Romanian Biotechnological Letters Vol. 15, No. 6, 2010 Copyright © 2010 University of Bucharest Printed in Romania. All rights reserved ORIGINAL PAPER 5690 An application of variance analysis for establishing the effect of the saturated fats and of the manganese ions concentrations from the food ration on the cholesterol levels. Received for publication, July 10, 2010 Accepted, November 8, 2010 VARGA MIOARA*, POPA CIPRIAN**, TAMBA-BEREHOIU RADIANA*** *Faculty of Biotechnology Bucharest (vargamioara@yahoo.com ) **FARINSAN S.A. Giurgiu (cipnpopa@yahoo.com ) *** Faculty of Biotechnology Bucharest (radianatamba@yahoo.com) Abstract One of the most used tools in biology, for examining the variation within the whole group of experimental values determined for a sample from a statistical population, is represented by the analysis of variance. Some theoretical aspects of this method are presented, in order to describe the influence of two factors upon one character of a statistical population with normal distribution. The previous defined concepts were applied for solving a problem, aiming to establish the effect of the saturated fats concentrations and of the of manganese ions concentration in the food ration on cholesterol levels. Keywords: sum of squares of deviations, degrees of freedom, variance Introduction In many problems of biology and agriculture, it is interesting to find out the influence of certain factors on a character of a statistical population that can be experimentally determined. Analysis of variance is a statistical technique applied to solve such situations, by the achievement of a study on the simultaneous activity of several variability factors and pointing out in the same time their interactions. This method was introduced in connection with the analysis of data and with the designing of agricultural field experiments. Some terms used to describe the analysis reflect this origin, for example “treatment”, “plot” and “block” as noted by R.E.Parker, 1973 [3]. In the present paper a control model for two factors of variability acting on the same character was applied, which was supposed to be normally distributed. After introducing the necessary theoretical elements for solving such problems, (based on the mentioned references) it was chosen the studying of the effect of the saturated fats concentrations and of the concentration of Mn ions in the food ration on cholesterol level, as was first discussed by G. Samboan, 1986 [4]. Material and Method A brief characterization of variance analysis method is following, as previously described by several authors [1], [2], [5]. It was supposed that upon the character of a statistical population, which in terms of probabilities is a random variable normally distributed with mean μ and dispersion 2 σ , two variability factors are acting simultaneously, their influence being evidenced by the mean of the X character. It was considered that the factor A has 1 2 , ,..., m A A A - m versions and the factor