By extending "Student's" t-test to differences higher than the first, a method is provided for analyzing the results of reyersal tests employing as many periods as are practical with the organism and test used. It is shown in Part II that identical results can be obtained by the methods of analysis of variance so that the investigator may at will use either the methods presented in Part I or those in Part II if but one attribute of the experimental units is measured. But, if the investigator has one or more other measures relevant to his experimental results and wishes to increase the precision of his tests through the use of covariance, the methods of Part II must be used.