I am new to statistics and I have been doing some reading on ANCOVA lately. There is something that is slightly confusing me:
When motivating the use of the ANCOVA model, many of the resources that I have found on the web describe some experiment, where a one-way ANOVA yields that the categorical independent variable indeed influences the continuous dependent variable. One example is the introductory part of this.
What I have read so far makes it seems like one needs to perform an ANCOVA to control for the effects of the covariates only if statistically significant differences between the population means were found in a one-way ANOVA beforehand. Is this correct or did I get something wrong?