Example of Analyzing a Simplex Centroid Design
main topic     interpreting results     session command     see also      

This example fits a model for the design created in Example of simplex centroid design. Recall that you are trying to determine how the proportions of the components in an herbal blend household deodorizer affect the acceptance of the product based on scent. The three components are neroli oil, rose oil, and tangerine oil. Based on the design points, you mixed ten blends. The response measure (Acceptance) is the mean of five acceptance scores for each of the blends.

1    Open the worksheet DEODORIZ.MTW.

2    Choose Stat > DOE > Mixture > Analyze Mixture Design.

3    In Responses, enter Acceptance. Click OK.

Session window output

Regression for Mixtures: Acceptance versus Neroli, Rose, Tangerine

 

 

Estimated Regression Coefficients for Acceptance (component proportions)

 

Term                Coef  SE Coef      T      P    VIF

Neroli             5.856   0.4728      *      *  1.964

Rose               7.141   0.4728      *      *  1.964

Tangerine          7.448   0.4728      *      *  1.964

Neroli*Rose        1.795   2.1791   0.82  0.456  1.982

Neroli*Tangerine   5.090   2.1791   2.34  0.080  1.982

Rose*Tangerine    -1.941   2.1791  -0.89  0.423  1.982

 

 

S = 0.490234    PRESS = 11.4399

R-Sq = 73.84%   R-Sq(pred) = 0.00%   R-Sq(adj) = 41.14%

 

 

Analysis of Variance for Acceptance (component proportions)

 

Source                DF   Seq SS   Adj SS   Adj MS     F      P

Regression             5  2.71329  2.71329  0.54266  2.26  0.225

   Linear              2  1.04563  1.56873  0.78437  3.26  0.144

   Quadratic           3  1.66766  1.66766  0.55589  2.31  0.218

     Neroli*Rose       1  0.15963  0.16309  0.16309  0.68  0.456

     Neroli*Tangerin   1  1.31728  1.31109  1.31109  5.46  0.080

     Rose*Tangerin     1  0.19075  0.19075  0.19075  0.79  0.423

Residual Error         4  0.96132  0.96132  0.24033

Total                  9  3.67461

Interpreting the results

The magnitudes of the coefficients for the three pure mixtures indicate that tangerine oil (7.448) and rose oil (7.141) produce deodorizers with higher acceptance levels than neroli oil (5.856).

Positive coefficients for two-blend mixtures indicate that the two components act synergistically or are complementary. That is, the mean acceptance score for the blend is greater than you would obtain by calculating the simple mean of the two acceptance scores for each pure mixture.

Negative coefficients indicate that the two components are antagonistic towards one another. That is, the mean acceptance score is lower than you would obtain by calculating the simple mean of the two acceptance scores.

The neroli oil by tangerine mixture is the only two-blend mixture that might be judged as significant (t = 2.34; p = 0.08)

For a general discussion of analysis results, see [1].