Using Fractional Factorial Experiments 2(5-1) in Complete Randomized Block Design to Study the Factors Affecting the Acidity of Yoghurt

Abstract

The study of design and analysis of experiments is one of the important studies that depend on
experimentation through observation, data collection and analysis in order to reach high-accuracy
scientific decisions and the lowest possible cost, and experiments are divided on the basis of the studied
factors into Simple Experimental Design and factorial experiments Factorial Experimental Design. It is
known that simple experiments are of limited use because they study the effect of one factor, and in most
cases the researcher needs to study the effect of more than one factor at the same time, so he turns to
factorial experiments, which allow estimating and testing each factor separately, in addition to measuring
the effects of the interaction between factors. Although the factorial experiment provides large quantities
of treatments, providing experimental units with a close degree of homogeneity represents a great
difficulty for the researcher, especially when the number of factors is more than (4). Therefore, part of the
treatments is taken according to the fractional factor experiment technique. The effect of (5) two-level
factors (high and low) was studied in the fractional factorial experiment 2(5-1) (half-repetition) in the
Complete Randomized Blocks. Data taken from Dairy Factory / Dairy Department. Skimmed milk powder
(A), inoculation temperature (B), incubation temperature (C), incubation time (D) and fat percentage
(E)). A half-repetition experiment was designed that includes main factors and some higher order
interactions. Small and non-significant interactions were combined with the important main effects to
obtain an estimate of the main effects and important interactions. The results showed by finding the
analysis of variance table that the main effects (A, D) were significant in addition to the binary interaction
(AD). The value of (P-Value) was less than the level of significance (0.05).