ALCOHOLISM AND BEHAVIOR OF WHITE RATS 243 



significant differences in the variability are found when the trials 

 are separated into groups of three. It may be concluded, then, 

 that there is a difference in the variabiUty of the tests and con- 

 trols in the first half of training, although when the 'failure' 

 rats are included this is hidden if all the twelve trials are taken 

 together. 



d. What is the probability that the test data and control data 

 for time are not random samples from the same population?^ It 

 is beheved that sufficient evidence has been presented to remove 

 the shghtest doubt from the conclusion that the tests as a group 

 took more time in learning the maze than did the controls. 

 So the presentation of the following method of comparing the 

 time data of the tests and controls is of more interest from a 

 methodological standpoint than from the standpoint of the 

 findings, which, it may be stated in advance, fully substantiate 

 the above conclusions. 



Although the x^ test is usually employed to measm*e the good- 

 ness of fit of a theoretical and an empirical curve, it also affords 

 a method of measuring how poorly two curves agree; it measures 

 the probability that two curves, differing as much as those in 

 question, will occur as the result of random sampling from a 

 single population. The following formula given by Pearson 

 (Biometrica, '11, p. 250) has been used: 



(NN^ 



2 ^ )^'<i^-{^ 



X 



2 = 2 r^' VN 



+ f' 



in which N = numbers in one sample; N' = numbers in the 

 other sample; f = frequency of a class in one sample, f = the 

 frequency of a class in the other sample. 



If the x^ test indicates that such differences as are found may 

 be expected to occur more often than once in twenty times 

 (once in twenty times corresponds to three times the probable 

 error), the curves could not be considered significantly different; 



2 We are pleased to acknowledge the large part our colleague, Prof. H. D. Fish, 

 has contributed in working out the methods used in this section. 



