Abstract
The Matrix Method was developed as a method of estimating population by age and number of people in each household, for a planned housing district. However, in use its accuracy has been very low by reason of an error in the theory. The purpose of this paper is to point out the error as well as to indicate the high degree of accuracy that becomes possible through correction of the error. The Matrix Method is based on the theory of the Markov chain. It is applicable to urban areas where transition probability from one type of household at time t to another type at time t+dt can be assumed so be constant, and where numbers and types of both outgoing households and incoming households which replace them can also be assumed to be constant during time t to time t+dt The error of the theory lies in its failure to consider the change that takes place in incoming households during the time dt. The verification of the rectification of this theory was made by comparing two estimated distributions of household groups, one calculated by the unrectified theory, the other by the rectified theory, with the actual numbers of household types and their distribution. According to the statistical test, the calculated level of significance of the corrected estimate was more than 90% whereas that of the uncorrected estimate was less than 0.01%.
