Classical vs. regression factor effects

If Xj is temperature and two experiments are carried out, one at a coded level of -1 and one at a coded level of -t-1, and we get a classical factor effect of -i-3.6% yield, it tells us that working at the -i-l coded temperature gives more yield than working at the -1 coded temperature. But this classical factor effect by itself doesn t tell us very much about how sensitive the reaction is to temperature because 5x, isn t included in the factor effect. 

in modem research using interval and ratio scales the 5x usually shouldn t be ignored. Let s add 8x, to the calculation to obtain b, as would be done with regression analysis. Because Xj went from a coded level of -1 to a coded level of -t-1, 5x, = 2. Thus, b (the factor effect in the coded factor space) = 8y,/8xJ = -i-3.6% per 2 coded units = -i-1.8% per coded unit. The fact that 8x is equal to 2 with this system of coding is why regression analysis of coded data gives results that are smaller by Vi from the results obtained from the classical approach  

This b still isn t very helpful because we don t know the factor effect in terms of 

This final, uncoded, by/bx information is more meaningful and useful to the researcher or engineer who deals with factors expressed on interval and ratio scales. 

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