One approach to comparing two means is to determine whether their actual difference is greater than their least significant difference (LSD). This least significant difference is a Student’s t-statistic multiplied by the standard error of the difference of the two means and is written as follows:
Relationship of the Difference between Two Means
Geometric Relationship of t-test Statistics
 • If the means differ exactly by their least significant difference, then the confidence interval circles around each mean intersect at a right angle. That is, the angle of the tangents is a right angle.
 • If the circles intersect so that the outside angle is greater than a right angle, then the means are not significantly different. If the circles intersect so that the outside angle is less than a right angle, then the means are significantly different. An outside angle of less than 90 degrees indicates that the means are farther apart than the least significant difference.
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Help created on 9/19/2017