248 
STATISTICS: W. A. SHEWHART 
PROC. N. A. S. 
ON THE MEASUREMENT OF A PHYSICAL QUANTITY WHOSB 
MAGNITUDE IS INFLUENCED BY PRIMARY CAUSES 
BEYOND THE CONTROL OF THE OBSERVER AND 
ON THE METHOD OF DETERMINING THE 
RELATION BETWEEN TWO SUCH 
QUANTITIES 
By W. a. Shewhart 
Research Laboratories of the American Tei^Ephone and Telegraph 
Company and the Western Ei^Ectric Company, Inc. 
Read before the Academy, April 25, 1922 
In order to relate the physical and chemical properties of carbon to 
the microphonic properties of this material, it has been found necessary 
to make measurements on physical quantities which are influenced by 
primary causes beyond the control of the observer. In many problems of 
the physical and engineering sciences it is possible for the observer to con- 
trol within narrow limits, the causes of variation of a quantity while it is 
being subjected to measurement. Certain problems arise, however, in 
these sciences as in the field of economics and biology wherein it is im- 
possible to do this. In general let Xi and X2 represent two quantities 
related to others Ui, U2, ... Ua, Vi, V2, . . . V^,; Wu W2 • . . Wf, in the 
following way: 
Xi = Fi {Uu U2, : . . Ua, Vu V2, ... V,) (1) 
X2 = F2 (Uu U2, ... Ua, W,, W2, ... W,) (2) 
where Fi and F2 represent unknown functional relations. In most physi- 
cal experiments it is possible to hold the t/'s, F's, and Ws, practically con- 
stant while a measurement is being made on either Xi or X2. In the last 
analysis, however, the C7's, V's, can never be held constant and in many 
cases, particularly where these symbols represent molecular phenomena, 
the variations about their mea,n values may become quite large. 
Thus, if Xi and X2 represent two microphonic characteristics of granular 
carbon which are functions of the physical and chemical properties rep- 
resented by the U's, F's, and Ws, it has been found necessary to apply 
certain statistical criteria to determine the nature of the cause complex 
controlling a single quantity such as either Xi or X2 and also to determine 
quantitatively the degree of relation existing between the two micro- 
phonic properties. As a result of such a study involving an analysis of 
thousands of measurements of the above type, certain conclusions which 
are of general interest have been reached in respect to the practical appli- 
cation of statistical methods in connection with physical measurements 
of this character. 
