RESULTS OF THE WORLD'S FAIR HEARING TESTS 545 



Relation of Hearing to Other Factors 



In the preceding section it was shown that hearing acuity varies to 

 quite an important extent with the age and sex of the group. The 

 next problem is to identify any other factors to which hearing acuity 

 is related to a significant degree. A sensitive method of determining 

 whether such factors exist is provided by the control chart technique 

 developed in connection with the statistical control of manufactured 

 product.* When the hearing tests results, corrected for age and sex 

 differences, were plotted on a control chart there was very definite 

 evidence of lack of statistical control. This indicates that one or 

 more factors exist to which hearing is significantly related, and ex- 

 perience in other fields in which control chart technique has been 

 applied suggests an excellent chance of being able to identify these 

 factors. The most straightforward procedure would have been to 

 make a careful study of those individuals whose tests fell outside of 

 the control chart limit and discover the factors responsible for the 

 abnormal scores. This was not feasible at the Fairs, and other less 

 direct methods were used as described below. 



In the discussion which follows, a judgment must often be made as 

 to whether an apparent relation between hearing and some factor 

 under discussion is significant. The customary formula for the 

 significance of a mean 



(T 



Cm — — p> 



■\n 



where o-m is the standard deviation of the mean of a group of n observa- 

 tions and a is the standard deviation of a single observation, has not 

 been used, because modern statistical theory shows that this relation 

 is valid only for data which are in a state of statistical control. The 

 data of this section do not meet this requirement, and attempts to 

 use the above relation as the sole test of significance are often mis- 

 leading. The judgments which are expressed as to the significance of 

 a relation are based upon the consistency with which the relation 

 appears when the data are broken up into small groups. Space does 

 not permit showing all the evidence on which these judgments are 

 based, but the summaries which are presented indicate the magnitude 

 of such relations as are judged to exist. 



Place of Residence 



Data from the New York and San Francisco Fairs were compared to 



discover any diff"erences which might be attributed to sectional 



* W. A. Shewhart, "Statistical Method from the Viewpoint of Quality Control" 

 (Grad. School, U. S. Dept. of Agriculture, 1939). 



