notes509fall11sec71

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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:
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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:
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 7

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online