A note on lower bounds for the number of common factors

It is shown that the lower bounds for the number of common factors, established by Guttman [1954] and modified by Kaiser [1961], cannot decrease as the number of observed variates is increased. The result implies that the lower bounds cannot become weaker if the number of observed variates is increased and the number of factors remains constant.This paper is based on a section of a thesis submitted to the Department of Statistics of the University of the Witwatersrand in fulfillment of the requirements for a M.Sc. degree.Presently at the National Institute for Personnel Research, Johannesburg, South Africa.