ANCOVA Examples Using SPSS

ANCOVA Examples Using SPSS

Statistical Package for the Social Sciences (SPSS) is a program for analyzing data collected by researchers in the social sciences. An ANCOVA (Analysis of Covariance) is used to analyze data in which there is one or more independent variables and a dependent variable when the researcher wants to remove the influence of one or more predictor variables on the dependent variable.

Data requirements. In all GLM models, the dependent(s) is/are continuous. The independents may be categorical factors (including both numeric and string types) or quantitative covariates. Data are assumed to come from a random sample for purposes of significance testing. The variance(s) of the dependent variable(s) is/are assumed to be the same for each cell formed by categories of the factor(s) (this is the homogeneity of variances assumption).

Regression in GLM is simply a matter of entering the independent variables as covariates and, if there are sets of dummy variables (ex., Region, which would be translated into dummy variables in OLS regression, for ex., South = 1 or 0), the set variable (ex., Region) is entered as a fixed factor with no need for the researcher to create dummy variables manually. The b coefficients will be identical whether the regression model is run under ordinary regression (in SPSS, under Analyze, Regression, Linear) or under GLM (in SPSS, under Analyze, General Linear Model, Univariate). Where b coefficients are default output for regression in SPSS, in GLM the researcher must ask for "Parameter estimates" under the Options button. The R-square from the Regression procedure will equal the partial Eta squared from the GLM regression model.

The advantages of doing regression via the GLM procedure are that dummy variables are coded automatically, it is easy to add interaction terms, and it computes eta-squared (identical to R-squared when relationships are linear, but greater if nonlinear relationships are present). However, the SPSS regression procedure would still be preferred if the reseacher wishes output of standardized regression (beta) coefficients, wishes to do multicollinearity diagnostics, or wishes to do stepwise regression or to enter independent variables hierarchically, in blocks. PROC GLM in SAS has a greater range of options and outputs (SAS also has PROC ANOVA, but it handles only balanced designs/equal group sizes).

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