Interaction and Response Comparison

Why it matters

Learning the mean effect of a setting change is useful; but this value does not mean you can expect the same gain in every operating condition. When factors work together, the effect of one can depend on the level of the other. This dependence is called interaction. If a change in A gives a small difference when B is low and a large difference when B is high, there are two separate facts: a mean effect can be calculated for A, and this effect changes with the condition. It is not necessary to pick one of these facts and delete the other. For the decision to be set up correctly, both are reported together. Especially once it is clear which combination will be applied in production, the condition-specific difference becomes directly important.

The starting point of the interaction calculation is the difference of differences. First you compare the A high and A low responses at the same B level. Then you subtract these two A effects from each other. In this way you find how much the effect of A changes when B changes. The sign rule of the calculation must be defined at the start; if the order of subtraction changes, the sign changes. Observing a difference close to zero does not prove that there is certainly no interaction. Measurement and run variability can mask small effects. In the same way, a difference that looks large is not taken as a universal result on very few observations. The numerical size, the reliability of the data and the precision required by the decision are evaluated together.

A line chart showing the cell means can make this structure easier to read. The A levels are on the horizontal axis, the response on the vertical axis, and the B levels on separate lines. If the slopes of the lines differ, the conditional effects differ. The lines do not necessarily have to cross; moving apart or coming closer can also indicate interaction. A chart does not replace the calculation. The axis range can make a small difference look large, and the mean points can hide the spread between replicates. For this reason the cell counts, the raw results and the difference calculation are kept visible. It is verified that the visual impression and the numerical decision rest on the same comparison.

Response comparison is not only finding the highest number. Strength, cycle time and defect rate carry different units and different purposes. Adding them directly does not create a meaningful success score. The primary response and the safety and quality limits are set in advance; the decision is made among the candidates that meet these limits. If an option raises strength but breaks the safe condition, a high mean does not save it. Between two acceptable options, a difference in capacity or resources can be discussed separately. It is written clearly with which priority the result was selected. The interaction calculation informs this decision; by itself it does not replace all the production requirements.

Formula