Analysis of covariance
DescriptionAnalysis of covariance (ANCOVA) allows to compare one variable in 2 or more groups taking into account (or to correct for) variability of other variables, called covariates. Analysis of covariance combines oneway or twoway analysis of variance with linear regression (General Linear Model, GLM). How to enter dataIn this example (data from Wildt & Ahtola, 1978) data are entered for 2 factor variables named "FactorA" and "FactorB". The variable "VarY" is the dependent variable and there is one covariate "VarX". Required inputIn the dialog box for ANCOVA you select:
ResultsLevene's test for equality of variancesPrior to the ANCOVA test, Levene's test for equality of variances is performed. If the Levene test is positive (P<0.05) then the variances in the groups are different (the groups are not homogeneous), and therefore the assumptions for ANCOVA are not met. Homogeneity of regression slopesThe interpretation of ANCOVA and the associated adjusted means relies on the assumption of homogeneous regression slopes for the various groups (Huitema, 1980). If this assumption is not met (P<0.05) the ANCOVA results are unreliable. Tests of BetweenSubjects EffectsIf the calculated Pvalues for the two main factors A and B, or for the 2factor interaction is less than the conventional 0.05 (5%), then the corresponding null hypothesis is rejected, and you accept the alternative hypothesis that there are indeed differences among groups. When the 2factor interaction (FactorA*FactorB) is significant the effect of factor A is dependent on the level of factor B, and it is not recommended to interpret the means and differences between means (see below) of the main factors. Estimated marginal meansIn the following tables, the marginal means (sometimes referred to as "corrected means") with standard error and 95% Confidence Interval are given for all levels of the two factors. Also, differences between groups, with Standard Error, and Bonferroni corrected Pvalue and 95% Confidence Interval of the differences are reported. General Linear ModelSince this ANCOVA procedure is an implementation of the General Linear Model (GLM), the procedure:
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