A one-way ANOVA simply means that you are testing one factor. Now, you might test that particular factor at two levels. You might test a particular factor three levels, and so on. To contrast, a two-way ANOVA means that you are testing two factors. You might be testing those two factors each at two levels. You might be testing those two factors at three levels, or four levels, and so on.
Use: Refer to the description in this glossary under the heading Analysis of Variance (ANOVA). In the case of a two-way ANOVA, you would be testing two factors instead of just one factor. So referring to the example listed above, in addition to testing for the flavor of the medicine, you might be also testing for different colors. The two factors would be: flavor and color.
