The interpretation of Mallows's C-p-statistic

When selecting variables in multiple-regression studies, the model with the lowest value of Mallows's C-p-statistic is often chosen. It is shown here that when the estimate of sigma(2) comes from the full model an adjusted C-p, (C) over bar(p), has the property that E((C) over bar(p)) = p. It Is suggested that a procedure be adopted which involves testing whether) It is model with minimum (C) over bar(p) is really better than a simpler model. Tables approximating the null distribution of the test statistics are given.