Statistical and Historical Analyses of Nations Which Deviate From the Size-Density Law

We examine nations which deviate significantly from the ?2/3 sizedensity slope previously observed for the aggregated political subdivisions of 98 modern nations and previously derived from the theory of timeminimization. We correct Stephan’s original list of deviant nations, demonstrate that all slopes more negative than ?2/3 were due to the erroneous inclusion of cities in the original data sets, develop a theory to account for the less negative deviant slopes, and test the theory both through statistical manipulation of current data and through analysis of available historical data.     

The end of rapid increase in the use of oral anovulants? Some problems in the interpretation of time series of oral use among married women

Several problems in the interpretation of time series of oral anovulant usage are discussed, among them the shifting marriage-duration distribution over time. Standardization fails to negate the conclusion that the rate of increase in the proportion of women using orals has slackened since January 1966. Separate analyses by duration-specific rates of use and by marriage cohorts show that the two factors sustaining the initial spectacular growth rate in the use of orals-the ever—higher initial use rates of new marriage cohorts and the rapid adoption of orals among earlier cohorts at later durations—have lost their sustaining force. Further analysis indicates that concern over the pill as a health hazard is a major deterrent to substantial increase in oral usage. A final distribution of women by risk status with respect to oral use, and current and prospective oral use, shows that under present circumstances the maximum oral use rate will be considerably less than unity.     

The evolution of an abortion counseling service in an adoption agency

As a natural outgrowth of its original function as an adoption agency, the Spence-Chapin Adoption Service moved into abortion counseling. The main concern at the Service was to help the woman make a decision which she considered the right one for herself and the child. The decision to have an abortion is a complicated choice, necessitating counseling for the mother, reputed father, and families involved. Counselors help the woman understand what is involved with an abortion, alternatives to abortion, and how to use contraception so she will not need a future abortion.     

ON THE OPTIMAL ASYMPTOTIC TESTS FOR THE EFFECTS OF CLOUD SEEDING ON RAINFALL (1) THE CASE OF FIXED EFFECTS

In this paper we consider a sequence of experimental units {u_n} which are t o be treated according to some random scheme. A general randomized design is suggested for the purpose. Asymptotic tests, optimal in some sense, are derived for testing the absence of the effects of the treatment. These tests are applicable in various situations, for example, when the treatment effects are additive or when they are multiplicative. Based on the asymptotic power of the tests obtained, optimality of various designs is discussed. The randomized designs discussed here have a wide range of applicability, e.g. in weather modification experiments and bio-assay.     

A Theorem on Products of Random Variables, With Application to Regression

It is shown that the product of two independent random variables in the domain of attraction of the normal distribution is also in the domain of attraction of the normal distribution, while if the product is in the domain of attraction of the normal distribution and one of the variables has finite variance, the other is in the domain of attraction of the normal distribution. This result is applied to prove the asymptotic normality of the regression coefficient in a linear regression when the error variance is not necessarily finite.     

Forecasting births in post-transition population: stochastic renewal with serially correlated fertility

Time series analysis of fertility can improve demographic forecasts. The optimal forecast and its variance for births to an age-structured population subject to serially correlated random fertility are developed. The general case in which the fertility process had arbitrary autoregressive structure is dealt with and then the 4 special cases of white noise, 1st-order autoregressive, 2nd-order autoregressive, and random walk are considered. Consequently, it is determined that the predictions and their variances are highly sensitive to the autoregressive structure of fertility and, therefore, if stochastic models are to be used for prediction, they must emphasize this aspect of the problem. Preliminary empirical efforts to model the time series of U.S. fertility from 1917 to 1972 proved unsuccessful, but it is obvious that at least a 2nd-order autoregressive scheme is require d. The analysis proveded should be helpful in: 1) any application of the procedures requires a successful parameterization of the fertility process; 2) fertility variations could be decomposed into the effects of nuptiality and marital fertility and then births and marriages could be jointly predicted; and 3) the simplifying approximations should be dropped and each age-specific rate could be analyzed and predicted.