Malcolm E. Turner

The Regression Analysis of Causal Paths

The purpose of this presentation is to acquaint biologists and biometricians with an important tool, path analysis. This tool can be of help in dealing with complex causal networks. These often, though not always, prove amenable to common regression technics. Path analysis, originated by Sewall Wright [1918], is a convenient approach to regression problems involving two or more regression equations. For those unskilled in statistics, path analysis provides one method of depicting regression problems by simple diagram. The path diagram, commonly representing the flow of cause and effect, often permits one to write estimators of parameters immediately upon inspection. Path analysis thus facilitates the process of abstraction for both mathematician and biologist. The analytic process is here explained, two computational algorithms (rules-of-thumb) are given, and an example involving feedback is detailed. Inclusion of feedback, and thus homeostasis, is an important feature of this presentation. Since Wrights early work [1918, 1921, 1924, 1934, and others] the treatment of multiple equations has been extensively developed in econometrics (see especially Hood and Koopmans, [1953]) but generally without use of the standardized regression coefficients used by Wright or of the path diagrams and algorithms which characterize Wrights technic. Wright himself [1921] used unstandardized coefficients and the term path regression, but in general [1954] has favored the standardized form. Tukey [1954] in a critical review pointed out advantages in working with unstandardized regression coefficients. Recently Kemp-

A Biometric Theory of Middle and Long Distance Track Records

It has been often observed that a plot of average velocity againist distanice or time for world track records suggests a continuous monotonic underlying relationship. Several attempts to discern the nature of this relationship empirically by seeking linearizing transformations have been made with varying degrees of success. The purposes of this paper are to describe an attempt to explain the observed curve by a biometric theory alnd to consider the problem of estimating unkniown parameters occurring in the theory. The theory is applied to world record data of 1959 and records which are below par are pointed out. The development is based on the work of A. V. Hill [1927].

Glucose as Adjunct to 3,3-Dimethyl-1-Phenvltriazene in its Action upon Sarcoma 180

Summary The effects of intraperitoneal injections of 3,3-dimethyl-1-phenyltriazene dissolved in peanut oil and of subcutaneous injections of glucose, separately and in combination, upon growth rate of Sarcoma 180 in mice were measured. The triazene markedly depressed tumor growth. This effect was only slightly altered by injections of glucose. Glucose itself had a slight effect upon tumor growth. The triazene disappeared rapidly from the abdominal cavity. By acidification and coupling with N-(1-naphthyl)-ethylene-diamine, it could be demonstrated in tissue. Triazene injections were without effect on blood sugar.