Sums of Squares - Type I, II, III, and IV Sums of Squares
In general, we can test the significance of partial correlations, in effect controlling for other effects, or we can enter the variables in a stepwise fashion, controlling for all other factors that were previously entered and ignoring those that have not yet been entered. In essence, this is the difference between Type III and Type I Sums of Squares (the terminology was introduced in SAS, e.g., see SAS 1982; detailed discussions can also be found in Searle, p. 461; Woodward, Bonett, & Brecht, 1990, p. 216; or Milliken & Johnson, p. 138). Another "intermediate" strategy would be to control for all other main effects when testing a particular main effect, for all main effects and two-way interactions when testing a particular two-way interaction, for all main effects, two-way interactions, and three-way interactions when testing a particular three-way interaction, and so on. Sums of squares for effects computed in this manner are called Type II sums of squares. Thus, Type II sums of squares control for all effects of the same or lower order, while ignoring all effects of higher order.
Finally, for some special designs with missing cells (incomplete designs), you can also compute so-called Type IV sums of squares; this method is discussed in the context of incomplete (missing cell) designs. For a detailed (and more technical) discussion of the different procedures for testing hypotheses in unbalanced and incomplete factorial designs, see also the General Linear Model (GLM) Introductory Overview, and in particular Six Types of Sums of Squares.