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?


1 Answer 1


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.

x1 = rnorm(50, 3.124, 3.806)
x2 = rnorm(50, 6.295, 4.015)

        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 

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