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    What are the "Reduced" T^2 and Q Statistics?

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    Hotelling's T^2 (T-squared) and Q residuals (sum squared residuals) are often reported in units which are sensitive to the total number of variables in the data, and the number of components and particular preprocessing used for a model. As a result, comparison of values reported by different models, or setting a standard alarm level for all models requires normalizing the statistics.

    A common way to normalize the statistics is to divide by a confidence limit calculated from each model's particular data and parameters (In PLS_Toolbox and Solo, the default confidence limit is at the 95% level.) The Reduced Q and Reduced T^2 are simply the statistic divided by the corresponding confidence limit.


    In PLS_Toolbox and Matlab, you can view the exact value used to normalize by viewing the following fields in a model:

    q_limit = model.detail.reslim{1}
    t2_limit = model.detail.tsqlim{1}

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