244 E. C. MACDOWELL AND E. M. VICARI 



but if it shows that curves as different may be expected to occur 

 less often than once in twenty times, they would be considered 

 significantly different. 



The number of rats is too small to permit the calculation of 

 X" from curves based on the averages of each rat. But by using 

 every trial of every rat, enough numbers are obtained. How- 

 ever, the actual time at the beginning and the end of training 

 is so very different that it would not be possible to make satis- 

 factory distribution cm*ves by seriating these directly. For 

 this reason ratios were substituted for the actual trials. A 

 standard smooth curve was estabhshed by interpolation from 

 the means of the control rats for each successive trial in training. 

 For each trial of each rat (tests and controls) the ratio to the 

 corresponding point on this assumed standard curve was calcu- 

 lated. In obtaining these ratios the smaller number was always 

 divided into the larger; when the actual time was longer than 

 the standard, the ratio was called 'plus,' when shorter, 'minus.' 

 These ratios, tests and controls separately, were next seriated 

 upon a scale with equality (ratio = 1.00) as the central point 

 and 'plus' ratios of increasing size extending to the right, 'minus' 

 ratios of increasing size extending to the left. Figure 6 shows 

 the distribution curves for these ratios grouped in classes of 

 1.725 in width, and also into classes 2.625 wide. The solid 

 line represents the controls, the broken line the tests. In one 

 pair of curves x" = 58.5; on the other hand, x^ = 44.5. The 

 value for P given in biometrica tables (p. 25, table XII) for both 

 these values of x^ and the number of classes in each curve is 

 0.000,000. In other words, the odds against these pairs of 

 curves being random samples from the same population are at 

 least greater than 1,000,000 to 1. 



e. Conclusions based on the time data. The data on time have 

 been summarized in various ways with three groupings of the 

 rats: 1) 'completes,' 2) 'completes' and 'incompletes,' 3) 'com- 

 pletes,' 'incompletes,' and 'failures;' averages per rat for the 

 different periods of the training, averages per rat for each day 

 by itself, males and females separately and together, the three 

 strains grouped separately and together; in each method of 



