Talk:Factor analysis and ANOVA

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• an easy graphical method for visualizing the connections between factors and outcomes is a graph like the incidence graphs we used in class. Here factors point to outcomes.
• In the factor analysis in process control section, note the parallel between the linear function presented and a gain array used earlier.
• for anova analysis, note too that the weight of each factor depends on the degree of difference between the treatments. Thus in the boiler fouling example, if we had chosen a smaller temp range (e.g. 409, 410, and 410 vs 400, 450, and 500) then we will see a smaller effect.
• for the first example, it seems like it woudl be more appropraite to fit all three of the varaibles at the same time vs independently. Plus it would be better to allow some sort of an intercept. The fouling rate calcualted at the end seems way off for the intermediate value observed. Should be more like 1 or 2.

An online reader pointed out that the range of the data fed into an ANOVA analysis determines the range of the predictions. Thus if you try to extrapolate outside of this range you will tend to get odd results. This inability to extrapolate is generally true for any non-mechanistic model, be it linear or nonlinear. This point should be emphasized in future versions of the lecture + the text PeterWoolf 11:34, 29 July 2009 (EDT)