FACTORS IN THE GROWTH OF GIRLS1

Abstract

The intercorrelations of seventeen physical measurements of girls of various age groups have been analyzed to determine: 1) the portion of the variance at each age which may be ascribed to a general growth factor; 2) the group and special factors which may be necessary to account for the residual correlations at each age; 3) whether one estimate of the general and group factors may be used at all ages, in the study of the growth of the factors, and 4) the relationship of such factors, both general and group, to the age at which puberty occurs. The intercorrelations have been analyzed by the bi-factor technique developed by Holzinger (4). This method of factor analysis assumes a general factor to account for the positive character of the correlational matrix, and independent group factors to account for higher correlations within a restricted group of measurements than would be produced by the general factor alone. To the general factor is ascribed as much of the variance of each individual measure as is consonant with the magnitude of the correlation coefficients and with the postulated group factors. The residual correlations are then accounted for by group factors which are the general factors common to a restricted group of residuals, and by special factors for each measurement. The analysis presented in this paper will show that it is possible to obtain an excellent fit to the present correlation tables by such an assumption of general, group, and special factors, all independent of each other. It would have been possible, however, to have postulated group factors without a general factor, even though the correlations are all positive. In such a case the group factors must either overlap, as they do in most multiple factor analyses, where each factor has loadings in practically all of the measurements, or the group factors must themselves be correlated, not independent. The choice between these methods of factoring the observed correlations must be made not on mathematical grounds but in view of such questions as: Which method gives the most understandable and parsimonious description of the factors? Which analysis gives results of most use to the geneticist or student of child development in his effort to understand the underlying phenomena? The subjects of the study are girls enrolled in the Laboratory Schools of the University of Chicago. The measurements, made by physicians -on the staff of the schools during the years 1927-37, are as follows: height, arm span, length of right forearm, length of right lower leg, sitting height, weight, bi-iliac diameter, bi-trochanteric diameter, chest girth, chest width, chest depth, shoulder width, head length, head width, head height, lung capacity, and right hand squeeze. The technique used in making and recording each measurement is described by Bolmeier (1). The measurements were made as nearly as possible on the date of the child's birthday. For the records used in this study the average date of