INDUSTRIAL MATHEMATICS 289 



"Since inductive inferences are only probable, or, in other words, since repeti- 

 tions of any operation under the same essential conditions cannot be expected to 

 give identical results, we need a scientific method that will indicate the degree of 

 observed variability that should not be left to chance. Hence it appears that the 

 use of mathematical statistics is essential to the development of an adequate 

 scientific method, and that mathematical statistics may be expected to be of 

 potential use wherever scientific method can be used to advantage." 



More specifically, there are five recognizable types of industrial engi- 

 neering activity in which statistical theory either is, or should be used. 



(a) In studying experimental data to determine whether the observed 

 variations should be regarded as accidental or significant. An example 

 is found in the field of geochemical prospecting. The surface soil overlying 

 regions in which there is oil contains a higher proportion of hydrocarbons 

 and waxes than occur in other locations. Chemical analysis of surface soil 

 therefore affords a means of prospecting for oil. Mr. Eugene McDermott 

 writes: 



"In the geochemical method, it was found necessary to determine between 

 samples showing significantly high analysis values, and those which were normal 

 values. These normal sample values, of course, had considerable variation be- 

 tween themselves, due to analysis and in larger part sampling errors. After 

 examining these data for a long period of time, it was decided to approach the 

 problem statistically. This disclosed at once that areas surveyed could be divided 

 into positive (having significant values, and hence favorable from the standpoint 

 of petroleum possibilities), negative (no significant values and unfavorable for 

 petroleum) and marginal (indeterminate). The latter case is always the most 

 difficult one in surveying, and while we are now able to recognize it, further work 

 is needed to fully interpret it. This kind of mathematics is being applied at the 

 present moment, and bids fair to solve the problem." 



{h) In planning the kind of experiments from which such data arise. 

 Whether variations are or are not significant depends in no small degree 

 upon the fashion in which the data were taken. Consideration of the 

 experiment in advance from a statistical point of view often results in 

 economy of procedure, or even points the difference between a trustworthy 

 and a meaningless result. 



The following example is quoted from an address by Dr. R. H. Pickard, 

 Director of the British Cotton Research Association: 



"To illustrate the advantage of good experimental design I may refer to some 

 experiments carried out at the Shirley Institute to find the effect of various treat- 

 ments on a quality of cloth. This quality varies considerably at different parts 



