C532 Nov 7 2011

# C532 Nov 7 2011 - C532: ANOVA & Regression Modeling Nov 7...

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C532: ANOVA & Regression Modeling Nov 7 2011 Y. Cao 1 Topics: 1) ANOVA model with more than 2 treatment groups; 2) Application of dummy variables and 3) Learn to use SPSS procedure Univariate to do the analysis. Datasets : np423aug2007.sav We have three ways to do ANOVA (analysis) in SPSS. 1) a simple linear regression (with one outcome variable only, this is the meaning of so called simple; 2) a procedure called Univariate ANOVA and 3) a direct ANOVA procedure. In our case with only one outcome, they are all equivalent. Q : When should we use a dummy variable (or more than one dummy variable)? A: It happens when we are using ANOVA model to represent a regression model and when the explanatory variable stands for treatment groups (nominal categorical variable). A dummy variable is a numerical variable, but not like continuous variable for instance Age or Body Weight, it plays a role like a switch that can turn on and off various parameters (coefficients for the regression model/equation). Sometimes we use more than one dummy variable because whenever the number of treatment groups are more than two then one dummy variable will not sufficient for us to distinguish the groups. The merit of using dummy variable or dummy variables is that we can represent many (multiple) groups in one regression equation and therefore there is no need to assign an equation to every group! Another advantage could be when we can find the group differences through different equations for each group that also can be obtained directly from the unique regression equation with the dummy variable/variables: assign proper dummy variable values to the groups and get a regression equation for each group and then it will give mean values from the individual equations. We will see this soon. Q : How many do we need, if we need dummy variables? A : We will need j-1 dummy variables for a categorical explanatory variable with j levels. In our case, j generally represents the number of treatment groups in a clinical trial or sampling. Now, let us see in more detail.

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C532: ANOVA & Regression Modeling Nov 3 2010 Y. Cao 2 In the case of two treatment groups, j=2 so we need j-1=2-1=1 dummy variable only. In mathematical language or the SPSS output table, a matrix can be used to represent the dummy variable/variables. This is for a 2-treatment group trial. If we have three treatment groups (j=3) then the matrix looks like we need j-1=3-1=2 dummy variables. In our next real example, there are j=4 groups, therefore, we need 3 dummy variables. We could assign X1=1 if treatment group =1 and otherwise X1=0; assign X2=1 if treatment group =2 and otherwise X2=0; and X3 =1 if treatment group =3 and otherwise X3=0. The last group will be represented by the
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## This note was uploaded on 01/03/2012 for the course C 532 taught by Professor Long during the Fall '11 term at Palmer Chiropractic.

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C532 Nov 7 2011 - C532: ANOVA & Regression Modeling Nov 7...

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