Description: Fractional factorial design is an approach in applied statistics that allows experiments to be conducted efficiently by using only a fraction of a full factorial design. This method is particularly useful when there are multiple factors to study, but the total number of possible combinations is too large to be managed in a reasonable time or with available resources. By selecting a fraction of the combinations, estimates can be obtained about the effects of the factors and their interactions without the need to conduct all possible tests. This type of design is based on the theory of randomization and analysis of variance, allowing researchers to infer conclusions about the population from a smaller sample. The main characteristics of fractional factorial design include the reduction of the number of experiments, the ability to identify significant effects, and the flexibility to adapt to different experimental situations. This approach is especially relevant in fields such as engineering, agriculture, and product research, where process optimization and cost reduction are essential.
History: Fractional factorial design was developed in the 1920s by statistician Ronald A. Fisher, who is considered one of the pioneers in the field of experimental statistics. Fisher introduced the concept of full factorial design and later the idea of fractionating these designs to make them more manageable. Over the years, this approach has evolved and been refined, becoming a fundamental tool in experimental research and industry.
Uses: Fractional factorial design is used in various fields, including product research, engineering, agriculture, and biomedical research. It allows researchers and professionals to optimize processes, identify significant factors affecting outcomes, and reduce costs in experiments. It is especially useful in situations where resources are limited or when a rapid evaluation of multiple variables is sought.
Examples: A practical example of fractional factorial design can be found in the food industry, where a recipe is to be optimized. Suppose three ingredients (A, B, and C) are being tested at different levels. A full factorial design would require 27 combinations (3 levels of A x 3 levels of B x 3 levels of C), but by using a fractional factorial design, only 9 representative combinations could be selected to evaluate the effect of the ingredients on the final product’s flavor. Another example is found in pharmaceutical research, where multiple doses and formulations of a drug can be evaluated without the need to conduct all possible trials.
