In addition, the "one-way" part of one-way ANCOVA refers to the number of independent variables. However, when the covariates are categorical, the analysis is not often called ANCOVA. Note: You can have more than one covariate and although covariates are traditionally measured on a continuous scale, they can also be categorical. This third variable that could be confounding your results is called the covariate and you include it in your one-way ANCOVA analysis. As such, compared to the one-way ANOVA, the one-way ANCOVA has the additional benefit of allowing you to "statistically control" for a third variable (sometimes known as a "confounding variable"), which you believe will affect your results.
However, whereas the ANOVA looks for differences in the group means, the ANCOVA looks for differences in adjusted means (i.e., adjusted for the covariate). Like the one-way ANOVA, the one-way ANCOVA is used to determine whether there are any significant differences between two or more independent (unrelated) groups on a dependent variable. The one-way ANCOVA ( analysis of covariance) can be thought of as an extension of the one-way ANOVA to incorporate a covariate. One-way ANCOVA in SPSS Statistics Introduction
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