In a fractional factorial design, if the A bar is the longest, can we simply conclude that "A has an effect on the response"? As seen in U20, if the A column is aliased with BC, that bar may represent the combined signal of A + BC.
The question for this section is as follows:
After identifying a potentially significant effect with a small number of runs, what else should be investigated?
Screening is the first wave for reducing candidates
Screening is the process of identifying candidate factors from a large number of factors to focus on in subsequent experiments. The contrast, Pareto chart, and half-normal plot in the results table summarize which effects appear to be larger than the background noise. However, the length of the bar does not automatically resolve the following:
- Is another effect aliased in that column?
- Is there a lack of replication, making it difficult to estimate the error?
- Was the same data looked at multiple times during the process of selecting effects?
- Was the hierarchy of main effects and interactions maintained?
- Is the magnitude significant in actual units?
Therefore, the results of screening are closer to a list of follow-up questions than a "list of confirmed effects."
The same A contrast can mask different causes
In a three-factor half fraction, if C=AB, then A=BC. If the hidden response equation contains a coded A coefficient of 6 and a BC coefficient of 5, the A contrast in the first fraction will be 22, which is the sum of the two effects. This is a value that has not yet separated the factorial effect of A (12) from the effect of BC (10).
Adding the opposite fraction, i.e., C=-AB, inverts the sign relationship between A and BC. In this foldover, the A contrast becomes 2. In the 8 runs combining the two folds, we can separately calculate the A effect as 12 and the BC effect as 10.
| Analysis Step | Contrast labeled as A | Interpretable range |
|---|---|---|
| First 4-run fraction | 22 | Combined signal of A and BC |
| 4-run foldover | 2 | Signal of A and BC combined with opposite signs |
| Combining the two fractions | A=12, BC=10 | Teaching fixture separating the two effects |
These numbers are a noise-free synthetic example to illustrate the structure. In real data, we need to consider the estimation uncertainty and run-to-run variation together.
Pareto and half-normal are not verdicts
A Pareto chart shows the absolute effects in descending order. A half-normal plot looks at whether many small effects are located near the baseline and whether large candidates deviate from the line. In designs without replication, we also rely on methods that assume that most of the small effects are inactive, such as Lenth-type pseudo standard errors.
If that assumption is broken, the baseline itself becomes unstable. If there are many effects or large aliased interactions, even small bars are not automatically errors. Do not delete terms based solely on p-values or bar rankings; instead, consider the design aliases and prespecified scientific questions together.
Grouping insignificant terms into the error will change the tests for the remaining terms. Do not hide the selection process of choosing terms and creating the error from the same data; instead, document the hierarchy and sparsity assumptions, sensitivity analysis, and follow-up validation data.
Subsequent experiments are chosen to match the remaining ambiguity
Not every screening requires a full foldover. The next design depends on the remaining questions.
- If main effects and two-factor interactions are aliased, separate the columns with a foldover or selective runs.
- If the number of important factors has been reduced, perform a higher resolution or full factorial experiment with only those factors.
- If the center point is off the line, move to the curvature question of U22.
- If you are actually going to use the prediction conditions, perform confirmation runs in new independent units.
Additional runs are determined not by "more," but by "which alias, curvature, or prediction to resolve."
In-Silico Lab: Separate one column into two effects
- Starting with true A coefficient of 6 and true BC coefficient of 5, confirm the first A contrast.
- Change BC to 0 and see how the combined A effect approaches the first contrast.
- Set A to 0 and make only BC large to see if an "A bar" is created.
- After combining the foldover, see if A and BC are each restored.
Follow the first screening and foldover
In a 4-run fraction where C=AB, A and BC are the same column. Add 4 foldovers to see how the two contrasts are separated.
If this is your first time: What should I press?
- 1. Read the question firstIn the Lab title, check the one thing you will compare this time.
- 2. Change just one conditionInitially, change only one of the inputs: n, effect, or spread.
- 3. new composite specimen pressureNew synthetic data is created. The same conditions may vary depending on the sample.
- 4. Pictures and calculation results CompareWrite in one sentence what moves and what stays the same before and after the change.
If it gets stuckresetGo back to see the default results and change just one condition. This Lab is not a correct answer tester but a pattern observation tool.
Synthetic observations of the same settings
calculation result
If we determine that A is the cause based on just the first bar, we miss BC. It must be recorded that the effect selection criteria and additional design were selected after viewing the data.
educational synthetic modelbjs-screening-sequence-v1. One row is one independent simulation or design run unless otherwise indicated. It cannot be used for actual research, quality, or regulatory decisions.
Each row in the Lab represents a composite run of a coded treatment combination. The first four and the four foldover runs are different phases; in a real experiment, these would be designed as separate experimental units with a randomized run order.
Interpret JMP results in conjunction with design information
Pareto·half-normal reads effect candidates and alias information together.
Recheck the hierarchy, residuals, and estimation uncertainty of the selected terms.
See before execution if additional runs isolate any confusion.
After finding candidate large effects in the Screening Effect Plots, check the Alias information and Design Evaluation to see what those bars are confounded with. In Fit Model, examine the hierarchy of selected terms, the uncertainty in the estimates, and the residuals. In the Foldover or Augment evaluation, check before running which columns the additional runs actually separate.
The goal is not to memorize the click sequence. The key is that the ambiguity left by the first result is connected to the new information provided by the next design.
Example of a result statement
In a 4-run half fraction, the A/BC alias contrast was significant. Instead of concluding that this is the main effect of A, we added the other four runs from the opposite fraction. In the combined analysis, the effects of A and BC were separated, and term selection maintained the hierarchy. This result is a candidate for further screening and requires independent confirmation experiments before applying it to actual conditions.
Concluding the module
- Screening is a step to reduce the number of candidate important effects.
- Pareto and half-normal plots do not replace alias and selection processes.
- Pooling is an analytical decision that relies on sparsity.
- Foldover changes the sign relationship to separate specific aliases.
- Screening results are not the final cause or optimal condition until independent confirmation.
In the next module, we will see how the center points placed in the screening design reveal the limitations of the linear model.
Supplemental Materials
- NIST/SEMATECH · Analysis of fractional factorial designs
- JMP Help · Analysis of Screening Results
- JMP Help · Augment Design Platform Options
This article and the Lab are educational synthetic materials and should not be used as evidence for actual research, process, quality, or regulatory decisions.