Prism uses a unique set of terms.

•When there are two data sets, Prism offers the nested t test. We chose that name because it best describes the use of this test. You want to compare two treatment groups. There is another nested variable that needs to be accounted for, but that is not the primary goal. The term is not widely used and is sometimes used in a very different sense to mean a two-sample or indepependent sample t test.

•When there are three or more data sets, Prism offers nested one-way ANOVA. We use that name because it best describes the use of this test. You want to compare three or more treatment groups. There is another nested variable that needs to be accounted for, but that is not the primary goal.

Other books and programs generally use the term nested two-way ANOVA in both cases, because one factor (rat in this example) is nested within another factor (treatment). The analysis accounts for two factors (one nested) so the analysis is named nested two-way  ANOVA.

Another term for nested ANOVA is hierarchical ANOVA.