Rules for Finding Test Denominators
1. The denominator for testing a term U is the mean square for the leading eligible
random term below U in the Hasse diagram.
2. An eligible random term V below U is leading if there is no eligible random term that
is above V and below U.
3. If there are two or more leading eligible random terms, then we must use an
approximate test (Satterthwaite).
4. In the unrestricted model, all random terms below U are eligible.
5. In the restricted model, all random terms below U are eligible except those that
contain a fixed factor not contained in U.
Rules for Finding Expected Mean Squares
1. The representative element for a random term is its variance component.
2. The representative element for a fixed term is a function Qequal to the sum of the
squared effects for the term divided by the degrees of freedom.
3. The contribution of a term is the number of data values Ndivided by the number of
effects for that term (the superscript for the term in the Hasse diagram), times the
representative element for that term.
4. The expected mean square for a term U is the sum of the contributions for U and all
eligible random terms below U.
5. In the unrestricted model, all random terms below U are eligible.
6. In the restricted model, all random terms below U are eligible except those that
contain a fixed factor not contained in U.