Two-Factor Full Factorial Design

Why it matters

The effect of a factor can change depending on how the other conditions are held. Changing only one setting and then moving to the other looks easy; but this path does not observe all the combinations. A full factorial design closes this gap by planning all combinations of the selected levels. The four conditions required for two factors at two levels each form a small table. Even so, the same table makes it possible to examine the means of the conditions, the comparison of each factor and the importance of changing together. This gain comes not from collecting many measurements at random but from setting up the comparisons in a balanced way from the start.

Each cell in the design table is a single factor combination. Having two results in the same cell does not mean there are two different conditions; it is two independent runs of the same condition. Replicates must be made on new specimens and with a defined setup. The measuring instrument rereading the same part does not show run variability. This distinction matters especially when the amount of data looks large. Many readings do not remove the information limit of a small number of independent experiments. The strength of the plan depends, before the number of rows, on which experimental unit each row represents. In a design without replicates, it is harder to separate random fluctuation from the difference between conditions.

A balanced design allocates an equal number of independent replicates to each condition. In this way, when the high and low levels of one factor are compared, the other factor is represented with equal weight. The main effect, in this scope, is the mean response at the high level minus the mean response at the low level. A positive value does not always mean better; the desired direction of the response is set beforehand. For example, a rise in strength may be useful while a rise in the number of defects is unfavorable. Also, the mean effect does not show that the same effect exists in every condition. Reporting only the main effects without seeing the cells can oversimplify a design in which changing together matters.

The calculations in this lesson give a simple, reproducible starting point. No generally valid certainty is drawn from a small sample. Differences within a condition are examined as measurement problems, run deviation or process variability. A condition that is unsafe is not selected because it gave a high response. The order in which the conditions were run does not have to be the same as the standard order of the table; random run order and the management of days are planned separately. The words full design do not say that all possible temperatures and times were tried. They state only that all combinations of the selected levels are covered. This limit must be kept when the results are carried into production.

Formula