C532 Nov 9 2011

C532 Nov 9 2011 - C532: ANOVA & Regression Modeling Nov...

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C532: ANOVA & Regression Modeling Nov 9, 2011 Y. Cao 1 Topics: learn about ANCOVA model .and realize it with the general linear model procedure in SPSS. Datasets : C530_clbp.sav References: lecture note and PCCR books on statistics. In general, we can say that ANCOVA, an abbreviation of analysis of covariance, is a combination of 2 types of ANOVA. In common situation, we say that the ANOVA model is where X1 represents a nominal categorical variable, for example, treatment group; in the other case, X1 can be a continuous type of variable like Age, or RMQ. Both are simple linear regressions. In the first case, so called one way ANOVA model, we have one nominal categorical variable (a fixed factor) to explain the outcome. A fixed factor, we say so because the levels of the factor, like treatment groups 1, 2, 3 and 4 (or A, B, C, D or whatever name you like), once assigned (usually randomly) to a patient, they are fixed/constant . Now, we want to include one more variable to predict the outcome, this comes out a continuous variable, called covariate , to explain more variations in the outcome. Covariate means the continuous variable vary together with the fixed factor to affect the outcome. After considering this supplementary covariate, we then want to adjust the group means (in SPSS, it is called Estimated Marginal Means ), meaning usually we would like to change it a little bit on the original group means. Then, ANCOVA is born. It is a multiple linear regression. Correspondingly, the ANOVA table for ANCOVA is a combination of the 2 ANOVA tables. See the lecture notes, the 3 tables on page 1. ANCOVA is to test/ compare mean differences between factor levels (in our case, treatment groups) and adjusted for the effect of the covariate(s). ANCOVA will generally increase our power to detect true meaningful group mean differences because the inclusion of the covariate will usually explain more variability in the outcome variable (the Y).
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C532: ANOVA & Regression Modeling Nov 15, 2010 Y. Cao 2 However, adding covariate(s) will reduce the degrees of freedom, so, if the added covariates only accounts for little variability in the outcome variable, then it might actually decrease the statistical power. In a simple ANCOVA modeling, in order to predict the outcome variable Y, we use 2 explanatory variables: one is a nominal categorical variable X 1 as the fixed factor (because the levels of it are fixed) and one continuous variable X 2 ( covariate ). Therefore, the model equation looks like:
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C532 Nov 9 2011 - C532: ANOVA & Regression Modeling Nov...

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