Confidence Intervals Based on the Mean Absolute Deviation of a Normal Sample

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Abstract
Confidence intervals for the population mean of a normal distribution can be determined from the distribution of the variate , analogue to Student's t-distribution but based on the mean absolute deviation d instead of the standard deviation. The H-distribution is derived: the frequency function is symmetric about zero, with central ordinate (1/φ) √ (1-n -1); asymptotically it is normal, N(0, √(φ/2)). An approximate formula for the calculation of the percent values is developed and numerical factors tabulated by which the mean absolute deviation of a normal sample of size n is to be multiplied in order to obtain 95 percent and 50 percent confidence limits of the mean, for n =2(1)15(5)30, 40, 60,120. It is shown that the increase in length against confidence intervals from the standard deviation and Student's t is negligible. The usefulness of confidence intervals from the mean absolute deviation for estimating the precision of measurements in Physics is discussed.

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