Suppose I have sets A and B of normally distributed data so that:
A: mean=250, SD=200, N=25 B: mean=248, SD=200, N=20
Clearly, there is no statistically significant difference between the means (p=0.9736). But does this mean that the means are equal or that we have no evidence to suggest otherwise? Considering the huge standard deviation it seems intuitively unlikely that the means are equal. But this is what the null hypothesis says and based on the the t-test we didn't reject that.
Having such noisy data, how can one quantify how equal the means are?
Update This question arose from a discussion between myself and a colleague who was testing the effect of two drug treatments on biological samples. As the test revealed an insignificant difference between treatments, my colleague assumed this allows him to claim that the treatments have the same effect. With the example above I tried to show that this is not necessarily the case. But I didn't know the proper terminology to make things more quantitative. Hence this question.