208 



STATISTICAL TREATMENTS 



served in an experiment is likely to be influenced by several factors. A 

 truly efficient experiment tests the effect of several factors at the same 

 time. Simple statistical tests become extremely difficult in this case, how- 

 ever. Each factor might act independently or might interact with one or 

 more of the other factors. 



Analysis of variance is a system of treating such experimental data. 

 Since the actual analysis is intimately tied to the design of the experiment, 

 a discussion of analysis of variance is given in the following chapter on 

 experimental design. 



Regression and correlation 



One of the most important things we might wish to find from an 

 experiment is the relationship between a pair of variable quantities. In 

 any experiment, changes in x might produce proportional changes in 

 y. The relationship is a straight line, but which straight line best fits the 

 results? If the data are very good, the points on the graph deviate very 

 little from the line that best describes the relationship, and the line, 

 called the regression line, can be drawn by eye. If the results include a 

 larger error, visual inspection might suggest any of several lines to fit 

 the points, as is true with the data shown in Fig. 15-3. Obviously x has 

 an effect on y, and y = a -\- hx,^ but what is the true slope h and the in- 

 tercept a? 



Fig. 15-3. A scatter diagram showing three 

 alternative straight Hnes that might be drawn 

 through the points. 



^ Note that the symbols here are different from those given in Chapter 14. The 

 expression y = mx + 1? is the same straight line. Here a is substituted for h and 

 b for m. 



