Data set 4 has N=12 (not normal)
I used the Shapiro Wilks test to test for normality and any p value < .05 was not normal.
I have to compare set 1 to set 2, set 1 to set 3 and set 1 to set 4.
Being that I am comparing a normal set to non-normal, which test should I use. I would think the Mann-Whitney Test but I want to be sure.

#### katxt

##### Active Member
I think many folk would just proceed with the MW test and few people would complain. However you should note that this is a test of medians and not means. It also assumes that the two groups being tested are much the same shape, just shifted relative to each other. This isn't the case here because one is normal and the others aren't, but how much effect that will have is hard to judge. The MW test can give a significant result if the shapes of the two distributions are noticeably different, even though the medians may be the much the same. A resampling test could be the answer if there is likely to be strong criticism of the MW test.
Also note that if you are doing three tests, then you should adjust the critical level for significance downwards (to perhaps 0.02) to protect against false positives.

#### Karabiner

##### TS Contributor
I think many folk would just proceed with the MW test and few people would complain. However you should note that this is a test of medians and not means. It also assumes that the two groups being tested are much the same shape, just shifted relative to each other. This isn't the case here because one is normal and the others aren't, but how much effect that will have is hard to judge. The MW test can give a significant result if the shapes of the two distributions are noticeably different, even though the medians may be the much the same. A resampling test could be the answer if there is likely to be strong criticism of the MW test.
Also note that if you are doing three tests, then you should adjust the critical level for significance downwards (to perhaps 0.02) to protect against false positives.
But the MW test does not test medians. The MW test does not assume same shapes, because it is a test on ranked data, which do not have shapes.

With kind regards

Karabiner

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#### Karabiner

##### TS Contributor
Hello,
I hope you can help. I am working with numerical data and I wish to compare means.
Data set 1 has N=30 (normally distributed)
Data set 2 has N=24 (not normal)
Data set 3 has N=24 (not normal)
Data set 4 has N=12 (not normal)
I used the Shapiro Wilks test to test for normality and any p value < .05 was not normal.
I have to compare set 1 to set 2, set 1 to set 3 and set 1 to set 4.
Being that I am comparing a normal set to non-normal, which test should I use. I would think the Mann-Whitney Test but I want to be sure.
You have a total n of 90, and you have n > 30 for any pairwise comparison, so normality assumptions are of no interest here.
What REALLY is of interest here is whether you have interval scaled data, whether the variances markedly differ between groups,
and what you want to find out at all. Maybe you want to perform an omnibus test for your grouping variable i.e. oneway analysis
of variance, with pairwise post-hoc tests.

With kind regards

Karabiner

#### Vthompson

##### New Member
Thank you very much for your help!!