From Measurement Errors to Normal Distributions: A Brief History and Its Pedagogical Implications

• Activity Number: 185
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Teaching of Statistics in the Health Sciences
• Author(s): Ilhan Izmirli*
• Companies: George Mason University
• Keywords: Normal Distributions ; Error measurements

Abstract

Normal distributions, arguably the most pervasive constructs in statistics, provide us with very important data distribution patterns. As such, they are among the most fundamental concepts introduced in a basic statistics course. Not only are they immensely useful thanks to the Central Limit Theorem derived by Laplace in 1778, but they also afford a very convenient way of establishing the idea of continuous distributions (i.e., a means of computing the probability of an observation x being in an interval (a,b) where a and b are real numbers) without using calculus.

The normal distributions are, of course, widely applicable and numerous examples are given in introductory texts related to such wide-ranging topics from anatomy to finance. One very important application, however, usually goes unmentioned: physical quantities that are expected to be sum of several independent processes (such as measurement errors) often have a distribution that is approximately normal.

Ironically, the development of the normal distributions can, in fact, be traced back to the formal study of errors, starting with Roger Cotes' (1682 - 1716), and continuing on with many distinguished scholars su