Analysis of Mixture Designs

Analyzes balanced and unbalanced constrained mixture designs; the analysis of mixture experiments amounts to a multiple regression with the intercept set to zero. The mixture constraint - that the sum of all components must be constant - can be accommodated by fitting multiple regression models that do not include an intercept term. See also the General Linear Models (GLM) facilities for options to analyze mixture experiments, and experiments involving mixture and process (non-mixture) variables.

General

Element Name Description
Detail of computed results reported Specifies the detail of computed results reported. If Minimal detail is requested, Statistica 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.
Model 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.
Mixture tolerance Specifies a value used while verifying the mixture constraint, i.e., that the component values for each run sum to a constant +/- tolerance (the mixture total, plus or minus the tolerance value).
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.
Standardized effects If this option is selected, the Pareto chart of effects and the probability plot of effects will be produced for the standardized effects, that is, for the effects divided by their respective standard errors.
Original components If this option is selected, the normal plot of coefficients and the Pareto chart will be produced for the coefficients estimated for the original (untransformed) components (and not for the coefficients pertaining to the pseudo-components).
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).
Correlation matrix 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.
Review factor settings Choose this option to review the factor settings (high, low) for factors in the 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.