Samples 121 



rence in per cent due to chance alone of a deviation as great as 

 (or greater than) one from an expected ratio of 3 : 3. 



Samples 



The student might well be inclined to ask why it is necessary 

 to apply statistical methods in genetics and why they were in- 

 vented in the first place. If we cross two Nemesia plants whose 

 genotypes are Bmbm, we should get a ratio of three white to one 

 blue-margin, and we should get exactly such a 3 : 1 ratio if we 

 had an infinite number of offspring. Similarly, if we tossed a 

 coin an infinite number of times, we should get heads and tails 

 in exactly equal numbers. However, the student must be aware 

 that an infinite number of plants does not exist and that there 

 is no such thing in our finite world as an infinite number of 

 tosses. If we raise 100 or 200 or even 1000 plants, we still do 

 not have the entire theoretical population of offspring that might 

 be produced from such a cross. What we have is a sample, and 

 from this sample we must judge whether or not the entire popu- 

 lation would be segregating into a 3 : 1 ratio. Samples are 

 subject to the laws of chance, and statistical methods are applied 

 to the sample to determine whether the variation shown by the 

 sample from the theoretical ratio is merely the degree of vari- 

 ation that chance alone would produce in a given percentage of 

 samples or whether the variation is so great that it is highly 

 improbable that the observed ratio could be considered a sample 

 of the theoretical ratio we are considering. 



Statistical methods are also applied to finite populations which 

 are so large that it is impractical to examine every individual of 

 the population. If we have a carload of ears of corn to be sold, 

 the purchaser must, of course, have an idea of the quality of the 

 corn before he purchases it. Since it would be impractical to 

 examine every ear, he examines merely a small sample, and on 

 the basis of that sample he judges what he will pay for the 

 entire carload. Obviously, such a sample will not be an exact 

 picture of the whole population, but if it is obtained in a purely 

 random manner, and if it is reasonably large, it will furnish a 

 sufficiently accurate estimate of the whole carload. 



