Statistical graphics: mapping the pathways of science.

This chapter traces the evolution of statistical graphics starting with its departure from the common noun structure of Cartesian determinism, through William Playfair's revolutionary grammatical shift to graphs as proper nouns, and alights on the modern conception of graph as an active participant in the scientific process of discovery. The ubiquitous availability of data, software, and cheap, high-powered, computing when coupled with the broad acceptance of the ideas in Tukey's 1977 treatise on exploratory data analysis has yielded a fundamental change in the way that the role of statistical graphics is thought of within science-as a dynamic partner and guide to the future rather than as a static monument to the discoveries of the past. We commemorate and illustrate this development while pointing readers to the new tools available and providing some indications of their potential.

The centercept: an estimable and meaningful regression parameter.

Linear regression is a mathematical model that is employed broadly throughout all of social science research. The choice of parameterization for linear models has important substantive and statistical implications. This article examines the typical parameterization chosen, which includes a parameter for slope and a parameter for the y-intercept. The article demonstrates that the centercept has an interpretive advantage over the traditionally used y-intercept and that the centercept is typically estimated more accurately.

Adjusting for differential base rates: Lord's paradox again.

When the responses of 2 or more groups to the relative effects of some stimulus are compared, it is often important to adjust statistically the estimates of those effects for baseline differences among those groups. This is often the case in experiments on heart rate for animals of different ages. How should such adjustment be done? Among the competing methodologies are (a) subtract the base rate, (b) divide by the base rate, and (c) covary out the base rate. Because each can give a different answer, the choice is crucial. This article shows that this is an example of Lord's Paradox and that Rubin's Model for the measurement of causal effects allows researchers to understand what the assumptions are underlying the validity of each adjustment strategy. The answer for heart rate data is almost surely Methodology (a).

Predicting adult stature without skeletal age and without paternal data.

The RWT method for predicting adult stature from childhood variables uses the current recumbent length and weight of the child, the stature of each parent, and the skeletal age of the child as predictor variables. There is only a small increase in the errors of prediction if population mean values are substituted in the prediction equations when the father's stature, the skeletal age of the child, or both these variables are unknown. This modified method is more generally applicable than the original RWT method.

Late elongation of the cranial base.

A single logistic curve was fitted to serial data for three cranial base lengths (S-N, Ba-N, and Ba-S) in 33 boys and 26 girls. Elongation during pubescence plus adolescence is greater in boys than girls for each length. The maximum rate of pubescent elongation occurs earliest in Ba-N. There are no consistent sex differences in the maximum rates of elongation but they occur considerably earlier in girls. Similarly, girls reach 95% of their adult lengths at younger ages than boys.

Speed vs reaction time as a measure of cognitive performance.

Choosing mean reaction time or mean speed (it's reciprocal) as the dependent variable in cognition experiments is frequently done for no better reason than convenience. It is shown that sometimes this choice is crucial in determining the order of the obtained effects. Moreover, it is proved that when the order of the effects is dependent upon the choice of the transformation, the assumption of homogeneity of variance is not true and hence ANOVA may not be justified. Alternative strategies are proposed to deal with this data-related problem.

Individual growth in stature: a comparison of four growth studies in the U.S.A.

Patterns of growth in stature of subjects from the four major U.S. longitudinal growth studies are compared by means of a two-component model for individual growth. Problems inherent in the comparison of data from independent growth studies, such as those arising from different methods of sampling subjects and scheduling measurements and the occurrence of atypical subjects, are considered and solutions are offered. Statistical tests of the individual growth parameters revealed significant, but small, differences among the samples in the magnitude of the contributions of prepubertal and adolescent growth to mature stature and in the velocity of growth. No differences between samples in the timing of the adolescent component were detected.

Two programs for predicting adult stature for individuals.

Two computer programs are described which use the new RWT method to predict adult stature for individuals. This method, developed and described by Roche et al. is the best and most accurate one available to date. The two programs are prepared with different aims in different languages. Program 1 is interactive, written in BASIC and is aimed for the clinician who needs predictions for just a few individuals at a time. Program 2 is written in FORTRAN and is meant for large-scale batch processing. It is thought that this mode is better for the researcher who is more interested in large-scale testing of hypotheses about such things as the efficacy of intervention programs in human growth.

Hereditary and environmental determinants of growth in height in a longitudinal sample of children and youth of Guatemalan and European ancestry.

The effects of hereditary and environmental factors upon the growth in stature of children living in Guatemala City has been studied. Heights at yearly examinations were fitted, by individual, to a double logistic curve in samples of Guatemalan and European children attending a private school in Guatemala City. These two samples differed genetically yet shared the same environment. Their growth was compared, by a multivariate analysis of the parameterized curves, to that of children from the Berkeley Growth Study, genetically similar to the European sample, yet living in different environments. The European children in Guatemala grew, before adolescence, more similar to Guatemalan and differed significantly from the Berkeley sample children. However, the amount of growth during the adolescent years experienced by the European children was similar to that of the Berkeley sample and differed from their Guatemalan counterparts.

The RWT method for the prediction of adult stature.

The Roche- Wainer- Thissen (RWT) method estimates the adult stature of an individual from data recorded at a single childhood examination. The data required are recumbent length, nude weight, midparent stature, and hand-wrist skeletal age. If necessary, a measurement of the child's stature can be transformed to be approximately equivalent to recumbent length with little loss of accuracy. When applied to data from three longitudinal growth studies, the prediction errors with the RWT method were smaller than those with the method of Bayley and Pinneau.

A double logistic comparison of growth patterns of normal children and children with Down's syndrome.

A double logistic model was used to compare six parameters of growth in standing height of 31 children with Down's syndrome with 136 children from the California Guidance Study. Multivariate analysis of variance of the growth data showed that while there were significant differences in all six parameters favouring the normal over the Down's children, there were no significant differences with respect to error of fit. Multivariate analysis with final height as a covariate revealed that differences between the normal and the Down's children in the prepubertal and adolescent components were explainable by differences in final height. In summary, the double logistic model, when applied to this sample of Down's children, identified those well defined logistic components which are characteristic of the growth of normal children, the differences being those of degree, not of form.