In a two-way ANOVA with interaction (subjects times students, with replication), if SS_ Total = SS_ Rows + SS_ Cols + SS_ Interaction + SS_ Error , the degrees of freedom for the interaction term when there are r rows, c columns, and n replications per cell is:

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CSS Statistics QUESTION #1983

Question 1

In a two-way ANOVA with interaction (subjects \(\times\) students, with replication), if \(SS_{Total} = SS_{Rows} + SS_{Cols} + SS_{Interaction} + SS_{Error}\), the degrees of freedom for the interaction term when there are \(r\) rows, \(c\) columns, and \(n\) replications per cell is:

rc - 1
(r-1)(c-1)✔️
rc(n-1)
rcn - 1

Correct Answer Explanation

In a two-way ANOVA with \(r\) row levels, \(c\) column levels, and \(n\) replications per cell, the degrees of freedom for interaction is \((r-1)(c-1)\). The error df is \(rc(n-1)\) and total df is \(rcn - 1\).

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