A univariate and multivariate examination of measurement error in anthropometry

Replicate anthropometric measurements on 20 male and 22 female Eskimos were examined using analysis of variance, product-moment correlation coefficients, and canonical variates with Mahalanobis' D² distances. Analysis of variance indicated that 12 of the 16 variables could be measured comparably by two investigators. Those variables with readily defined endpoints yielded the highest correlations between the results of two anthropometrists. The multivariate analysis demonstrated a high level of discrimination between two sets of data taken on the same group of subjects. This suggests that population comparisons using data from two or more investigators could be significantly affected by measurement error.     

Morphometric analysis of Cartesian coordinates of the human skull

A method for locating the three dimensional coordinates of cranial landmarks with respect to the Frankfort, midsagittal, and coronal planes is presented. Sliding calipers were used to obtain the distances from left and right porion and apex to each landmark, except for a few points where spreading calipers are required. In the present example, 35 landmarks (for a total of 105 measurements) were located for each of 35 Peruvian precolumbian skulls. These distances were entered into a program (SKULL) which calculates the Cartesian coordinates of each landmark. The XYZ coordinates of each landmark contain all the information necessary for calculation of the distances between any two landmarks, and these distances may also be obtained as output from program SKULL, if desired (595 distances if all 35 landmarks are used). Reliability of the location of coordinates was determined by comparing computed distances among selected landmarks from program SKULL with traditional anthropometric measurements. Satisfactory agreements were found. Direct multivariate analysis of the coordinates of the landmarks produced insights not available in traditional multivariate analysis of conventional anthropometric measurements.     

Bivariate versus multivariate allometry: A note on a paper by Jungers and German

Jungers and German (1981) found differences when they compared 1) coefficients of allometry from bivariate plots of log measurements versus log body weight with 2) those coefficients from the first principal component of the log measurements excluding body weight. It is argued here that an arbitrary choice of unit for “internal size” is all that separates these coefficients. When the unit is chosen to make internal size isometric with body weight the coefficients agree rather well.     

Digital dermatoglyphics in the Basque population: univariate and multivariate comparison with other Spanish populations

We have analyzed dermatoglyphic finger patterns in a Spanish Basque population (841 males and 911 females). Bimanual and sexual comparisons have been carried out by means of contingency analysis. The results in the Basque population are compared with those of other Spanish populations, based on univariate (chi 2 contingency test and Student's t-test) and multivariate (principal components analyses) statistical methods. Bilateral distribution asymmetry and sexual dimorphism were observed in the Basque sample. The results of the chi 2 test for pattern types in males and females show statistically significant differences between the Basques and other Spanish populations, with the exception of the males from El Bierzo. Comparing populations with regard to the Pattern Intensity Index, the differences observed are much lower; therefore, this confirms what other authors have suggested regarding the limited usefulness of indexes in populational comparisons. In the Caucasian variation range of pattern types, Basques are located in the high part with regard to arches, in the low part with regard to whorls and radial loops, and in an intermediate part in relation to ulnar loops and overall pattern intensity. Results of the multivariate comparisons show which populations are more or less distant from the Basque population and which variables are significant in contributing to these population relationships.     

A Bayesian analysis of multivariate doubly-interval-censored dental data

A Bayesian survival analysis is presented to examine the effect of fluoride-intake on the time to caries development of the permanent first molars in children between 7 and 12 years of age using a longitudinal study conducted in Flanders. Three problems needed to be addressed. Firstly, since the emergence time of a tooth and the time it experiences caries were recorded yearly, the time to caries is doubly interval censored. Secondly, due to the setup of the study, many emergence times were left-censored. Thirdly, events on teeth of the same child are dependent. Our Bayesian analysis is a modified version of the intensity model of Harkanen et al. (2000, Scandinavian Journal of Statistics 27, 577-588). To tackle the problem of the large number of left-censored observations a similar Finnish data set was introduced. Our analysis shows no convincing effect of fluoride-intake on caries development.     

A note on epidemics in heterogeneous populations.

Recent analysis has shown the importance of heterogeneity for understanding the course of epidemics. However, the results generally rely on computer models or the assumption that the population consists of internally homogeneous subgroups. This note presents some analytic results for the more general case, in which any distribution can characterize population heterogeneity in susceptibility under proportionate mixing. At any moment, epidemics in such a situation resemble classic epidemics, with rate of spread governed by the average susceptibility of those not yet infected. But, over time, this average susceptibility falls at a rate proportional to the dispersion of susceptibility among those not yet infected. The author concludes by noting some implications of heterogeneity for understanding epidemics.     

Analysing environments for plant breeding purposes as exemplified by multivariate analyses of long term wheat yields

Summary A previous attempt to relate long term yields from the Western Australian wheat belt to climatic factors proved only partially successful. Here, principal component analysis has been used to examine the patterns of variability created by those socio-economic factors which may have obscured any underlying relationship which existed between yield and climate. In fact, these analyses revealed the existence of variation peculiar to particular groups of years, a result which could explain why many attempts to relate crop yields directly to climatic factors have proved unsuccessful. The plant breeding implications of these genotype x environment interactions are considered.     

A multivariate model for growth of populations

The “random environment” concept is used to model the growth of several interdependent populations. The vital rates are assumed to follow a multi-variate Ornstein-Uhlenbeck process; important properties of this process and of the integrated process (representing log of population growth) are developed. Application to a predator-prey situation is considered and a technique for the estimation of unknown parameters is developed.     

Effects of maternal food restriction during lactation on craniofacial growth in weanling rats

Adult Holtzman rats were submitted during suckling period to a food restriction with or without protein or carbohydrate restoration. Twenty-one-day-old weanling pups were compared with controls of 9, 13, 17, and 21 days of age. Lateral craniofacial roentgenographies were taken. The length in midsagittal plane of each bone and its angle with respect to the vestibular line were measured in males. In females, the brain and the left masseter muscle were weighed, and the muscle/brain ratios (neuromuscular index) were calculated. Food restriction altered skull size and shape. Size changes were due to arrested lengths in all studied skull bones. Shape variation was evident by orthocephalization changes, reflected in angulation changes of bones belonging to the frontoethmofacial (frontal, nasal, and maxillary bones) and to the occipitointerparietal (interparietal bone) complexes. Partial restorations by both protein or carbohydrate supplementation were found. Nutritional stresses during lactation affected orthocephalization through an altered growth ratio between two soft tissues functionally associated to the craniofacial complex: brain and masticatory muscles.     

Sexual dimorphism and mechanics of the human hip: A multivariate assessment

The present research was undertaken to determine the effects of sexual dimorphism in the human pelvis and femur on the mechanics of human locomotion. The analysis was based on six biomechanical variables determined from 25 male and 32 female skeletal remains from the Dickson Mound site. Discriminant function analysis indicates that the mechanical variables which primarily contribute to dimorphism are the moment arm of the gluteus medius and the torque produced by the abductors at the hip. These mechanical aspects of hip function produce greater pressure on the femoral head in females.