Date of Award


Degree Type

Master's Essay - Restricted

Degree Name

Master of Science (MS)


Mathematical and Statistical Sciences


Factorial designs of experiments are generally the most efficient designs to use when the changing of' two or more factors is to be studied. However, if there are many factors and/or the number of experiments that can be performed at once is less than that needed for a complete design, the design must be altered. There are two ways in which this can be accomplished. One method. is called confounding, i.e. the experiment is divided into blocks of a size which can be performed at once and the effects of unimportant comparisons (usually the higher order interactions) are confused with the block effects. The other method, fractional replication, is similar to confounding but has a different purpose. In this case, the experimenter may want to use only part of the design to direct him towards further .experimentation - it may be too expensive, too time-consuming or too impractical to carry out the complete design. The portion of the experiment performed is a block of a confounded design. The advantage of the fractional replication is that one can complete the design or another block of it to gain more information. However, to use fractional replication one must have reason to believe that certain factors do not interact, because these interactions are added to or subtracted from the main effects.