The availability of high speed computers has not only allowed persons in educational research to perform larger statistical analyses but also to think differently about their problems. The purpose of this thesis is to reexamine the methods of statistical calculus in the light of high speed computers and to present several special matrix operators which are especially useful. These operators are designed for simplicity and efficiency on high speed computers. Using these operators, we explore many different statistical techniques which are commonly used in educational research and show simple computational formulae. We observe that these statistics are computed more simply from the general linear model than from the usual computing procedures. We conclude that persons in educational research and in other areas need to place much more emphasis on mathematical models and much less emphasis on the special techniques which were developed for desk calculators.