STEVENS MA 331 - Lecture 15 Analysis of Covariance ANCOVA

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Lecture 15What is ANCOVA?Slide 3ANCOVA – the model.Slide 5Analysis of CovarianceANCOVAThis refers to the situation when the explanatory variables are both categorical and quantitative.The response variable however is always quantitative.We have data on 78 seventh grade high school students in a rural Midwestern school. The researcher was interested in the relationship between “self-concept” (as measured by a test designed by himself) and the performance of the student. The data for each student include:• GPA (not specified the period) (y, response variable)•OBS – an observation number (if an observation number misses it means that the corresponding student dropped the study)•IQ – score at a standard IQ test (IQ, explanatory variable)•Gender – self explanatory•Concept – score at the self designed test (CONCEPT, explanatory variable)•We analyzed this data with multiple regression. We did not look at the gender variable. We will correct this oversight.Recall:The model fitted for the example shown is:Where: - an overall constant - the effect due to categorical var (gender) - the regression coefficients - the explanatory variables - the response variable - the errors assumed to be normal and constant variance1 21 2ij i ij ij ijY X Xm t b b e= + + + +1 21 2,,iij ijijijX XYmtb beThe model is quite complex to describe in the case of two or more categorical variables but the software gives you answers regardless.The important issue is to be able to understand the answers and to make sure that the hypotheses under which these numbers were obtained are


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STEVENS MA 331 - Lecture 15 Analysis of Covariance ANCOVA

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