Do SEM calculations count as a statistical test? I am having a debate with a biology teacher assistant, where they claim that if SEM bars overlap, I cannot claim that their difference is not STATISTICALLY significant. Key word on statistically. They say that we have not carried out an actual statistical test to claim this. However, does the SEM not take into account the sample size as well as the standard deviation? Many of the websites I check, say that you can claim statistic significance with SEM bars. I need to know what is what, thank you.