A Multiple Factor Study of Eighteen Anthropometric Measurements of Iowa City Boys Aged Nine Days to Six Years

Abstract

battery has in addition a specific factor which is unique for that item. This theory made a contribution but was inadequate for applica tion in research areas where there was more than one common factor or where several group factors were present. In 1928 Profes sor Truman Kelley (4), now at Harvard Uni versity, presented a method in which he at tempted to overcome the shortcomings of Spearman's This method was at once highly complex and limited in the scope of its application. After several years of preliminary experi mentation, Professor L. L. Thurstone (n) of the University of Chicago published in 1931 a theory of multiple factor analysis by the use of which any number of common group factors might be isolated and weighted. The numerical values of the finally adjusted weightings correspond to zero-order correla tions between the factors and the variables in which they are present. According to Thur stone, a common factor in general is an ele mental or unitary ability, component, or basic trait which is common in greater or lesser de gree to all the variables, and a group factor is one which is present in a number of vari ables but not in all. Each group or common factor is assumed to be uncorrelated (16, p. 5?~-53 ) with the other group or common fac tors. Common factors were first determined by a least squares method, but Thurstone later developed a so-called center of gravity method which will be discussed. In this tech nique, the final adjustment of the factor load ings is accomplished by what is termed a logical method. Applied to psychological tests he found that the method isolated such factors as verbal ability, mechanical ability, memory of numbers, spacial imagery, etc. In other fields the factors vary, as for example in motor abilities where such factors as strength, speed, and motor educability have been identified (7, 19). Professor Harold Hotelling (3) of Colum bia in 1933 and Professor Kelley (5) in 1935 developed further methods of factor analysis, but some of the assumptions necessary to the use of these methods seem untenable to the writer (See discussion in Thurstone (16, p. 129-133) and on page 213 of this study); hence the Thurstone technique is used in this investigation. In the field of anthropometry, multiple factor analysis is at an early experimental stage. At the time the present research was projected the only application known to the writer was an unpublished study (7, p. 26-32 ) by Professor Charles H. McCloy of the Iowa Child Welfare Research Station. This study consisted of a survey analysis for eighteen an thropom?trie measurements at selected ages between birth and eighteen years. For males, analyses were made at nine days of age and at ages four, six, ten, fourteen, and eighteen years. For females, parallel analyses were made at ages nine days and four, six, ten, and thirteen years. Three group factors were found. These were tentatively identified as (1) a factor of linear growth, (2) a factor of cross-sectional growth and (3) a factor of fat growth. The first was largest in * This thesis was submitted in partial fulfillment of the re quirements for the degree of Doctor of Philosophy in the Graduate College of the University of Iowa and was directed by Dr. C H. McCloy.