378 



BELL SYSTEM TECHNICAL JOURNAL 



extensive series of tests of insulation resistance were made on this 

 material, care being taken to eliminate all known causes of variability. 

 Table 2 gives the results of 204 observations of resistance in megohms 

 taken on as many samples of the proposed substitute material. 

 Reading from top to bottom beginning at the left column and con- 

 tinuing throughout the table gives the order in which the observations 

 were made. The question is: "Should such variations be left to 

 chance?" 



No a priori reason existed for believing that the measurements form- 

 ing one portion of this series should be different from those in any other 

 portion. In other words, there was no rational basis for dividing the 



SHOULD THESE VARIATIONS BE LEFT TO CHANCE? 

 52 



10 



50 



5 

 I 

 O 

 O 48 



UJ 



2 46 



UJ 



O 44 



Z 



<n 42 



10 



"^ 40 



o 

 < 



[£ 38 

 UJ 



> 



34 





•• • 



•-• 



-•-s? 



• • 



10 20 30 



SAMPLE 



ANSWER: "NO" 



40 



50 



10 

 SAMPLE 



ANSWER; "YES" 



20 



Fig. 7. 



total set of data into groups of a given number of observations except 

 that it was reasonable to believe that the system of causes might have 

 changed from day to day as a result of changes in such things as atmos- 

 pheric conditions, observers, and materials. In general, if such a 

 change is to take place, we may readily detect its effect provided we 

 divide the total number of observations into comparatively small sub- 

 groups. In this particular instance, the size of the sub-group was taken 

 as four and the black dots in Fig. 1-a show the successive averages of 

 four observations in the order in which they were taken. The 

 dotted lines are the limits within which experience has shown that 

 these observations should fall, taking into account the size of the sam- 



