2o8 Bulletin 307 



APPENDIX 

 PART II 



STATISTICAL METHODS AS APPLIED TO ORCHARD SURVEYS 



GENERAL THEORETICAL CONSIDERATIONS 



The use of statistical methods in the study of horticultural problems, 

 as well as in the problems of the larger fields of agriculture and biology, is 

 increasing rapidly. Prof. Karl Pearson says, " Criticism demands now 

 quantitative exactness." Theories are not valuable until they are backed 

 up by experience, and experience is summed up by statistics. By con- 

 stantly widening the scope and increasing the numbers of cases upon 

 which figures are based, old principles may be corroborated or corrected, 

 new principles may be deduced, and the theory of orchard management 

 may have a practical foundation. 



THE PRINCIPLES UNDERLYING STATISTICS 



In order that one may study the figures in statistical tables more intel- 

 ligently, he must understand the basic principles of statistics and the 

 methods by which statistical results are obtained. 



Law oj probability and normal distribution 

 Whatever chance value an individual may have, a large number of 

 individuals, when classified according to their increasing values, are found 

 to distribute themselves more or less regularly. A few will be found at 

 the lowest value, increasing numbers at the higher values, until the maxi- 

 mum frequency is reached. From this point until the highest value in 

 the range of distribution is reached the frequency decreases. It makes 

 little difference whether the individuals composing the group, or popula- 

 tion as it is called, are orchards, poppies, human beings, or what not; or 

 whether the classes are different types of orchard management, stigmatic 

 bands, or heights; or whether the values are measured in terms of barrels, 

 dollars, integers, or inches; the great mass of the individuals lies very close 

 to a central value, with about equal numbers above and below it. Only 

 a few individuals are found at the extremes. Because of chance accidents, 

 each individual differs from the central value, but the law of probability 

 of error is that the algebraic sum of the positive and negative deviations 

 is zero. It is this normal distribution of a population about a central 

 point that underlies all statistical work. We can sum up very briefly, 

 therefore, the facts contained in a great mass of material by stating the 

 value of the central point or average. 



