LOGNORMAL EXTRAPOLATION AND INCOME ESTIMATION FOR POOR BLACK FAMILIES*

ABSTRACT. In studies of urban and state income distribution, the estimation of percentile incomes within intervals reported by the Bureau of the Census has often been done under the assumption that incomes are uniformly distributed. This paper shows that income may be significantly underestimated if the assumption is applied to lower-level percentiles in the black family income distribution. Consequently, conclusions about the level and determinants of the relative income of poor black families may be misleading.     

Least of the laity: the minimum requirements for a medieval Christian

This article investigates the minimum level of religious observance expected of lay Christians by church authorities, and the degree to which legislation and procedures attempted to enforce these standards.¹ Once baptized, a person entered the community of the faithful; and the medieval church was as much accountable for the health and salvation of the ignorant, the ambivalent, the disobedient or distracted as they were of the devout. From the twelfth century, theologians, clerical authorities and the laity turned with concerted enthusiasm to the question of lay observance, advancing high ideals for lay commitment and expanding opportunities for lay participation. Yet while acting to elucidate and advance these qualities, the church was nevertheless mindful of the number of Christians who might fail to reach even basic standards. The resulting balance of the ideal and the possible, and the degree to which it reached and was enforced upon the less-enthusiastic laity is explored here through expectations for knowledge, observance of sacraments, and participation in regular duties such as church attendance, tithe-paying and fasting. The result was a complex ideal of lay observance that was balanced by a tolerance of laxity and even failure, and a system which increasingly exhorted specific expectations but was hesitant to define contumacy or disobedience in many but the most obdurate or scandalous cases.