Sec. 1.2 PURPOSES OF STATISTICAL REASONING 7 



ard laboratory specimens will be tested from each company's prod- 

 uct. The test of each specimen will produce an "observation" from 

 the population of all such tensile strengths possible from that com- 

 pany's cement. All told, there will be twenty samples taken, ten 

 from each company. 



Would it be satisfactory to inform each company of the plans for 

 testing the cements and ask each company to provide ten specimens 

 of concrete for testing? Or, would it be better to go into the open 

 market and purchase a sack of each company's cement from each 

 of ten stores and have a laboratory uniformly make up the ten 

 testing specimens? Rather clearly the latter method would be much 

 more likely to produce specimens which were representative of the 

 respective strengths of those concretes at seven days of age. 



One of the purposes of statistical theory is to devise methods for 

 taking samples in such a way that they do yield essentially the same 

 information as is contained in the population which was sampled. 

 For the most part, that phase of statistics lies beyond the scope of 

 this book; hence no attempt will be made to do more than to remind 

 the reader of a few commonsense considerations from time to time. 



Suppose now that the ten sample specimens of concrete have been 

 tested for tensile strength at seven days of age, with the following 

 results : 



Cement Seven-Day Tensile Strength (lb./sq. in.) of Concrete 



No. 1 425, 410, 425, 460, 430, 445, 445, 415, 450, and 440 

 No. 2 420, 450, 405, 400, 400, 415, 435, 425, 400, and 430 



How do we decide from such evidence whether one concrete will, as 

 a rule, excel the other in tensile strength ; or if either or both conform 

 to pre-assigned standards for such building materials? Casual ob- 

 servation indicates that cement No. 1 tends to produce greater ten- 

 sile strength in its concrete than No. 2; but there are several speci- 

 mens from cement No. 2 that produced greater strength than certain 

 of the specimens from No. 1 cement. For example, five of the No. 1 

 specimens had tensile strengths at or below 430 pounds per square 

 inch, and two of the specimens of cement No. 2 had strengths greater 

 than 430 pounds per square inch. Without doubt, then, some batches 

 of cement No. 2 are better than some batches of cement No. 1. Such 

 a situation is met quite frequently in sampling studies; only rarely 

 do progressive improvements in methods or materials come on such 

 a large scale that all previous methods or materials are excelled with- 

 out exception. What is needed — and now available to a highly use- 



