Some Applications of Statistical Methods to the Analysis of Physical and Engineering Data

E ordinarily think of the physical and engineering sciences as being exact. In a m a j o r i t y of physical measurements this is practically true. It is possible to control the causes of variation so t h a t the resultant deviations of the observations from their a r i t h m e t i c mean are small in comparison therewith. In the theory of measurem e n t s we often refer to the "true value" of a physical q u a n t i t y : observed deviations are considered to be produced by errors existing in the method of making the measurements. 43 44 BELL SYSTEM TECHNICAL JOURNAL W i t h t h e introduction of the molecular theory and t h e theory of q u a n t a , it has been necessary to modify some of our older conceptions. T h u s , more and more we are led to consider t h e problem of measuring a n y physical q u a n t i t y as t h a t of establishing its most probable value. We are led to conceive of the physico-chemical laws as a statistical determinism to which " t h e law of great n u m bers" 1 i m p a r t s t h e appearance of infinite precision. In order to obtain a more comprehensive u n d e r s t a n d i n g of the laws of n a t u r e it is becoming more necessary to consider not only t h e average value b u t also t h e variations of t h e separate observations therefrom. As a result, t h e application of the theory of probabilities is receiving renewed impetus in the fields of physics and physical chemistry. Statistical Nature of Certain Physical Problems. As typical of t h e newer t y p e of physical problem, we may refer to certain d a t a given by Prof.