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Lecture 14

ADM2304 Lecture 14: 14

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Tony Quon

What is the effect of store location and advertising budget on mean sales? What is the effect of weather and trafc density on cost of road repair? Are there real differences in change time for brake replacement based on the manufacturer and vehicle type? In each example above, there is a strong chance of an interaction between the two factors making their effect on the outcome variable complex Important questions: Let A and B represent the two factors (i.e., manufacturer and vehicle type) and suppose that: The row factor A has a levels (number of manufacturers) The column factor B has b levels (number of vehicle types) There are ab treatment combinations Thus, if each treatment combination is represented r times in the sample then there are N = abr observations in the sample We are primarily interested in two questions: Do both factors affect the mean response or only one? If both do are the effects additive or do they interact? What To Do? We could do a oneway ANOVA on each of the two factors separately but why is that inadequate? Instead we introduce you to a TwoFactor ANOVA test: Just like a onefactor ANOVA, we create an F statistic where both the numerator and the denominator are estimates of the population standard deviation if the null hypothesis is true If it is not then the numerator is an overestimate of the SD and thus large F values give us reason to believe that the null hypothesis is false Again, though the method of calculating the F statistic is different, the rest of the analysis is the same Example: Brake Replacement Suppose we are dealing with three manufactures (A, B and C) and two vehicle types (car and SUV) Thus there are 6 treatment combinations If 5 of each treatment combination are measured, we have a sample size of N = 30 Possible Outcomes: Neither factor has an effect Only A has an effect Only B has an effect A and B have an additive effect (i.e., their inuences are independent) A and B have a nonadditive effect (i.e., their inuences are dependent)
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