I have data that include 20 samples divided into 2 groups (category A and category B). The groups are independent, none of the value in one group repeat in other. N(A) =14, N(B) = 6.

here is the data:

category A category B

0.0119888167559 0.023185483871

0.00101354303189 0.312090168227

8.95231103909e-06 0.503371693147

2.9580256165e-05 0.522824974411

0.0596266691309 0.114932864532

4.02612958098e-05 3.32126606662e-05

0.337753287524

0.0115114590662

0.19273480545

0.232453117898

3.69713102632e-05

3.00480769231e-05

0.192851577717

1.58790650407e-05

I would like to show that mean values of 2 groups differ significantly. But I am very confused which test statistic I should use.

Here are the tests that I've performed so far:

1. Wilcoxon rank sum test (Mann-Whitney test) (two-tailed)

W=20, p=0.07575

2. Student t-test (two-tailed)

t = -2,24259 p = 0,03775

3. Welch t-test (two-tailed, unpaired, correction=False)

t=-1.7109, p = 0.1376

So as you see 3 tests present 3 different probabilities...to be more complicated ...

4. Normality test (Shapiro-Wilk)

I've checked also the normality of my data, and the first group category A is normally distributed (Test Shapiro-Wilka = 0,704713, p 0,000413591, p<0.05) but second is not-category B (Test Shapiro-Wilka = 0,868539, p 0,220442, p>0.05) probably because of low number of samples.

A list of questions:

Q1: Can I assume that my data in 2 groups are normally distributed and use Student t test or Welch t-test?

Q2: OR Should I use non-parametric Mann Whitney test? (I've written that it has low power for low number of samples...)

Q3: Another think is the equality of variation between groups, when I assume that there are equal I can use Student t- test, if not I can use Welch t-test...should I first perform test for variant equality?

To summarize post - I need help to find a test that will be OK:

- small number of samples in one group (less than 10)

- unequal number of samples in groups

- data not normally distributed in one group

- showing the difference of means (optional)

I would really appreciate for any suggestions,

Please help!

PS. This is for publication. Since the probability from Student t-test is the most significant (p<0.05) I would like to stay with that result can I?

Best,

Agata