Analysis of 3**(K-p) and Box-Behnken Designs

Analyzes balanced and unbalanced 3**(K-p) designs, Box-Behnken designs, or other 3-level factorial designs, with or without blocking. The program will compute a complete analysis, estimate factor effects and regression coefficients, produce a large number of additional diagnostic results and graphs to help assess the goodness of fit for the model and model adequacy, etc., and compute various residual statistics for each run (observation). Note: You can also use the General Linear Models facilities to analyze unbalanced and incomplete designs of any complexity.

General

Element Name Description
Detail of computed results reported Detail of reported results; if Minimal detail is requested the program will compute factor effects and regression coefficients, the overall ANOVA table, and the Pareto chart of effects. At the Comprehensive Level of detail, the program will also report normal and half-normal probability plots of effects, and report and plot means. At the All results Level of detail, the program will also report surface and contour plots for the fitted model (for designs with fewer than 7 factors). If residual analyses are requested, different residual statistics and graphs are also reported at the Comprehensive and All results Level of detail.
Blocking Indicate whether the design is blocked. If the experiment involves blocking, the categorical predictor variable that contains the blocking information (i.e., the codes to indicate to which block each experimental run belongs) must be the first variable in the list of categorical predictors (this is the default arrangement of blocking and experimental factors if the design was created via the standard Experimental Design tools).
Model, include Determines which terms will be included in the model. All ANOVA results, effect estimates, predicted and residual values, etc. will be computed based on this model.
Centered/scaled polynomials. When the Use centered & scaled polynomial option is selected (the default), the original factor settings are recoded so that the effect estimates are comparable in size to the linear main effect estimates. When this option is cleared, the coding for the quadratic main effects is the result of squaring the +/-1 coding for the linear main effects. In that case, the effect estimates are not comparable in size to the linear effect estimates.
ANOVA error Term Choose between two error terms for the analyses; the selected error term will be used in all tests for statistical significance and in the computation of standard errors. Note that Pure error will be estimated from duplicated (identical) experimental runs, so if no such runs are available this option is not applicable.
p, for confidence limits Specifies a probability value for establishing confidence intervals for parameter estimates, predicted responses, etc.
p, for highlighting. Specifies a probability (alpha) value that will be used for highlighting significant results in various results spreadsheets.
Generates data source, if N for input less than Generates a data source for further analyses with other Data Miner nodes if the input data source has fewer than k observations, as specified in this edit field; note that parameter k (number of observations) will be evaluated against the number of observations in the input data source, not the number of valid or selected observations.

Design Properties

Element Name Description
Displays design Displays a spreadsheet showing the unique runs (those with unique combinations of factor settings) in the experiment. In addition, for each unique run, STATISTICA computes the mean, standard deviation, and standard error of the mean (if there is more than one run for the respective unique combination of factor settings).
Correlations X'X Displays a correlation matrix of the columns of the current design matrix (X'X).
Correlations of effects Choose this option to compute a correlation matrix of all effects in the current design.

Residual Analysis

Element Name Description
Residual analysis Creates predicted and residual statistics for each run, and compute various results spreadsheets and graphs for these values (depending on the Level of detail selected for the reported results).
Creates statistics If the Extended residual statistics option is selected, the results spreadsheet will report for each run (observation) various residual statistics (in addition to the simple predicted and residual values), such as Mahalanobis distances, deleted residuals, etc.
Plots residuals Choose which type of residual values to use in plots; if the Plot Raw residuals option is selected, residual plots will use the raw residuals for each dependent variable for each case or run as the values to be plotted. If the Studentized deleted residuals option is selected, studentized deleted residuals will be plotted.

Box-Cox Transformation

Element Name Description
Box Cox transformation Creates (find) an optimal lambda value for the Box-Cox transformation; based on the computed value of lambda, you can determine the transformation from the family of power transformations (Box-Cox transformations) that minimizes the error variability (the unpredicted variation) in the dependent variable for the current model.
Max number of iterations Specifies the maximum number of iterations for the iterative search for the best value of lambda.
Minimum value of lambda You can specify the range (minimum, maximum) of values from which to search for the maximum likelihood estimate of lambda.
Maximum value of lambda You can specify the range (minimum, maximum) of values from which to search for the maximum likelihood estimate of lambda.
Delta for convergence, 1E-. Specifies the negative exponent for a base-10 constant Delta (delta = 10^-sdelta); the default value is 5 (.00001). This value is used as the target difference in successive estimates of Lambda that will terminate the search.

Profiling

Element Name Description
Displays profiling Displays profiling to inspect the predicted values for the dependent variables at different combinations of levels of the independent variables, to specify desirability functions for the dependent variables, and to specify a search for the levels of the independent variables that produce the most desirable response on the dependent variables.
Set factors at Use the options in the Set factors at group box to specify the current levels of the predictor variables for the prediction profile compound graph and for surface and contour plots.
User specified values Specifies the current level of each predictor variable.
Use factor grid Use the Factor grid options to specify the experimental range and the grid points for each of the predictor variables in the analysis.
Factor grid minimum Specifies the minimum values in the grid for the factors.
Factor grid maximum Specifies the maximum values in the grid for the factors.
Number of steps Specifies the number of intervals in the grid for the factors.

Desirability

Element Name Description
Show desirability function Displays profiling to inspect the predicted values for the dependent variables at different combinations of levels of the independent variables, to specify desirability functions for the dependent variables, and to specify a search for the levels of the independent variables that produce the most desirable response on the dependent variables.
Low values Specifies the low values for the dependent variables, below which the response is undesirable.
Medium values Specifies the medium value for the dependent variable, at which the response becomes increasingly desirable as it approaches the target value.
High values Specifies the high value for the dependent variable, above which the response is undesirable.
Desirability low values Specifies the desirability low values for the dependent variables, below which the response is undesirable.
Desirability medium values Specifies the desirability medium values for the dependent variables, below which the response is undesirable.
Desirability high values Specifies the desirability high values for the dependent variables, below which the response is undesirable.
s (Curvature, low) The desirability of responses need not decrease (or increase) linearly between inflection points in the desirability function. Perhaps there is a "critical region" close to a desired, intermediate response on a dependent variable beyond which the desirability of the response at first drops off very quickly, but drops off less quickly as the departure from the "targeted" value becomes greater. To model this type of desirability function requires "curvature" parameters to take into account the nonlinearity in the "falloff" of desirability between inflection points. In the s parameter and t parameter boxes, you can specify a value for the exponent of the desirability function (from 0.0 up to 50, inclusive) representing the curvature in the desirability function between the low and medium inflection points of the function, and between the medium and high inflection points of the function, respectively.
t (Curvature, high) The desirability of responses need not decrease (or increase) linearly between inflection points in the desirability function. Perhaps there is a "critical region" close to a desired, intermediate response on a dependent variable beyond which the desirability of the response at first drops off very quickly, but drops off less quickly as the departure from the "targeted" value becomes greater. To model this type of desirability function requires "curvature" parameters to take into account the nonlinearity in the "falloff" of desirability between inflection points. In the s parameter and t parameter boxes, you can specify a value for the exponent of the desirability function (from 0.0 up to 50, inclusive) representing the curvature in the desirability function between the low and medium inflection points of the function, and between the medium and high inflection points of the function, respectively.

Desirability Options

Element Name Description
Intervals Use the options in the Intervals group box to determine which intervals are shown along with the predicted values on the prediction profile compound graph.
Search options Use the options in the Search options (for optimum desirability) group box to specify the search for the optimum response desirability, either using general function optimization or using optimum desirability at exact grid points.
Show Spreadsheets with plotted values Specify that spreadsheets with profile plot data be produced along with the compound graph of the prediction profiles for each of the dependent variables.
Label conf/pred limits for pred. values Specify that confidence/prediction limits are labeled on the compound graph of the prediction profiles for each of the dependent variables.
Show text labels for factor settings Display the text labels for the dependent variables on the compound graph of the prediction profiles.
Fit options for desirability surface/contours Several methods are available for fitting surfaces/contours to the desirability values for surface/contour plots. The Spline method is the default, but you can select the Quadratic surface, Least squares, or Negative exponential method by selecting the respective option button.
Show the grid points Specify grid points to be shown on contour and surface plots for each of the dependent variables.