A step-down test for effects in unreplicated factorial designs

In textbooks it is often suggested that estimates of effects obtained in two-level factorial experiments should be illustrated by a half-normal plot. The effects corresponding to the estimates with biggest absolute values and deviating from a straight line on the plot should be selected as important. We make a formal statistical procedure in this spirit by using a suitable mathematical construction, which can be illustrated in the graph. Thus we may find effects which are significant with a chosen multiple level of significance. This means that there is a given small risk of declaring significant any factor effects, which are in fact void, independent of how many and which effects are possibly missing. There is some mathematics behind the method, but its use is very practical and simple.