A statistical test of the critical shape hypothesis for residential lots

Let us assume that there exists a certain activity that requires a fixed shape and size of space, and is so crucial for lots with detached houses that the value of such a lot is largely affected by whether or not it contains that space. If the hypothesis above (designated as the 'critical shape hypothesis') holds, then the frontage of a majority of rectangular lots with a fixed depth should be modules of a basic frontage unit. In the present paper we describe empirical tests of the critical shape hypothesis by using lot-shape data of rectangular lots in the Kitazawa area of Setagaya ward, Tokyo. It was found that, for any depth class, the distribution of frontage exhibits a weakly unimodal shape, but the concentration near the mode did not turn out to be significant in most depth classes. The modes that have significant concentrations around them do not show any systematic variation in relation to their depth classes. The critical shape hypothesis is therefore not supported by these empirical results. The property of unimodal marginal value of frontage can thus possibly be accepted in deducing a lot evaluation function.