Factorial Design Terminology

Design of Experiments Terminology

Alias structure

Alias structures are used in fractional factorial designs to determine which combinations of factors and levels will be tested.

Blocking

Blocking involves recognizing uncontrolled factors in an experiment – for example, gender and age in a medical study – and ensuring as wide a spread as possible across these nuisance factors. Read more about blocking.

Classification factor

A classification factor is an element that cannot be specified or set by the experiment designer, but can be used in sample selection. The sex of a subject is an example of a classification factor.

Confounding

Confounding occurs when we can’t be sure which factors – or combinations of factors – are affecting a result. Blocking can help to minimize confounding. Read more about confounding.

Experimental factor

An experimental factor is one that can be modified and set by the person designing the experiment.

Factor

Factors are elements in your experiment – whether in your control or outside of it – that affect the outcomes. Read more about factors.

Fractional factorial

Experiment design that tests only a subset of the possible factor-level combinations. Read more about Fractional factorial.

Full factorial

Experiment design that tests the full set of possible factor-level combinations. Read more about full factorial.

Interaction

Factor interactions occur when multiple factors affect the output of an experiment.

Level

Every treatment factor in an experiment will have at least two levels. These might be minimum and maximum values, discrete groups (for example, ‘male’ and ‘female’), or designated ranges (for example, ages 25-34; 35-44; etc).

Nuisance factor

A nuisance factor is the opposite of a treatment factor – an element that is of no interest for the experiment, but needs to be considered anyway in case it skews results.

Qualitative factor

A qualitative factor is a treatment factor that contains a number of categories.

Quantitative factor

A quantitative factor is a treatment factor that can be set to a specific level as required.

Replicates

Replicates are multiple experimental runs of the same factors and experiments. You do this so you can get a sense of the variability in the data set. Good expansive article on Replicates and Repeats here from MiniTab.

Treatment factor

A treatment factor is an element that is of interest to you in your experiment, and that you will be manipulating in order to test your hypothesis.

 

Six Sigma Black Belt Certification Factorial Design Questions:

Question: Which of the following best describes a controlled variable whose influence on a response is being studied? Taken from (ASQ sample Black Belt exam.)

(A) Replicate
(B) Version
(C) Level
(D) Factor

Answer: D, Factors. Replicates are multiple experimental runs with the same settings, so A is invalid. B is nonsensical. C, Level, is the treatment (or option) available for each factor. D is a straight vocabulary question. Collect your right answer and move on!

Six Sigma Green Belt Certification Factorial Design Questions:

Question: The following chart was developed by a six sigma team to measure reactions on two different products:

temperature by product

In this chart, temperature represents the

(A) repetition
(B) factor
(C) response
(D) level

Answer: Response. The products are the 2 elements that we are examining to see how they change the system. On product x the temperature is 30 and on product y the temperature is 100. That makes the products the factors and the temperature the response. Repetition and level are nonsensical answers. See Factorial Design terminology.

Question: Which of the following graphs represents a factorial experiment with the strongest interaction?

(A)


(B)

(C)

(D)

Answer: C – See how the responses for each element (B+ and B-) are completely different when the factors are changed (from A- to A +)? In choice A, both elements move up in lock-step. They agree. In choice B both elements drop – yes, one more precipitously than the other. But both agree. Similarly in choice D – both elements hold steady despite the factors changing. That leaves choice c as the factorial experiment with the strongest interaction. See Factorial Design terminology.

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