STATISTICAL METHODS IN PROTOZOOLOGY 



455 



error of the difference between any two quantities. This formula 

 is given by 



P.E. of {x — y) = V{F.E. of ,r)^' + {F.E. of y)' ^ 

 As an illustration of the use of this equation, let us consider 

 the following distribution of the number of spines for parents and 

 offspring in a family of Difflugia corona. 



For parents we have a mean number of spines of 4.391 with a 

 probable error of 0.094 and for offspring a mean of 4.145 with a 

 probable error of 0.094. 



The difference between these tw^o means is 0.246 and the prob- 

 able error of this difference is given by 



P.^.diff. = VF.£.r + P.E.,' = V(.o94)^ + (.094)^ = 0.133 



Therefore 



Diff. _ 0.246 _ 



P.E.Ain.~ 0.133 ~ * ^ 

 Referring to Table 2, we find that the area from the center of the 



X 



normal curve to an 



P.E. 



of 1.85 is 0.387. Thus, we may state that 



the chance of the occurrence of a difference as large as or larger 

 than the one observed is 0.5 — 0.387 or o.i 13. Since we have no a 

 priori knowledge as to whether or not the parent or the offspring 

 has the greater number of spines, we should allow for the pos- 

 sibility of this difference being in either direction by using twice 

 0.1 13 or 0.226, Thus we may say that if we repeat the above experi- 

 ment many times we would expect as large a dift'erence as did 

 occur, to appear about 23 times in 100 even though there were 



^ This is the most frequently used equation of a general set of formulse 

 giving means and standard deviations for simple functions such as sums, 

 differences, products and quotients of one or more variables. These general 

 equations will be found in references Dunn (1929) and Pearl (1923). 



