CHAPTER II. 



METHODS OF STATISTICAL ANALYSIS. 



Before taking up the actual data with which we have to deal, a 

 brief discussion of the statistical formulas employed will be necessary 

 although it is not possible to give an adequate introduction to the use 

 of the statistical methods. These methods are complicated and many 

 pitfalls abound in the field of statistical reasoning. This section may, 

 however, give the reader definitions of terms and a general conception 

 of the method of attack. 



The first statistical constant to be determined for a series of meas- 

 urements is the arithmetic mean or average value. This is simply the 

 sum of all the observations divided by their number. It is already 

 familiar to the physiologist and need not be discussed further. 



The second statistical constant with which we shall have to deal 

 in the treatment of these data is a measure of the deviation of the 

 individual measurements from their average value. Physiologists in 

 common with psychologists and other investigators have sometimes 

 measured the variation in their observations by obtaining and aver- 

 aging the differences between the individual readings and the general 

 average. Thus an average deviation, or an average dispersal, of the 

 individual measurements about the general average for the whole 

 series of individuals dealt with, is obtained. This average deviation is 

 very useful for some purposes, but for more refined work has three 

 disadvantages. (1) Some of the measurements are smaller while others 

 are larger than the general average for the whole series of individuals 

 dealt with. Thus some deviations are positive while others are nega- 

 tive in sign. In obtaining an average value which shall furnish a 

 true measure of scatter both above and below the mean, it is necessary 

 to disregard the signs and thus to do violence to one of the laws of math- 

 ematical usage. (2) The significance to be attached to a deviation is 

 considered proportional to its actual magnitude. It may be legitimate 

 to regard a large deviation as both absolutely and relatively more 

 important than a small one. (3) The average deviation is poorly 

 suited for use in more complicated statistical work. 



The larger deviations can be given a proportionately greater weight 

 by squaring all the deviations, summing these squares, and dividing 

 by the number of deviations to obtain the mean-square deviation. The 

 square root of this mean-square deviation is the measure of variation, 

 scatter, or dispersal most used by the statistician. It is called the 

 standard deviation, S. D. or a. There are great practical advantages 

 in the use of the standard deviation, in that it is particularly suited 



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