Analysing your Results (Effects)

 

Under the Analysis node on the left-hand tree structure, click on each response you want to analyse and simply work your way along the analysis buttons from left-to-right. For the Transform, start with None and proceed by clicking on the Effects button.
 

 

The Half-Normal plot & Pareto Chart provide a visual means of identifying important effects and assessing their statistical significance. Click on the effects you think are important – on the former plot these are the effects farthest to the right and away from the green triangles, which represent differences between the replicated points or background noise,

 

while the Pareto Chart provides statistical thresholds to test the significance of the effects selected

 

 

Example: In this example, A: Magnesium Stearate, B: Granulation Paste Type & D: Granulation Blend Time, together with the AD interaction (dependent relationship between Magnesium Stearate & Granulation Blend Time) are the largest effects and statistically significant. Although the AB interaction on the half-normal plot is to the right of the line passing through the green triangles (noise) & the small effects which appear no different from the noise, it is not a statistically significant effect according to the Pareto Chart.

Aliasing: In the case of a fractionated design, you should always check the aliasing. Either click the Alias List button, or right click on an effect in a plot (e.g., AD is aliased with BC here). Since A and D are both significant large effects, it is more likely to be the AD rather than the BC interaction that contributes largely to this effect. Remember, main effects and 2-Factor Interactions are more common than 3-Factor Interactions. Choose the aliased effect which makes most sense to you to carry forward to the next step of the analysis. If in doubt you can always add or “augment” further runs to de-alias or untangle effects. (See the augmentation tipsheet)

Hierarchy: If Design Expert asks “Would you like the hierarchy corrected automatically?” respond “Yes”. This ensures that if you select an interaction, but not the main effects of the factors involved, DX will automatically include the main effects in order to preserve the hierarchy of your model and a suitable testing of its effects

Analysing your Results (ANOVA)

 

Mean Square column refers to the variance or signal associated with each term (e.g., variation in hardness due to Magnesium Stearate is 136.95, while residual or noise variation is just 1.12).

F Value, next column, is the signal-to-noise variance ratio (e.g., the signal or effect due to Magnesium Stearate is 122.26 times that due to the noise)

P-value, final column, is the probability of observing a signal-to-noise ratio as large as in the previous column purely by chance (i.e., the risk of you making the wrong the decision about the importance of an effect)

There are also tests for evidence of:

Curvature compares the average of the centre point results with the prediction at the centre of your design (c.f. Intercept Coefficient Estimate). The difference is the Centre Point Coefficient Estimate

Lack of Fit the ratio of variance due to effects not previously selected to include in your model with the Pure Error. If you fail to include large effects then this will inflate the Lack of Fit. Use effect and diagnostic plots (e.g., residuals (ei) vs. Factor) to identify potential effects to include to improve your model

Curvature: close agreement between your replicate observations can artificially lead to evidence of significant lack of fit or curvature. If you confirm there is real evidence of curvature, then interpret the Model Graphs with caution. Predictions made inside the low and high settings will be unreliable

ANOVA: By default the ANOVA results come with comments designed to help you interpret the output. If the annotations do not appear, select Annotated ANOVA on the View menu. Help to interpret any value on the output can be gained by highlighting the value and either pressing the F1 key or right clicking and selecting Help

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