The Median Is the Message: Wilson and Hilfertys Experiments on the Law of Errors

Abstract

Data are reanalyzed from an important series of 19th century experiments conducted by C. S. Peirce and designed to study the plausibility of the Gaussian law of errors for astronomical observations. Contrary to the findings of Peirce, but in accordance with subsequent analysis by Frchet and Wilson and Hilferty, we find normality implausible and medians an attractive alternative to means for the analysis.

One of the first necessities of the discussion of any statistical problem is to study the data themselves.

E.B. Wilson (1923)

KEY WORDS::

• Law of errors
• Sample mean
• Sample median
• Standard deviation