Test and prediction in factorial models with independent variance estimates

The multiple inference character of several tests in the same application is usually taken into consideration by requiring that the tests have a multiple level of significance. Also, a prediction problem in an application with several possible predictor variables requires that the multiple inference character of the problem be considered. This is not being done in the methods commonly used to choose predictor variables. Here, we discuss both the test and prediction methods in two-level factorial designs and suggest a principle for choosing variables which is based on multiple inference thinking. By an example use demonstrated that the principle proposed leads to the use of fewer prediction variables than does the Akaike method.