454 RESEARCH IN PROTOZOOLOGY 



having the facts for a sample, we are able to form some judgment 

 as to the mean value of the unknown universe from which this 

 sample was drawn. 



The discussion given for the probable error of the mean is in 

 general paralleled when we consider the probable error of any 

 statistical constant. We find that such constants have variabilities 

 that are functions of the variability of the individuals and of the 

 size of the sample. The following set of equations presents the 

 probable errors of the more important of the statistical constants: 



TABLE 5 

 TABLE OF PROBABLE ERROR FORMULA 



The knowledge of any constant and its probable error suffices 

 to tell us the value and variability of the attribute under discussion, 

 but in many cases, we wish to consider the value of a given at- 

 tribute in comparison with the value of the same attribute for 

 a dififerent sample. For instance, we may have determined the 

 mean value of a certain measurement for an experimental group 

 and the mean value of the same quantity for a control group, 

 and we immediately ask the question — does this mean for the 

 experimental group differ from the mean for the control group? 

 Obviously, this question is not limited to a mere comparison of the 

 arithmetic values of these means, but implies a discussion of the 

 question as to whether or not the difference of these means is a 

 significant one when we consider variability of the individuals in 

 the two samples involved. To answer this question, we shall need 

 to take the difference between the means in question and consider 

 this difference in the light of the probable error of the difference. 

 Thus, we feel the need for a formula to represent the probable 



