Dummy Variables and the Relationship of Deaf and ... - NESUG

NESUG 2008Statistics & AnalysisMethod of AnalysisSometimes in statistics, variables have two or more distinct levels, such as machines or operators. Often times thesevariables are referred to as categorical variables. In order to properly analyze the data using these types of variables, onemust take into account the fact that variables with multiple levels may have separate deterministic effects on the responsevariable. In situations like this, the implementation of dummy variables is highly useful.There are many ways to set up dummy variables so long as they are linearly independent of other variables in the model. Theparticular set up used in this research codes deaf = 1 and hearing = 0. It should be said that a variable with a levels willemploy the use of a-1 dummy variables. Since the study only concerns deaf and hearing siblings, only one dummy variableis necessary.As stated before, only one dummy variable was needed. The general model that will be constructed takes on the form:Y (o 1 0 1X= β + β X ) + Z ( α + α ) + εIn the model Z represents the dummy variable, and it can be seen that if Z=0 the hearing model becomes:and when Z=1 the deaf model becomes:Y = β + X 10βY = β + α ) + ( β + )X(0 0 1α1Now with two regression models, differences between the deaf and hearing samples can be tested. It is easy enough to showthe two samples are in fact different yet something else may be shown. A difference only concludes that there are tworegression lines present, but does not show how the lines differ from one another. Four situations arise:Situation 1: Two distinct regression models with different slopes, and different intercepts (4 parameters).Situation 2: Two distinct regression models with equal slopes, and different intercepts (3 parameters).Situation 3: Two distinct regression models with different slopes, and equal intercepts (3 parameters).Situation 4: One distinct regression line with equal slopes and equal intercepts (2 parameters).Identifying one of these situations gives even more information than a simple difference between the two samples. Thesesituations tell us whether or not deaf and hearing siblings begin at the same levels, or different levels, and whether or not theyprogress at the same, or a different rate. As an aid to the analysis performed on the data, scatter plots have been provided.AnalysisIn order to test each situation, the appropriate F-tests must be constructed using extra sums of squares (ESS). The ESS aresimply calculated as:ESSTest Parameter= SSRe gression− SSParametersnot testedThat is, the extra sums of squares that are produced by the addition of the respective test parameters. Once the ESS areobtained, the formal F-test may be performed as in any ANOVA or regression analysis.Fortunately, SAS produces tests based on these ESS, which it calls Type III Sums of Squares. The trick in obtaining theType III SS for a regression model involves using The GLM Procedure. The following code was used to obtain the necessarytests for deciding which situation is present:2