Glossary

• Alias: When the estimate of an effect also includes the influence of one or more other effects (usually high order interactions) the effects are said to be aliased (see confounding). For example, if the estimate of effect D in a four factor experiment actually estimates (D + ABC), then the main effect D is aliased with the 3-way interaction ABC. Note: This causes no difficulty when the higher order interaction is either non-existent or insignificant.
• Analysis of variance
  Analysis of variance
  In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
  
   (ANOVA): A mathematical process for separating the variability of a group of observations into assignable causes and setting up various significance tests.
• Balanced design: An experimental design where all cells (i.e. treatment combinations) have the same number of observations.
• Blocking
  Blocking (statistics)
  In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups that are similar to one another. For example, an experiment is designed to test a new drug on patients. There are two levels of the treatment, drug, and placebo, administered to male...
  
  : A schedule for conducting treatment combinations in an experimental study such that any effects on the experimental results due to a known change in raw materials, operators, machines, etc., become concentrated in the levels of the blocking variable. Note: the reason for blocking is to isolate a systematic effect and prevent it from obscuring the main effects. Blocking is achieved by restricting randomization.
• Center Points: Points at the center value of all factor ranges. Coding Factor Levels: Transforming the scale of measurement for a factor so that the high value becomes +1 and the low value becomes -1 (see scaling). After coding all factors in a 2-level full factorial experiment, the design matrix has all orthogonal columns. Coding is a simple linear transformation of the original measurement scale. If the "high" value is X_h and the "low" value is X_L (in the original scale), then the scaling transformation takes any original X value and converts it to (X − a)/b, where a = (X_h + X_L)/2 and b = (X_h−X_L)/2. To go back to the original measurement scale, just take the coded value and multiply it by b and add a or, X = b × (coded value) + a. As an example, if the factor is temperature and the high setting is 65°C and the low setting is 55°C, then a = (65 + 55)/2 = 60 and b = (65 − 55)/2 = 5. The center point (where the coded value is 0) has a temperature of 5(0) + 60 = 60°C.
• Comparative design: A design aimed at making conclusions about one a priori important factor, possibly in the presence of one or more other "nuisance" factors.
• Confounding
  Confounding
  In statistics, a confounding variable is an extraneous variable in a statistical model that correlates with both the dependent variable and the independent variable...
  
  : A confounding design is one where some treatment effects (main or interactions) are estimated by the same linear combination of the experimental observations as some blocking effects. In this case, the treatment effect and the blocking effect are said to be confounded. Confounding is also used as a general term to indicate that the value of a main effect estimate comes from both the main effect itself and also contamination or bias from higher order interactions. Note: Confounding designs naturally arise when full factorial designs have to be run in blocks and the block size is smaller than the number of different treatment combinations. They also occur whenever a fractional factorial design is chosen instead of a full factorial design.
• Crossed factors: See factors below.
• Design
  Design
  Design as a noun informally refers to a plan or convention for the construction of an object or a system while “to design” refers to making this plan...
  
  : A set of experimental runs which allows you to fit a particular model and estimate your desired effects.
• Design matrix
  Design matrix
  In statistics, a design matrix is a matrix of explanatory variables, often denoted by X, that is used in certain statistical models, e.g., the general linear model....
  
  : A matrix description of an experiment that is useful for constructing and analyzing experiments.
• Effect
  Effect
  Effect may refer to:* A result or change of something** List of effects** Cause and effect, an idiom describing causalityIn pharmacy and pharmacology:* Drug effect, a change resulting from the administration of a drug...
  
  : How changing the settings of a factor changes the response. The effect of a single factor is also called a main effect. Note: For a factor A with two levels, scaled so that low = -1 and high = +1, the effect of A is estimated by subtracting the average response when A is -1 from the average response when A = +1 and dividing the result by 2 (division by 2 is needed because the -1 level is 2 scaled units away from the +1 level).
• Error
  Errors and residuals in statistics
  In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...
  
  : Unexplained variation in a collection of observations. See Errors and residuals in statistics
  Errors and residuals in statistics
  In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...
  
  . Note: experimental designs typically require understanding of both random error
  Random error
  Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measures of a constant attribute or quantity are taken...
  
   and lack of fit error.
• Experimental unit: The entity to which a specific treatment combination is applied. Note: an experimental unit can be a
  • PC board
  • silicon wafer
  • tray of components simultaneously treated
  • individual agricultural plants
  • plot of land
  • automotive transmissions
  • etc.
• Factor
  Factor
  A factor, a Latin word meaning 'who/which acts', may refer to:In commerce:* Factor , a person who acts for another, notably a mercantile and/or colonial agent* Factor , a person or firm managing a Scottish estate...
  
  s: Process inputs an investigator manipulates to cause a change in the output. Some factors cannot be controlled by the experimenter but may affect the responses. If their effect is significant, these uncontrolled factors should be measured and used in the data analysis. Note: The inputs can be discrete or continuous.
  • Crossed factors: Two factors are crossed if every level of one occurs with every level of the other in the experiment.
  • Nested factors: A factor "A" is nested within another factor "B" if the levels or values of "A" are different for every level or value of "B". Note: Nested factors or effects have a hierarchical relationship.
• Fixed effect: An effect associated with an input variable that has a limited number of levels or in which only a limited number of levels are of interest to the experimenter.
• Interaction
  Interaction (statistics)
  In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the simultaneous influence of two variables on a third is not additive...
  
  : Occurs when the effect of one factor on a response depends on the level of another factor(s).
• Lack of fit error: Error that occurs when the analysis omits one or more important terms or factors from the process model. Note: Including replication in a designed experiment allows separation of experimental error into its components: lack of fit and random (pure) error.
• Model
  Statistical model
  A statistical model is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more random variables. The model is statistical as the variables are not deterministically but...
  
  : Mathematical relationship which relates changes in a given response to changes in one or more factors.
• Nested Factors: See factors above.
• Orthogonality
  Orthogonality
  Orthogonality occurs when two things can vary independently, they are uncorrelated, or they are perpendicular.-Mathematics:In mathematics, two vectors are orthogonal if they are perpendicular, i.e., they form a right angle...
  
  : Two vectors of the same length are orthogonal if the sum of the products of their corresponding elements is 0. Note: An experimental design is orthogonal if the effects of any factor balance out (sum to zero) across the effects of the other factors.
• Random effect: An effect associated with input variables chosen at random from a population having a large or infinite number of possible values.
• Random error
  Random error
  Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measures of a constant attribute or quantity are taken...
  
  : Error that occurs due to natural variation in the process. Note: Random error is typically assumed to be normally distributed with zero mean and a constant variance. Note: Random error is also called experimental error.
• Randomization
  Randomization
  Randomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population ....
  
  : A schedule for allocating treatment material and for conducting treatment combinations in a designed experiment such that the conditions in one run neither depend on the conditions of the previous run nor predict the conditions in the subsequent runs. Note: The importance of randomization cannot be over stressed. Randomization is necessary for conclusions drawn from the experiment to be correct, unambiguous and defensible.
• Regression discontinuity design: A design in which assignment to a treatment is determined at least partly by the value of an observed covariate lying on either side of a fixed threshold.
• Replication
  Replication (statistics)
  In engineering, science, and statistics, replication is the repetition of an experimental condition so that the variability associated with the phenomenon can be estimated. ASTM, in standard E1847, defines replication as "the repetition of the set of all the treatment combinations to be compared in...
  
  : Performing the same treatment combination more than once. Note: Including replication allows an estimate of the random error independent of any lack of fit error.
• Resolution: In fractional factorial designs, "resolution" describes the degree to which the estimated main-effects are aliased (or confounded) with estimated higher-order interactions (2-level interactions, 3-level interactions, etc). In general, the resolution of a design is one more than the smallest order interaction which is aliased with some main effect. If some main effects are confounded with some 2-level interactions, the resolution is 3. Note: Full factorial designs have no confounding and are said to have resolution "infinity". For most practical purposes, a resolution 5 design is excellent and a resolution 4 design may be adequate. Resolution 3 designs are useful as economical screening designs.
• Response
  Dependent and independent variables
  The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...
  
  (s): The output(s) of a process. Sometimes called dependent variable(s).
• Response surface
  Response surface methodology
  In statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an...
  
  : A designed experiment that models the quantitative response, especially for the short-term goal of improving a process and the longer-term goal of finding optimum factor-values. Traditionally, response-surfaces have been modeled with quadratic-polynomials, whose estimation requires that every factor have three levels.
• Rotatability: A design is rotatable if the variance of the predicted response at any point x depends only on the distance of x from the design center point. A design with this property can be rotated around its center point without changing the prediction variance at x. Note: Rotatability is a desirable property for response surface designs (i.e. quadratic model designs).
• Scaling factor levels: Transforming factor levels so that the high value becomes +1 and the low value becomes -1.
• Screening design: A designed experiment that identifies which of many factors have a significant effect on the response. Note: Typically screening designs have more than 5 factors.
• Test plan
  Test plan
  A test plan is a document detailing a systematic approach to testing a system such as a machine or software. The plan typically contains a detailed understanding of what the eventual workflow will be.-Test plans:...
  
  : a written document that gives a specific listing of the test procedures and sequence to be followed.
• Treatment: A treatment is a specific combination of factor levels whose effect is to be compared with other treatments.
• Treatment combination: The combination of the settings of several factors in a given experimental trial. Also known as a run.
• Variance components: Partitioning of the overall variation into assignable components.

See also

• Glossary of probability and statistics
  Glossary of probability and statistics
  The following is a glossary of terms. It is not intended to be all-inclusive.- Concerned fields :*Probability theory*Algebra of random variables *Statistics*Measure theory*Estimation theory- Glossary :...
  
  
• Notation in probability and statistics
• List of statistical topics

External links

• A Glossary of DOE Terminology at statistics.com