364 Quantitative Characters 



After plotting these means, we could calculate the mean and 

 the standard deviation of the means. If we did, the standard 

 deviation of the means would give us the standard error of the 

 original population. If we then added the standard deviation 

 of the means to the mean of the original sample, and if we also 

 subtracted this standard error from the original mean, we should 

 have a range of values in which the mean of another sample of 

 similar size would fall in about two-thirds of the cases. Except 

 as an exercise to check the method, there would be no necessity 

 for studying large numbers of samples, and, indeed, sometimes 

 this would be impossible. The standard error of the mean of a 

 sample can be calculated from the formula 



S.E.x = 



V 



n 



which merely says that the standard error of the mean equals 

 the standard deviation divided by the square root of the num- 

 ber of individuals in the population. The probable error is the 

 same value multiplied by the constant 0.6745. Let us refer again 

 to the Fi of the Nicotiana cross. When the mean is written, 

 X = 40.78 zb 0.32, it means that if we took a large number of 

 other samples from this same Fi, the mean of these samples 

 would fall within the values 40.46 and 41.10 about two-thirds of 

 the time and would be less than 40.46 and greater than 41.10 in 

 about one-third. If the probable error is used, the mean is 

 written x = 40.78 rb 0.22, and the means of other samples would 

 fall within the values 40.56 and 41.00 in half the cases. Obvi- 

 ously, the greater is either the standard error or the probable 

 error of a given constant, the less reliable is that constant. It 

 matters not whether the standard error or the probable error is 

 used, provided that the one used is clearly indicated. 



Formulae for both the standard error and the probable error 

 of the standard deviation and for the standard error and the 

 probable error of the coefficient of variability and the calcula- 

 tions for these errors in the Fi population are given in Table 21. 



