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DOE mean plot

Definition

A DOE mean plot shows the average response at each level of factors in a designed experiment. DOE stands for design of experiments. By comparing level means on a common response scale, the plot helps identify factors associated with larger average changes. It is also called a main effects plot. It supports investigation but does not, by itself, establish statistical significance or reveal every interaction between factors.

What it means

An experiment might vary processing temperature, material type, and machine speed while measuring product strength. For each factor, the plot summarizes the response at its tested levels, usually connecting the means. A large vertical difference suggests a larger average effect over the other settings represented in the design. The meaning of better depends on the objective: higher strength, lower waste, or a response close to a target are different goals.

How it works

Use the experimental design and response records to group observations by each factor level. Calculate the relevant mean for each group and display factor panels using a consistent vertical scale. In a balanced design, simple marginal means often provide a useful main-effect summary. Interpret the plot alongside the design structure, replicate variation, and interaction analysis. Missing runs, imbalance, blocking, or confounding can complicate a simple comparison. A plotted line joins tested level means; it does not establish the response at untested intermediate settings.

Three practical examples

• Manufacturing experiment: a team compares mean defect counts at tested machine settings while also checking variation and interactions.
• AI experiment: researchers summarize mean evaluation results for model settings across a deliberately designed set of runs, accounting for repeated-run variability.
• Process development: engineers compare average drying time at selected temperatures and airflow levels, using the plot to guide further analysis rather than choose settings blindly.

Think of it this way

Think of a set of small scorecards, each showing the average result at the tested settings of one control. The common scale makes differences easy to compare. The analogy is limited because one control may behave differently depending on another. A scorecard averaging over those combinations can hide a strong joint effect.

Worked example

Consider a fictional balanced experiment with two factors, A and B, each at low and high levels. The four cell means are: A low/B low = 10, A high/B low = 20, A low/B high = 20, and A high/B high = 10. Assume each cell has the same number of observations.
The mean at A low is (10 + 20)/2 = 15, and at A high it is (20 + 10)/2 = 15. B also has means of 15 at both levels. Both main-effect lines are flat. Yet changing A from low to high increases the response by 10 when B is low and decreases it by 10 when B is high. The effects cancel in the marginal average. An interaction plot or suitable model reveals this reversal. A flat DOE mean plot therefore does not justify declaring both factors irrelevant. Without replicate data or another justified error estimate, these four cell means also do not provide a complete significance analysis.

Illustrative case study

In a fictional packaging trial, an analyst uses a DOE mean plot to identify a temperature setting with a lower average defect rate. Before recommending it, the team checks whether the setting behaves consistently across materials and whether the run order could have mixed its effect with a machine warm-up trend. It inspects raw observations and variation rather than relying on means alone. The candidate setting is then assessed in a confirmation experiment appropriate to the process. This scenario illustrates the plot's role in an investigation; it does not report a real quality improvement.

Common misconceptions and mistakes

A steep line is not automatically statistically significant, and a flat line does not rule out interactions. Comparing slopes across panels with different vertical scales is misleading. Factor labels such as low and high describe tested settings, not necessarily equal physical changes across different factors. The plot summarizes location, usually the mean, and can conceal changes in spread. Selecting the best level of each factor independently can produce a poor combination when interactions matter. Observational group means should not be presented as results of a randomized experiment when no such design was used.

Business use

The plot is useful for communicating experimental findings to people who need to understand which settings deserve attention. Keep the response unit, objective, tested levels, and design limitations visible. Present uncertainty or supporting replicate information where appropriate, and include interaction and raw-data views when they affect interpretation. For AI experiments, distinguish changes in a metric from changes meaningful to the intended application. Confirm promising settings instead of assuming that the visually best average will reproduce under new conditions.

People also ask

Is a DOE mean plot the same as a main effects plot?

The terms are commonly used for this factor-level mean display.

Does the plot include interactions automatically?

An ordinary main-effects display does not; additional interaction analysis is needed.

Should the highest mean always be selected?

No. The desired direction or target comes from the project objective, and the full combination of settings must be considered.

Check your understanding

Both main-effect lines are flat in the worked example. Can the factors still matter?

Answer: Yes. Their effects reverse across the other factor's levels and cancel in the averages. Examine the interaction before concluding that either factor is unimportant.

Related terms

• Design of experiments
• Main effect
• Factor
• Factor level
• Analysis of variance
• Replication (statistics)
• Blocking
• interaction effect
• response variable
• replication
• confirmation run

Learn next

Learn how a two-factor factorial design combines settings, then calculate marginal means by hand. Draw both a main-effects plot and an interaction plot from the same four cell means. Next study replication, uncertainty, and confounding so visual differences are interpreted in the context of a valid experimental design.

• Factorial design
• Factor

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Sources

NIST/SEMATECH e-Handbook, DOE mean plot: https://itl.nist.gov/div898/handbook/eda/section3/eda33c.htm . NIST, mean-plot interpretation and objectives: https://www.itl.nist.gov/div898/handbook/pri/section5/pri593.htm . NIST, comparison with raw-data plots: https://www.itl.nist.gov/div898/handbook/pri/section6/pri612.htm . Primary handbook excerpts were consulted. The interaction calculation and case are original illustrations; editorial review remains pending.

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