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Color coded table for easy interpretation

Table plots in The UnscramblerŽ X

The first part of the ANOVA table is a summary of the significance of the global model. If the p-value for the global model is smaller than 0.05, it means that the model explains more of the variations of the response variable than could be expected from random phenomena. In other words, the model is significant at the 5% level. The smaller the p-value, the more significant (and useful) the model is.

The error p-value should be large as the error should be random and not be explaining the variation in the response.

Total error should also have a small p-value, so that the model is valid.

Effect summary

This table plot gives an overview of the significance of all effects for all responses. There are three values per effect and per response:

  • Significance: This coded value indicates if the effect is significant for the specific response. See the Significance levels and associated codes table
  • Effect value: This is the value of the effect for the specific response variable. The bigger in absolute value the more important if the design variable
  • p-value: Result of the test of significance for the effect. See the Significance levels and associated codes table for more information
Effect Summary table

Effect Summary table

 
P-value Negative effect Positive effect Color code
>= 0.10 NS NS red
[0.10:0.05] ? ? yellow
[0.01:0.05] + pale green
[0.005:0.01] – – + + light green
\< 0.005 – – – + + + dark green
    Significance levels and associated codes

The sign and significance level of each effect is given as a code:

NS: non significant. ?: possible effect at the significance level 10%.

Note: If some of the design variables have more than 2 levels, the Effects Overview table contains stars (*) instead of ”+” and ”–” signs.

Analyze this table by:
Checking the Response Variables
Look for responses which are not significantly explained by any of the design variables (gray columns). This may be because there are errors in the data, these responses have very little variation, these responses are very noisy, or their variations are caused by non-controlled conditions which have not been included in the design.

Checking the Design Variables
Look for rows which contain many ”+” or ”–” signs and are green: these main effects or interactions dominate. This is how to detect the most important variables.

 

Response surface

This plot is used to find the settings of the design variables which give an optimal response value, and to study the general shape of the response surface fitted by the Response Surface model or the Regression model. It shows one response variable at a time.

This plot can appear in various layouts. The most relevant are:

  • Contour plot;
  • Landscape plot.
Interpretation: contour plot

Look at this plot as a map which tells how to reach the experimental objective. The plot has two axes: two predictor variables are studied over their range of variation; the remaining ones are kept constant. The constant levels are indicated in the RS table.

Interpretation: landscape plot

Look at this plot to study the 3-D shape of the response surface. Here it is obvious whether there is a maximum, a minimum or a saddle point.

Response surface plot, with contour layout Response surface plot, with landscape layout
Response surface plot, with contour layout Response surface plot, with landscape layout

The response values are displayed as contour lines, i.e. lines that show where the response variable has the same predicted value. Clicking on a line, or on any spot within the map, will show the predicted response value for that point, and the coordinates of the point (i.e. the settings of the two predictor variables giving that particular response value).

To interpret several responses together, print out their contour plots on color transparencies and superimpose the maps.

 

Response surface table

This table is used to set the parameters of the response surface.

Design variables
In a response surface only two design variables can vary the others are fixed.
To select the variables to vary tick/untick the box in the Display column.
To set the value for the fixed variable enter the value manually in the column Value to display. By default this value is the average value.
For category variables select one of the levels using the drop-down list.

Response variables
Only one response variable can be plot at a time. Select the variable to plot by ticking/unticking them.

Once all the modifications are done, click the Generate Surface button to generate a new response surface.

Response surface table
Response surface table

 

 

PLS-ANOVA Summary table

This table presents the effect values for all variables as well as their significance levels and p-values.

PLS-ANOVA Summary table

PLS-ANOVA Summary

 
P-value Negative effect Positive effect Color code
>= 0.10 NS NS red
[0.10:0.05] ? ? yellow
[0.01:0.05] + pale green
[0.005:0.01] – – + + light green
\< 0.005 – – – + + + dark green
    Significance levels and associated codes

NS: non significant.
?: possible effect at the significance level 10%.