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Fecundability – the monthly probability of conception – incorporates both physiological and behavioural elements that vary across a woman's reproductive life span. How much of the variation in fecundability during the reproductive period can be attributed to age-related changes in physiology, and how much to variation in coital frequency? We use a mathematical model of fecundability to consider this question. Intra-uterine mortality has an important effect on fecundability: effective fecundability (the likelihood of a conception that results in a live birth) is less than half of total fecundability (the likelihood of any conception) at nearly all ages when coital frequency is held constant. The change in effective fecundability with increasing coital frequency is non-linear: it declines with increasing frequency. At all coital frequencies, the effects of increasing physiological age are greatest at the youngest and oldest reproductive ages, while between the ages of 20 and 30 physiological change has only...

"This report contains recommendations reflecting the views of the ASA Technical Panel on the Census Undercount concerning [U.S.] Census Bureau procedures and plans in the fall of 1982." The report consists of technical statistical advice on measurement and estimation problems. A response by Barbara A. Bailar, reflecting the views of the U.S. Census Bureau, is also included (pp. 257-60).

Since the seminal work of Brass and Coale demographers have become highly skilled in the estimation of demographic parameters from indirect data. In many developing countries the classical sources of demographic data--registration of vital events or periodic censuses--are far from adequate. Brass Coale and their coworkers have developed a powerful set of techniques based on simple survey or census questions to replace the classical methods. This paper adds to the literature of numerical studies and regression analyses by providing and employing an analytic technique for studying the sensitivities of the estimates to the assumptions that underlie them. This new technique provides algebraic expressions which are both more general and easier to interpret than computer results. The authors illustrate the use of the analytical method in the simplest and most widely used technique--Brass childhood survivorship method. The notation and assumption of Brass childhood mortality method is set forth a general theory of errors for this estimator is developed and 4 specific analyses of practical interest are provided. As a general conclusion the technique is relatively robust with regard to poor choice of the mortality probability schedule as long as the estimation of age M is not very different from the average age A of the target children--children of mothers aged x. Errors caused by poor choice of density are more difficult to guard against; additional information that improves the accuracy of density is the only safe recourse. Good estimates of the infant mortality rate are difficult to obtain from Brass method. If the authors are willing to model exactly how certain specific demographic assumptions are violated they can derive algebraic expressions for the bias in the estimate. The theory rests on an application of differential calculus. Although not exact the results in this paper should be regarded as indicative of the type of bias introduced its magnitude and the factors on which it depends.

Changes in smoking behavior in various population subgroups can be estimated by using a technique that also has applications in other demographic work. The technique is especially valuable where the available aggregate data for such things as age groups or survey intervals are irregular. When tested on smoking statistics from the New Zealand census which is conducted every 5 years and aggregates age group data in 5-year increments the method achieved statistically comparable results using irregular data to estimate the transition rates into and out of the population of smokers in the U.S. The method estimates net transition rates 1st by considering data for regular age groups and then expanding the formula to include irregular age groups. It also considers the special treatment necessary for the final open interval. Underlying the method is the assumption that age-specific growth rates of population subgroups are approximately constant within the age intervals specified by the data population. The technique produces better estimates the smaller the age intervals are and weak results for the open-ended age group. Changes in the proportions of the population married and single employed and unemployed or healthy and sick also may be estimated by the method. The technique can be used to study more than 2 population groups such as the proportion of light medium and heavy smokers.

Power transformations can often simplify the task of describing behavior in data that consist of positive measurements or counts. Tukey's diagnostic techniques based on two-dimensional plots are useful in searching for a suitable transformation in two types of data structures: multiple batches at different levels, and two-way tables. To these, we add plots for finding transformations in two other structures: a single batch, and y versus x. The basis for plots that indicate transformations for symmetrizing and for straightening is explored using second-order series approximations. For all four techniques, when the plot is roughly linear with slope 1 — p, the power of a transformation indicated by the plot is p. Each plot indicates whether any power transformation can be effective in achieving a desired objective.

Population projections are key elements of many planning and policy studies but are inherently inaccurate. This study of past population projection errors provides a means for constructing confidence intervals for future projections. We first define a statistic to measure projection errors independently of the size of the population and the length of the projection period. A sample of U.S. Census Bureau and United Nations projections indicates that the distributions of components of the error statistic are relatively stable. We then use this information to construct confidence intervals for the total population of the United States through the year 2000. We find that for projections of total population size, simple projection techniques are more accurate than more complex techniques.