ANTIBODIES II 21 



antibody that may be in short supply, (b) The goal of such experi- 

 ments is not usually an estimate of the actual inhibiting dose of any 

 one particular hapten, but an estimate of the relative inhibiting power 

 of two different haptens ; in other words, a ratio. It is quickly 

 found that attempts to calculate the standard error of a ratio from 

 the standard errors of the two numbers involved leads one into 

 Higher Statistics. 



It might seem to the non-serologist that in the simple type 

 of inhibition study shown schematically in Tables 2-2 and 2-3 sta- 

 tistical methods could be applied and would be helpful, but this is 

 not generally the case either. To begin with, inhibition experiments 

 are ordinarily interpreted as if inhibition were an all-or-none 

 phenomenon. Thus from the first line of Table 2-2 we conclude 

 that for complete inhibition (tube 4, counting from the left) of 

 the amount of serum used in the experiment 1/16 of the amount 

 of hapten H contained in a unit volume of stock solution is sufficient. 

 But for all we know the amount of hapten in tube 4 may be any- 

 where from 1.02 to 1.98 times the minimal inhibiting dose (MID) 

 of H. If tube 4 contains 1.02 MID, then tube 5 in turn contains 

 only 0.51 MID, and the unavoidable accidental variations in experi- 

 mental conditions are not likely to cause tube 5 to give a nega- 

 tive reading, though they well might make tube 4 positive. But if 

 tube 4 contains 1.98 MID, which is equally possible, then tube 5 

 would contain 0.99 MID, and a slight variation in the conditions 

 of the experiment might mean that tube 5 would read negative in- 

 stead of positive. Thus in different experiments our estimate of the 

 smallest amount of hapten that will completely inhibit a given amount 

 of antiserum might vary from 1.0 to 2.0 to 0.5 mM. An experimenter 

 is likely to feel that he is wasting his time in averaging numbers like 

 1.0, 2.0, and 0.5, not to speak of trying to estimate a standard devia- 

 tion and a standard error of the resulting mean. 



Also, it must be realized that, just as the results with hapten H 

 might vary from 1.0 to 2.0 to 0.5 mM, so the results with hapten H' 

 might vary from 0.25 to 0.5 to 0.125 mM. It is expected that the 

 variations in estimated MID's of the two haptens will generally 

 go in the same direction ; indeed, this is one of the reasons for run- 

 ning all the tests simultaneously, but it is apparent that the ratio 

 of the apparent MID's might vary from 16 to 1. 



