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?
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$\begingroup$ Please show us the details: how were the standard errors computed, how was the t-test conducted, and how have you determined that the t-test result is not significant and at what level of significance? $\endgroup$– whuber ♦Commented Feb 7, 2017 at 20:55
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$\begingroup$ I calculated the standard errors and t test on an online programme! I determined the t test result to be significant as the t statistic was greater than the critical value! The level of significance was P<0.05. $\endgroup$– Carlamarita HazelgroveCommented Feb 7, 2017 at 20:57
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$\begingroup$ You need to find out exactly what each of these "standard errors" represents and you need to confirm that they (and the t-test) were correctly computed. However, overlap (or non-overlap) of standard errors or confidence intervals is not usually a valid hypothesis test--so it is premature to assert there's any kind of "contradiction." See stats.stackexchange.com/questions/31657 and stats.stackexchange.com/questions/18215, for instance. $\endgroup$– whuber ♦Commented Feb 7, 2017 at 21:06
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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.
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2$\begingroup$ This will be correct and useful if the standard errors are approximately the same and neither of the sample sizes is extremely small. $\endgroup$– whuber ♦Commented Feb 7, 2017 at 22:51