It is well known that Yates' algorithm can be used to estimate the effects in a factorial design. We develop a modification of this algorithm and call it modified Yates' algorithm and its inverse. We show that the intermediate steps in our algorithm have a direct interpretation as estimated level-specific mean values and effects. Also we show how Yates' or our modified algorithm can be used to construct the blocks in a 2 k factorial design and to generate the layout sheet of a 2 k−p fractional factorial design and the confounding pattern in such a design. In a final example we put together all these methods by generating and analysing a 26-2 design with 2 block
