Glossary
A
A(Model)
This is the A-efficiency of an experimental design for a given model including the intercept. This is one of the metrics used in the software to characterize the quality of an experimental design with respect to its ability to screen active (i.e statistically significant) effects among all the model terms. The higher the value for A-efficiency, the better is the experimental design according to this metric. For example, A(ME), refers to the A-efficiency of an experimental design for a main-effects model including the intercept. This is presented under Catalog Search.
AIC
This is the value for the Akaike Information Criterion for the corresponding linear regression model. This is one of the metrics used in the software to characterize the statistical quality of a linear regression model. The lower the value, the better is the model according to this metric. This metric is presented during modeling under Model details.
AICc
This is the value for the corrected Akaike Information Criterion for the corresponding linear regression model. This is one of the metrics used in the software to characterize the statistical quality of a linear regression model. The lower the value, the better is the model according to this metric. This metric is presented during modeling under Modeling results and Model details.
Avg pred var (ME)
This is the average prediction variance of an experimental design for a model with only the intercept and all main effects. This is one of the metrics used in the software to characterize the quality of an experimental design with respect to the precision with which predictions can be made using a model with only the intercept and all main effects. This is presented under Catalog Search.
Avg ρ (E1,E2)
This is the average correlation between any single effect column of type E1 with any single effect column of type E2 for an experimental design. The effect type E1 or E2 may correspond to MEs, IEs, QEs or SOEs. The correlation between two effect columns is an indication of how independently their effects can be estimated from each other. The lower the correlation, the more independent are the estimates of the effects. This information is presented under the aliasing tab in Detailed comparison.
B
Balance (ME)
If true, all design columns of the experimental design have the same number of upper and lower levels. This information is presented under the aliasing tab in Detailed comparison.
BIC
This is the value for the Bayesian Information Criterion for the corresponding linear regression model. This is one of the metrics used in the software to characterize the statistical quality of a linear regression model. The lower the value, the better is the model according to this metric. This metric is presented during modeling under Model details.
Blocking
If True, the experimental design has one column associated with a blocking (or grouping) variable. A blocking variable or a nuisance variable is a variable that you do not directly control but which can impact your results if not taken into account. For all experimental designs previously selected using catalog search (which can be found under My DoE items), the existence or non-existence of a blocking variable is indicated using True/False. The option to include an experimental design with a blocking variable is presented in Define your experiment under Catalog Search. Use this link to learn more about blocking variables.
C
Center points
Number of test combinations where the settings for all the three-level quantitaive factors are set to the middle levels of their respective individual input ranges. In some cases, this may be desired by the user to test for non-linear effects by performing experiments at the middle levels of all three-level quantitative factors more than once. As a side effect, the higher the number of center points, the more replicates you have in your design. This is presented under Catalog Search.
Condition number
This is the ratio between the maximum and minimum eigen value of the information matrix of the model matrix. Similar to VIF, this number quantifies the degree of multicollinearity between terms in your model. As a rule of thumb, if the condition number is between 10 and 30, this is considerate to indicate a moderate level of multicollinearity, where as values greater than 30 indicate a strong level of multicollinearity. This is presented under Model details.
Corner
If True, the experimental design has at least one test combination where the levels for all three-level quantitative factors are set to their respective extreme (either upper or lower) values in their individual input ranges. In some situations, this may be desired by the user when testing extreme combinations of the input variables is considered to be informative. This is presented under Catalog Search in the summary table and also under Detailed comparison.
D
D(Model)
This is the D-efficiency of an experimental design for a given model including the intercept. This is one of the metrics used in the software to characterize the quality of an experimental design with respect to its ability to screen active (i.e statistically significant) effects among all the model terms. The higher the value for D-efficiency, the better is the experimental design according to this metric. For example, D(ME), refers to the D-efficiency of an experimental design for a main-effects model including the intercept. This is presented under Catalog Search.
DF pure error
For an experimental design, this is the number of degrees of freedom available to estimate the pure error, which is defined as the number of replicated points in the design, and is calculated as the difference between the total number of runs in and the number of runs with unique test combinations. The higher the degrees of freedom to estimate the pure error (i.e the greater number of replicated test combinations), the better is the estimate of the RMSE (which is the estimate of the run-to-run standard deviation), which in turn makes the statistical significance tests more powerful. This is presented under Catalog Search and .
F
Foldover
If this is true for a design, then this means that except for the center runs (test combinations where all three-level quantitative factors are set to their middle levels), all other test combinations have their opposite test combinations also present in the same design. The majority of OMARS designs are also foldover designs, however, there are non-foldover OMARS too available in the software. Non-foldover OMARS designs often possess capabilities to fit larger and more complex regression models than their foldover counter parts. This is presented under Design detail.
G
G (ME)
This is the G-efficiency of an experimental design for a given model including the intercept. This is one of the metrics used in the software to characterize the quality of an experimental design with respect to the precision with which predictions can be made using the given model including the intercept. The higher the value for G-efficiency, the better is the experimental design according to this metric. For example, G(ME), refers to the G-efficiency of an experimental design for a main-effects model including the intercept. This is presented under Catalog Search.
I
IE
Two-factor interaction or IE columns are obtained by multiplying main-effect columns corresponding to two different factors. Such effects allow the user to study whether the effect of changing the level setting of one input variable on the response variable is dependent on the specific level that is set for another input variables. Most modern processes always have some interaction effects at play. Hence, such type of effects are always interesting to study.
M
Max ρ (E1,E2)
Maximum correlation between any single effect of type E1 with any single effect of type E2. The effect type E1 or E2 may correspond to MEs, IEs, QEs or SOEs. This information is presented under Catalog Search.
ME
Main effect. These are the first-order linear effects that are considered in the linear regression model.
Min Pow (ME,IE)
Minimum statistical power to detect any single active IE under a base model with the intercept and all MEs preincluded (assuming α=0.05, signal-to-noise ratio equal to 1). This information is presented under Catalog Search.
Min Pow (ME,ME)
Minimum statistical power to detect any single active ME under a base model with the intercept and all MEs preincluded (assuming α=0.05, signal-to-noise ratio equal to 1). This information is presented under Catalog Search.
Min Pow (ME,QE)
Minimum statistical power to detect any single active QE under a base model with the intercept and all MEs preincluded (assuming α=0.05, signal-to-noise ratio equal to 1). This information is presented under Catalog Search.
N
N
Number of tests in the design i.e run size of an experiment.
O
OMARS
If true, the experimental design is an OMARS design. For more information on OMARS designs click here. This information is presented under Design detail.
P
PEC(0,x) (Model)
When the user assesses designs with only two-level quantitative (or categorical) factors, the PEC(n,x) (Model) simplies to PEC(0,x) (Model).
PEC(n,x) (Model)
PEC - Projection estimation capacity. This is one of the metrics used in the software to characterize the quality of an experimental design with respect to its ability to estimate a variety of interesting models. This is presented under Catalog Search. For example, if PEC (n,x)(ME+IE) = 4.2 for a design, then this means that the design is capable of estimating a model with the intercept, all MEs and all IEs for any single subset of ‘n’ three-level quantitative factors with any single subset of 4 two-level quantitative (or categorical) factors, and can estimate the same type of model for any single subset of ‘n’ three-level quantitative factors with 20% (0.2) percent of all possible subsets of 5 two-level quantitative (or categorical) factors. Refer here for more info.
PEC(x,0) (Model)
When the user assesses designs with only three-level quantitative factors, the PEC(x,n) (Model) simplies to PEC(x,0) (Model).
PEC(x,n) (Model)
PEC - Projection estimation capacity. This is one of the metrics used in the software to characterize the quality of an experimental design with respect to its ability to estimate a variety of interesting models. This is presented under Catalog Search. For example, if PEC (x,n)(ME+IE) = 4.2 for a design, then this means that the design is capable of estimating a model with the intercept, all MEs and all IEs for any single subset of 4 three-level quantitative factors with any single subset of ‘n’ two-level quantitative (or categorical) factors, and can estimate the same type of model for any of the 20% (0.2) percent of all possible subsets of 5 three-level quantitative factors with any single subset of ‘n’ two-level quantitative (or categorical) factors. Refer here for more info.
PoS
Probability of Success or PoS is a metric used to describe how well a certain combination of the settings of the input variables produces the desired response variables within the user specified tolerance intervals. This is presented under Optimization. For more information on Probability of Success, click here.
PRESS
This is the value for the Predicted residual error sum of squares for the corresponding linear regression model. This is one of the metrics used in the software to characterize the statistical quality of a linear regression model. The lower the value, the better is the model according to this metric. This metric is presented during modeling under Model details.
Q
QE
Quadratic effect or QE columns are obtained by multiplying a main-effect column corresponding to a specific factor by itself. It is possible to study the non-linear effects of certain factors by including their respective QE in the model.
R
Rank(ME+SOE)
Rank of a model matrix with all MEs and SOEs. This number represents the total number of effects (from the set of all MEs and SOEs) that can be jointly estimated in a single model. This number directly reflects the size of the largest complex model that can be estimated using the given experimental design. This metric is presented during modeling under Catalog Search and Model details.
RSE
Relative standard error of estimates or RSE refers to the standard error for the estimates for each model term assuming $\sigma^2$ (i.e run-to-run process error variance) is equal to one. In simple terms, this quantifies the size of the intervals around an estimated value for a coefficient in your regression model.
The lower the RSE for a specific term in your model, the smaller the size of the interval around its estimate, and therefore, the greater the likelihood of detecting such a term as active (i.e statistically significant).
Replicates
Number of unique test combinations that have more than one occurrence in the experimental design. Having more replicates in the design, primarily, has one advantage and one disadvantage.
The advantage is that larger numbers of replicates in a design allows you to more accurately divide the estimated error variance in your model into two parts: the part that accounts for the variance that is not captured by the terms included in your model (commonly referred to as the lack-of-fit error variance) and the part that accounts for the variance from the average values for each test combination replicated more than once (commonly referred to as the pure error variance). Comparing these two of variance is what is commonly referred to as a lack-of-fit test. This test gives you an indication on whether you are missing some terms in your model. This test can only be performed when there is at least one replicate (ideally more) in the design.
The disadvantage is that the having more replicates (i.e duplicated runs) in the design instead of more unique ones, results in a design which can fit a model with only a smaller number of terms.
RMSE
Root mean squared error is the estimate of the run-to-run standard deviation after fitting a given model. This is one of the metrics used in the software to characterize the statistical quality of a linear regression model. This metric is presented during modeling under Model details.
R2 adj
This is the value for the $R^2$ adjusted for the corresponding linear regression model. This is one of the metrics used in the software to characterize the statistical quality of a linear regression model. The higher the value, the better is the model according to this metric. This metric is presented during modeling under Model details.
S
SOE
Any two-factor interaction column or a quadratic effect column is referred to as the second order effects (two-factor interaction effects and quadratic effects)
V
VIF
Variance inflation factor or VIF refers to the degree to which the variance associated with a given estimate (i.e coefficient) of a model term is inflated due to multicollinearity with other terms in the same model. As a rule of thumb, if the VIF value for a term is greater than 5, this indicates that the term is highly correlated with one or more other terms in the same model.
Y
y-predicted
Prediction value for the average value for a response variable based on the given regression model. This is presented under Profilers during the optimization step.
Page last modified on 3 March 2025