Confounding and Resolutions
Confounding occurs when two factors are associated with each other or “travel together” and the effect of one is confused with the effect of the other. Resolution describes the degree to which estimated main effects are confounded with estimated 2level interactions, 3level interactions, and so on.
Confounding
Confounding occurs when two factors are associated with each other or “travel together” and the effect of one is confused with the effect of the other. For example, in order to improve team performance, a soccer coach asks his team to run two miles a day while the players decide to take vitamins. In this case the effects of running two miles a day and taking vitamins will be confounded since it will not be possible to identify the effect of them on team performance independently.
Confounding occurs whenever a Fractional Factorial design is chosen instead of a Full Factorial design. The consequence of confounding in DOEs is that the values calculated for main effects will have error coming from inclusion of higher order interactions in the calculation and interaction effects will be unknown. However Fractional Factorials also cost a fraction of the Full Factorial designs and therefore in the tradeoff between cost and accuracy, they are preferred.
DV 1  DV 2  DV 3  output response of 3 input variables 200 + 3 * dv1  12 * dv2 + 8 * dv3 + 2 * dv1 * dv2  dv1 * dv3 


1  0  0  0  200 
2  0  0  10  280 
3  0  10  0  80 
4  0  10  10  160 
5  10  0  0  230 
6  10  0  10  210 
7  10  10  0  310 
8  10  10  10  290 
DV 1  DV 2  DV 3  output response of 3 input variables 200 + 3 * dv1  12 * dv2 + 8 * dv3 + 2 * dv1 * dv2  dv1 * dv3 


1  0  0  10  280 
2  10  0  0  80 
3  0  10  0  230 
4  10  10  10  290 
Resolution
Resolution describes the degree to which estimated main effects are confounded with estimated 2level interactions, 3level interactions, and so on. The design resolution tells us how badly the design is confounded. Resolution III designs confound main effects with twofactor interactions. Resolution IV designs confound main effects with threefactor interactions (A+BCD), as well as twofactor interactions with other twofactor interactions (AB+CD). Resolution V designs confound main effects with fourfactor interactions, or twofactor interactions with threefactor interactions.
Higher resolution designs have less severe confounding, but require more runs. A resolution IV design is "better" than a resolution III design because we have lesssevere confounding pattern in the `IV' than in the `III' situation. However in most cases higherorder interactions are less significant than loworder interactions and therefore there is not much benefit to higher resolution designs that come at the cost of additional computational expense.