notes509fall11sec71 - STAT 509 Sections 7.1-7.2 Design of...

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STAT 509 – Sections 7.1-7.2: Design of Experiments • An engineer conducted an experiment to develop a prediction equation for the distance a catapult can throw a metal ball. • He manipulated two factors: (A) The angle of the catapult arm (measured in degrees) and (B) the height of the pin that supports the rubber band, measured at equally spaced locations. • For each factor, two levels were examined, a low level and a high level. Angle Levels: Height Levels: In the data set, we will always code the low level of a factor as –1 and code the high level as 1. Two distance measurements were taken at each treatment (factor level combination): Angle Height Distance 1 Distance 2 –1 –1 27 27 1 –1 81 67 –1 1 67 62 1 1 137 158 A 2 k factorial design measures a response at each treatment, using k factors each having 2 levels. The above experiment is a factorial design. Picture:
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Notation for Mean Responses in a 2 2 Factorial Design a = Average of responses when A (Angle) is high and B (Height) is low. b = Average of responses when B (Height) is high and A (Angle) is low. ab = average of responses when both A (Angle) and B (Height) are high. (1) = Average of responses when both A (Angle) and B (Height) are low. Catapult Experiment: The main effect of a factor in a 2 k factorial experiment is: (mean response at the high level of the factor) – (mean response at the low level of the factor) Estimated main effect of Angle: Estimated main effect of Height:
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