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 that particular factor three levels, or four levels, etc. 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 of each, etc.
Use: Refer to the description in this glossary under the heading Analysis of Variance (ANOVA).
