# Confounding Effects

Alias:

An alias occurs when two factor effects are confused or confounded with each other.

Balanced design:

A fractional factorial design, in which an equal number of trials (at every level state) is conducted for each factor.

Block:

A subdivision of the experiment into relatively homogenous experimental units.

The term is from agriculture, where a single field would be divided into blocks for different treatments.

Blocking:

When structuring fractional factorial experimental test trials, blocking is used to account for variables that the experimenter wishes to avoid. A block may be a dummy factor which doesn’t interact with the real factors.

Box-Menken:

When full, second-order, polynomial models are to be used in response surface studies of three or more factors, Box-Menken designs are often very efficient. They are highly fractional, three-level factorial designs.

Collinear:

A collinear condition occurs when two variables are totally correlated. One variable must be eliminated from the analysis for valid results.

Confounded:

When the effects of two factors are not separable. In the following example, A, B, and C are input factors and columns AB, AC, & BC represent interactions (multiplication of 2 factors).

Correlation coefficient (r):

A number between -1 and 1 that indicates the degree of linear relationship between two sets of numbers. Zero (0) indicates no linear relationship.

Covariates:

Things which change during an experiment which had not been planned to change, such as temperature or humidity. Randomize the test order to alleviate this problem. Record the value of the covariate for possible use in regression analysis.

Curvature:

Refers to non-straight line behavior between one or more factors and the response. Curvature is usually expressed in mathematical terms involving the square or cube of the factor.

Degrees of freedom:

The terms used are DOF, DF, do or V. The number of measurements that are independently available for estimating a population parameter.

Design of experiments (DOE):

The arrangement in which an experimental program is to be conducted and the selection of the levels of one or more factors or factor combinations to be included in the experiment. Factor levels are accessed in a balanced full orfractional factorial design. The term SDE (statistical design of experiment) is also widely used.

Efficiency:

A concept from R. A. Fisher. He considered one estimator more efficient than another if it had a smaller variance.

EVOP:

Stands for evolutionary operation, a term that describes the way sequential experimental designs can be made to adapt to system behavior by learning from present results and predicting future treatments for better response. Often, small response improvements may be made via large sample sizes.

The experimental risk, however, is quite low because the trials are conducted in the near vicinity of an already satisfactory process.

Experiment:

A test undertaken to make an improvement in a process or to learn previously unknown information.

Experimental error:

Variation in response or outcome of virtually identical test conditions. This is also called residual error.

Experimental Resolution

Residuals Resolution I:

An experiment in which tests are conducted, adjusting one factor at a time, hoping for the best. This experiment is not statistically sound (definition totally fabricated by the authors).

Residuals Resolution II:

An experiment in which some of the main effects are confounded. This is very undesirable.

Residuals Resolution III:

A fractional factorial design in which no main effects are confounded with each other, but the main effects and two factor interaction effects are confounded.

Residuals Resolution IV:

A fractional factorial design in which the main effects and two factor interaction effects are not confounded, but the two factor effects may be confounded with each other.

Residuals Resolution V:

A fractional factorial design in which no confounding of main effects and two factor interactions occur. However, two factor interactions may beconfounded with three factor and higher interactions.

Residuals Resolution VI:

Also called Resolution V+. This is at least a full factorial experiment with no confounding. It can also mean two blocks of 16 runs.