118 THE QUANTITATIVE METHOD IN BIOLOGY 



calculated a priori in the following way : — in the example under 

 consideration (one coin) the number of possible cases is two ; 

 both cases are equally possible ^ ; one case is favourable for 

 the event a and one for the event h. The probability {frequency) 

 of a given event is obtained by dividing the number of favourable 

 cases by the number of possible cases ^ ; thus for a and for b the 

 probability is J. 



The term probability is used here in a definite sense ; it is 

 a quotient. Since this term has, in the ordinary language, a 

 rather vague significance, it is a serious cause of misunderstand- 

 ing. Therefore it is preferable to replace it as often as possible 

 by the term frequency. 



It must be borne in mind, once for all, that the notion of 

 frequency represents an approximation, and that it has very 

 Httle practical significance, if any significance at all, when the 

 number of observations is too small. 



§ 93.— EXPERIMENTAL VERIFICATION : EXPERI- 

 MENTS WITH ONE COIN.— I have tossed a coin (a British 

 penny) 3000 times. In 150 series of 20 successive tosses the 

 events a and b were observed ^ : 



In 



Taking the event a (head), we see that its observed frequency 

 is variable within very wide limits— viz. ^ and \i * and that 

 in 120 out of the 150 series a deviation from the calculated 

 frequency (which is \%) exists. Therefore we are in danger of 

 being seriously deluded if we draw any conclusion from one 

 series of 20 tosses. 



In 30 series of 100 successive tosses the event a (head) was 

 observed : 



In I series 



.. 3 



.. 2 



>. I 



„ I 



„ 3 



.. 2 



43 times 



44 .. 



45 .. 



46 „ 



47 .. 



48 „ 



49 „ 



In I series 

 „ 6 

 ,. 4 

 >. 3 

 .. I 

 .. I 



50 times 



51 .. 



52 ,. 

 ■ 53 .. 



: 55 .. 



: 56 „ 



: 60 .. 



The calculated frequency is -^. The observed frequency is 

 variable between -^ and 1%. The concordance between the 



1 Both states of equilibrium are equally stable. 



2 Possible states of equilibrium of equal stability. 



^ I have used a penny which was worn flat on both sides. 

 ' The possible limits are ^ and |^. 



