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Comparing smoke and hormones level in two groups of people. Which test?
I'm analyzing some data for an article about hormones concentrations and smoking.
I was unsure whether to use parametric or non parametric tests to compare the groups, but since the sample number is high (> 100) i thought there would not be a significative difference.
For most of the hormones we're studying this is true, but we're having some problems with one of them.
The distribution of this hormone's values is not normal using D'Agostino omnibus normality test in both smokers and non-smokers groups (p ***) but comparing them with a F-test for difference in variance it tells me that variance is not significantly different (p > 0.09).
The two groups for this hormone are:
- Smokers: N 102, mean 7.993, SD 4.004, min 2.3, max 22.3
- Non-Smokers: N 194, mean 6.98, SD 3.472, min 1.5, max 28.3
I run Mann-Whitney because of the skewness and anormality of the data and it gave me a p > 0.06, so non significant. But if I use an unpaired t-test instead i have a p ≈ 0.025, significant!!
If I understood well the theory, for large numbers t-test and mann-whitney should be similar! And for the other hormones we studied this was true! but in this case parametric and non-parametric break the significancy limit. I know that 0.05 is a traditional alpha, but how should I interpretate this data?
Further more I run a test that correlates in the smokers group the numbers of cigarettes and the hormones level. While the other hormones give not significant correlation, there's again the same hormone of above that give two different results for parametric and non parametric test:
- Pearson (parametric) r 0.247, p 0.012
- Spearman (non-parametric) r 0.178, p 0.072
Again significant with parametric, non-significant with non-parametric. What's going on here? I suppose in this case there's no choice about the test because cigarettes per day cannot be parametric!
So i really need help to interpretate this data!!!
