We have another nuisance factor that has an effect on the response variable, but the effect is not of interest.

We have another nuisance factor that has an effect on the response variable, but the effect is not of interest. It is important that we have some experimental control with regard to the nuisance factor. If levels of nuisance variable cannot be measured / controlled, then the best we can do is to use one-way ANOVA and make sure to randomize the treatments to the experiment units. Why is such a randomization important?