Topic 10 - Topic 10 ANCOVA & RCBD Analysis of Covariance...

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1 Analysis of Covariance (Ch. 13) Randomized Complete Block Designs (Ch. 18)
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2 Review Recall the idea of confounding . Suppose I want to draw inference about a certain predictor. If meaningfully different interpretations would be made depending on whether a nuisance variable is included in the model, we say that the predictor of interest is confounded with the nuisance variable. (Both will be significant – if not it is collinearity instead.) In order to draw correct conclusions, the nuisance variable must be included in the model.
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3 Definitions We considered confounding for continuous predictors of interest, but it can certainly occur for categorical factors as well. We have different names for confounding depending on the situation: A (necessary) nuisance variable that is continuous is generally called a covariate . If it is another categorical factor, we usually refer to it as a blocking variable .
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4 Interaction In either case, we make an assumption that the nuisance variable does not interact with the predictor of interest. If there were interaction, then we have a more complicated interaction model and BOTH variables must become variables of equal interest. This becomes either Two-Way ANOVA or Multiple Regression. For now, assume no interaction.
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5 The Big Picture The nuisance variable does one of two things: Its inclusion MAY change our perspective in the sense that the pattern of differences (pairwise comparisons) for the factor of interest will change. Alternatively, its inclusion may simply be necessary to reduce the MSE so that we can actually see differences.
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6 Key to Understanding View ANCOVA and Blocking as one and the same. In both situations, we are removing variation due to a nuisance variable. We are also “adjusting” the response variable for the nuisance variable – and then will compare the ADJUSTED treatment means (which may differ from the actual treatment means). Comparisons of the unadjusted means could be inaccurate.
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7 Examples We now consider a couple of examples. In both examples, we will consider the effect of three standard treatments for a certain cancer. All patients are started on their respective treatment at the same time. The response variable is the lifetime of the patient in months after beginning treatment.
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8 Example Dataset I
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9 Example Dataset II
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10 Pairwise Comparisons Data Set I Data Set II GRP Mean N trt A 39.333 3 1 B 24.667 3 2 C 12.000 3 3 GRP Mean N trt A 12.000 3 1 A 11.667 3 3 A 11.000 3 2
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11 Conclusions? Example I Example II
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12 The missing piece? Each person is not at the same stage of disease. Some of them may have developed the
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This note was uploaded on 02/20/2012 for the course STAT 502 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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Topic 10 - Topic 10 ANCOVA & RCBD Analysis of Covariance...

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