# More on why this trick works

How does this trick work? You should only read on if you really want to know . . .

The Interval plot is designed to plot a confidence interval, or an estimate plus or minus a specified number of standard errors. It does this with the input being the raw data.

In this case, the data input for each group are not the raw data, but the three values locating the confidence interval: the estimate, lower limit and upper limit. We are only concerned with symmetric intervals, so we may call these values E - m, m, and E + m, where E is the estimate and m is the margin of error for the confidence interval.

It is easy to show that the (usual) sample deviation of these three equally spaced values is m, the margin of error. The Interval plot algorithm will calculate the standard error of these three points as m divided by √3, since the "sample size" is 3.  So with the three values as entered, the Interval plot with a setting of one standard error would plot an interval with (E - m/√3) and (E + m/√3) as the limits. We don’t want that; we want the limits to be ( E - m) and (E + m). This is achieved by entering 1.732 (√3) as the Multiple of the standard error.

Neat, hey!