Lyz,

It's not entirely clear what your asking. Between your question and the comment is sounds like you have three groups with (potentially) different means but each normally distributed. So, in R something like

```
set.seed(123)
ex_data <- data.frame(grp=rep(letters[1:3], each=20),
vals=c(rnorm(n=20, mean=0, sd=1), rnorm(20, 2, 1), rnorm(20,0,1)))
#mean values for each group
with(ex_data, tapply(vals, grp, mean))
# a b c
#0.1416238 1.9487428 0.1064852
```

Now you want to kow if the between-group differences are statically significant? If that's the case then you want to ANOVA and a correction to deal with the fact you are making multiple comparisons:

```
ex_data.aov <- aov(vals ~ grp, data=ex_data)
TukeyHSD(ex_data.aov)
# Tukey multiple comparisons of means
# 95% family-wise confidence level
#
#Fit: aov(formula = vals ~ grp, data = ex_data)
#
#$grp
# diff lwr upr p adj
#b-a 1.80711904 1.1053442 2.5088939 0.0000002
#c-a -0.03513857 -0.7369134 0.6666362 0.9920290
#c-b -1.84225761 -2.5440324 -1.1404828 0.0000001
```

If you mean the *variances* of your group data are different then you need to something a little - maybe Welch's ANOVA `oneway.test()`

in R, or a bootstrap approach.

In any case, this will all be covered in very introductory stats text. Make sure you understand what the numbers coming back from these tests actually mean before you report them

Can you be more clear with us? What kind of data you have?

Assume every group follow the gaussian distribution, but with different parameters. t test can be used to test every two groups.