# group differences means and standard deviation

The mean and standard deviation of the mass of owls in group 1 is 3.124(3.806) kg. The mean and standard deviation of the mass of owls in group2 is 6.295(4.015) kg.

Can I say that although the mean 6.295 vs 3.124 indicates a difference in mass between these two groups, large standard deviations indicate that this difference between groups may not be that significant?

Of course, statistical significance depends on sample sizes, which you do not provide. How many owls in each group?

If sample sizes are as large as $$n_1 = n_2 = 50,$$ then it seems the difference in means is statistically significant at the 5% level. I say "seems" because I show only one rough computation via simulation, using your sample means and SDs as population means and SDs. [But this is backed up by more careful computations, not shown.]

If you know sample sizes, as well as means, and standard deviations, then you can use standard formulas to do a formal t test and get an exact answer. [If you don't know the sample sizes, maybe you can pretend they are both 30 and see what happens.]

I recommend using a Welch 2-sample t test because I know of no reason to believe that the two populations have equal variances.

set.seed(2021)
x1 = rnorm(50, 3.124, 3.806)
x2 = rnorm(50, 6.295, 4.015)
t.test(x1,x2)

Welch Two Sample t-test

data:  x1 and x2
t = -2.0843, df = 94.492, p-value = 0.03983
alternative hypothesis:
true difference in means is not equal to 0
95 percent confidence interval:
-3.21332540 -0.07811769
sample estimates:
mean of x mean of y
3.184425  4.830147