One-way ANOVA, also called one-factor ANOVA, determines how a response is affected by one factor. For example, you might measure a response to three different drugs. In this example, drug treatment is the factor. Since there are three drugs, the factor is said to have three levels.
If you measure response to three different drugs, and two time points, then you have two factors: drug and time. One-way ANOVA would not be helpful. Use two-way ANOVA instead.
If you measure response to three different drugs at two time points with subjects from two age ranges, then you have three factors: drug, time and age. Prism does not perform three-way ANOVA, but other programs do.
If there are only two levels of one factor --say male vs. female, or control vs. treated --, then you should use a t test. One-way ANOVA is used when there are three or more groups (although the underlying math is the same for a t test and one-way ANOVA with two groups).
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