I asked a question here [how can i see if my data are coming from two different population?](https://stats.stackexchange.com/questions/230255/how-can-i-see-if-my-data-are-coming-from-two-different-population) and seems like I cannot correctly communicate and the person who is writing to me is making me confused. 

So I try to explain what I want , if you know any method, please just tell me the method, I will try to do it myself. 

I have two groups 
**Group A** with **n** number of **samples**
**Group B** with **m** number of **samples** 

The measurements have replicate 

I want to see if the Group A is different from Group B.
for example by the mean, or whatever else which makes statistically different or not different. 

Is there someone who can really guide me what to do?
Many thanks
Nik
['https://stats.stackexchange.com/questions/230343', 'https://stats.stackexchange.com', 'https://stats.stackexchange.com/users/127951/']
When thinking about a statistical problem, you should ask yourself what experiment you have.

You have two groups, with different sample size. You can calculate arithmetic mean over all your replicates. You will be able to use the means for comparison.

1:) Check if you can assume normality. Because your data is simple, you can just do a simple QQ plot or histogram.

2:) If you can assume normality, you should use paired t-test.

3:) If you can't assume normality, you should Wilcox signed-rank test
For comparing means of populations with different samples, the standard practice is applying a two-sample location test. Depending on the size of your data, you could implement either a t-test or a z-test (t-test is recommended for smaller sample sizes). 

In any case, since you want to find out if the groups are *different*, a two-sided test would be ideal for the purpose. Since the data has different sizes, it is generally accepted that a Welch's test is the best way of performing such comparison. The Welch's test assumes unequal variances, an assumption you could test yourself. In case you have reasons to believe that the variances are equal instead, it is recommended that you use a *paired* t-test.

In R, assuming your data is stored un vectors `x` and `y`

```
#Welch's t-test
t.test(x,y)

#paired sample test
t.test(x,y, paired = TRUE) 

#test for equality of variances
var.test(x,y) 

```