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Negative value of response in central composite design

Discussion in 'DOE - Design of Experiments' started by Handy Elfeky, Mar 12, 2024.

  1. Handy Elfeky

    Handy Elfeky New Member

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    I have used CCD under RSM to design a set of 13 experiments for 2 factors of 2 levels. In the attached images the results of the responses I got. The response is Max. absorbance and the negative value was replaced by zero. When the absorbance 0 is used, The Predicted R² is not as close to the Adjusted R² as one might normally expect; i.e. the difference is more than 0.2. This may indicate a large block effect or a possible problem with the model and/or data. In addition, the Normal Plot of Residuals is, I think, s-shaped. when the negative results were included in the model. The situation was different: i.e. The Predicted R² was close to the Adjusted R² and the Normal Plot of Residuals looked good. I don't know if it is possible to show the model with negative absorbance, Does it make sense?
     

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  2. Miner

    Miner Moderator Staff Member

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    Obviously changing the negative values to zero is not appropriate. I am not very familiar with absorbance, but based on the description below from Copilot, it might be possible that your model will work despite these negative values, if they are simply negative compared to a reference. The only way to be certain is to use it to make some predictions then run some verification experiments.

    If negative values are not physically possible, your only option is to change the design and rerun the experiment.
    Your design options are:
    1. Relocate your circumscribed CCD along the path of steepest ascent. (Recommended)
    2. Use an inscribed CCD; A face-centered CCD will not work unless you relocate it since one of the corner points had a negative value.
    3. Use a Box-Behnken design.
    Note: Per COPILOT AI:
    • Negative absorbance occurs when the sample transmits more light than the reference. This can happen due to various reasons, such as scattering of light or a lower analyte level in the sample compared to the blank.
     
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  3. Handy Elfeky

    Handy Elfeky New Member

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    Dear Miner,

    Thanks for your reply. In fact the negative absorbance response due to the tested sample contained some colloidal particles which affected the absorbance measurements. I just confused concerning showing this results for publication although the model analysed the data in a good manner. In addition I found that the predicted values in the model is also negative if they are not close to the actual values. I have already made some change in the design but as the low and high values is desirable to be used I'm expecting to face the same negative value in some experiments. When I used negative results for predictions, the solution from the model for verification experiments I think will be acceptable as the verification experiments are almost similar to the experiments with positive absorbance.
    I appreciate your help.
     
  4. Miner

    Miner Moderator Staff Member

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    If those samples were contaminated, you should run those experiments again.