# [R] type I and type III sums of squares

Thomas W Blackwell tblackw at umich.edu
Mon Aug 18 21:01:38 CEST 2003

```Paul  -

that will supply all the context needed to fully answer your
question.  A good, basic reference is:

George W. Snedecor and William G. Cochran (1980)
Statistical Methods, 7th edition.  Iowa State Univ. Press.
ISBN: 0-8138-1560-6; LC:  QA 276.12 .S591 1980

(I have the Taubman copy already checked out - others in the
Science Library.)  A more advanced reference is:

George A. Milliken and Dallas E. Johnson (1984)
Analysis of messy data (2 vols.)  Van Nostrand Reinhold, NY
ISBN: 0-534-02713-x;  LC:  QA 279 .M481 1984

(Science library only, more recent edition in Public Health library.)

The terms "type I" and "type III" are specific to SAS software.
Their precise definitions are given in the SAS documentation.
I don't have a copy handy.  George Milliken was a contributor
to the SAS software, so his definitions will coincide with SAS's.

HTH  -  tom blackwell  -  program in bioinformatics and department
of human genetics  -  u michigan medical school  -  ann arbor  -

On Mon, 18 Aug 2003, Paul Litvak wrote:

> I have been digging around in the FAQ's and online looking for an answer
> to my questions, and perhaps someone here can help me.
>
> For a statistical experiment, I need to run 3,000,000 ANOVAs, which is
> taking me a very long time. As a result, I have recoded my analyses in
> C. However, I cannot find the formula to calculate either the type I or
> type III sums of squares (in the case of my model, the two are
> equivalent). I know that the formula must be in the R source code, as
> they are able to calculate it, but I am not sure where. Does anyone know
> where I can find the explicit procedure for calculating this? A
> mathematical formula or the source code would be equally helpful. I am
> aware of the formula in matrix algebra, but is there a formulation that
> does not use matrix algebra?
>
> thanks very much in advance,
> Paul Litvak
> Department of Human Genetics
> University of Michigan

```