THE TEN PILLARS 



19 



It is axiomatic that any expression of confidence made in terms of normal 

 distribution, presupposes normal distribution; and that any such expression 

 concerning a distribution which is not normal is not only unwarranted, but 

 also useless, and may be quite misleading. There are statistical methods for 

 handling non-normal data, but they are not simple and are seldom used 

 correctly. Mainland's book 3 goes into some of these, using examples of 

 medical interest. 



-^x 



+ ^y. 



DEVIATION FROM MEAN VALUE 



Figure 1-7. Normal Distribution of Observations. Solid Curve: Area under curve be- 

 tween -a and +a includes 68 per cent of observations; between —2a and +2o, 94 per 

 cent; and between -3a and +3o, greater than 99 per cent. Blocks: Typical Observa- 

 tions of Heights of Thirty People at a Lecture. 



8. Expressions of Deviations 



The most common method of expressing a number of observations, x, of 

 the same phenomenon is by the common average, or arithmetic mean, x. There 

 are others, such as the median and the mode, which have some use in nearly 

 normal distributions, but only the mean will be considered. Deviations Ax 

 from the mean can easily be computed by subtraction, and then averaged, 

 the result being expressed as the mean deviation Ax from the mean x. 



A very common method of expressing the distribution is by the standard 

 deviation, a, defined as the square root of the average of the deviations 

 squared: 



a = y/Ax 2 , or a = y^Ax 2 /n 



