Measurement of physical quantities, at least, has reached a high level of standardization. However, in earlier days even the units for land measure had to be developed locally ad hoc, as explained in this account. (The linear unit rood was the ancestor of a surveyor’s rod, now 164 feet.)

A good idea of the inconvenience caused by the lack of absolute and invariable standards is furnished by a German treatise on surveying of the 16th century, which instructs the surveyor to establish the length of a rood thus: ‘Stand at the door of a church on a Sunday and bid 16 men to stop, tall ones and small ones, as they happen to pass out when the service is finished; then make them put their left feet one behind the other, and the length thus obtained shall be a right and lawful rood to measure and survey the land with, and the 16th part of it shall be a right and lawful foot." (Compton’s Pictured Encyclopedia, 1929 edition. Chicago: F. E. Compton & Company.)

Lacking a portable physical standard measure, these early surveyors depended on statistical regularity: They assumed that as long as the sample choice did not involve bias extreme values would tend to balance, so that the sum (rood) and the mean (foot) would be "average".

A precise statement of the principle of statistical regularity had to wait three centuries after the surveyors’ application for the statement and proof of Chebyshev’s inequality (1867).

Several basic statistical questions can be discussed in connection with this rude rood example:

Was the sample random? What was the sample space? We would need to know some social history to be sure whether most men in the district would be in church, so that the sampling frame was essentially the district.

Suppose the phrase"... as they happen to pass out when the service is finished was taken to mean "stop the first sixteen". Would this have caused any bias­say, overrepresentation of small feet? Custom might have led to an age factor, a status factor, or even a speed factor in the order of leaving church, and any one of these factors might conceivably have been correlated with foot length.

How could the surveyors have judged whether the standard they had calculated was satisfactory? They might have analyzed residuals. If comparisons showed that most men in the district had shorter left feet than the sample average, the first sampling attempt might have been considered unsuccessful in yielding a usable standard.

Good sampling, with avoidance of bias, requires imagination and knowledge of background conditions.

Kansas State University

Back to top

Back to contents of The Best of Teaching Statistics
Back to main Teaching Statistics page