This introduction to Wildt and Ahtola's (1978) Analysis of Covariance provides a good overview of the theory behind this option.
"A one-way layout describes any context involving a single qualitative independent variable, with any number of levels, and one or more covariates (quantitative independent variables). The one-way layout is common to both experimental and observational studies. In randomized experiments, the one-way layout is analogous to the completely randomized design, where test units are randomly assigned to treatment levels of a single qualitative independent variable." (Wildt & Ahtola, 1978)
Wildt, A. R., and Ahtola, O., (1978). Introduction. Analysis of Covariance. Thousand Oaks: SAGE Publications, Inc.