Al'l'LICAl ION or STATISTICAL METHODS 



lAHI.K II 

 Inspection Data on Transmitters 



that comparatively large differences exist between the av^erages 

 obtained for flifferent groups of transmitters by different groups of 

 observers. Similarly, comparatively large variations e.\ist in these 

 averages even when taken by the machines (the large difference 

 between the sensation and machine measures is due to a difference 

 in the standard used, corrections for which are not made in this table). 

 Are these differences significant? Is product changing? That is, 

 are the manufacturing methods being adequately controlled? Are 

 these results consistent with a random variation in the causes con- 

 trolling manufacture? These are the questions that w-ere raised in 

 connection with the interpretation of these data. The ordinary 

 theory of errors gives us the following answer. It will be recalled 

 that the standard deviation (or the root mean square deviation) of the 



average ax is equal to 



Va^" 



Also, from the table of the normal 



probability integral we find that the fractional parts of the area 

 within certain ranges are as follows: For the ranges X±(r, Xzt2cT, 

 and X±3(T, we have the percentages 68.268, 9o.450, and 99.730 

 resfxjctively. Obviously, it is highly improbable that the difference 

 between averages should be greater than three times the standard 

 deviation of the av'erage, providing we assume that all of the samples 

 were drawn from the same universe: In other words, that all of the 

 samples were manufactured under the same random conditions. 

 The fourth column, then, indicates practical limits to the variations 

 in the averages. It is obvious, therefore, that the differences between 

 the averages are larger than could have been expected, if the same 

 system of causes controlled the different groups of observations. In 

 other words the differences are significant and must be explained. 



