When a figure shows means and bars indicating one standard error above and below each mean, and the range defined by the bars in one group overlaps the mean of the other, then the results of a t-test would always fail to reject the null hypothesis that the means are equal.

Question

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When the range defined by the bars in one group overlaps the mean of the other, it means that there is some overlap between the two distributions. This overlap indicates that there is some uncertainty about whether the means are actually different. As a result, a t-test would fail to reject the null hypothesis that the means are equal.

When a Figure Shows Means and Bars Indicating One Standard