448 



RESEARCH IN PROTOZOOLOGY 



take measurements on more than one variable, and it is necessary 

 to consider their statistical description. 



In the example used above, not only the length but the breadth 

 of the trophozoites of Giardia bradypi was measured and a presen- 

 tation of the measurements v^^ith regard to both length and breadth, 

 along the same lines as the presentation as to length alone, v^ill 

 result in a frequency table in two dimensions such as is given in 

 Table 4. 



TABLE 4 

 CORRELATION OF LENGTH AND BREADTH OF TROPHOZOITES OF Giardia Bradypi 



Length in Microns 



Such a table is called a correlation table, and is made up by 

 entering in the cells of the table the frequencies with which the 

 various combinations of length and breadth occur in the actual 

 sample taken. For example, the frequency 21 in the table indicates 

 that there were 21 trophozoites of Giardia bradypi having a 

 breadth of seven microns and a length of thirteen microns. The 

 totals at the bottom of the table and at the right hand side obviously 

 give us the frequency distribution of the measurements of the two 

 variables. 



In biological material, tabulations of the type of the one above 

 tend to take a form which indicates that measurements in the 

 neighborhood of the center of the table are most frequent and 

 that as we depart from the center in any direction the measure- 

 ments become less frequent. A statistical description of such a 

 table will necessitate the determination of a centering point for 

 the table and a discussion of the way in which the points in the 

 table deviate from such a center. The centering point used for 

 such a table is that given by the mean values of the individual 

 frequency curves, and can therefore be found by computing the 

 means of the frequency distributions at the bottom and at the 

 right-hand margin of the table. We would naturally expect to 

 measure the variation of the measurements from this center by 



