My data shows that there is NO overlap of the standard errors of the mean but my unpaired two tailed t-test shows that the difference in the means is not statistically significant? How can I interpret this data: is the difference in means significant or not?
If standard errors do not overlap then the difference in means must be at least 2 standard errors apart. The standard error of the difference between means is 1.44 x the standard error. Multiply that by 2 (approximately the t) the difference has to be about 3 standard errors apart.