Hotelling´s T2 statistic is the multivariate counterpart of the Student´s t and is used in The Unscrambler® X as a powerful tool for outlier detection in many applications. Outlier statistics are used in identifying if samples are different to those used in developing a calibration and for samples that are predicted based on a calibration model.
The Hotelling´s T2 is a measure of how extreme a sample is relative to the model. The Hotelling´s T2 limit is set during the model building stage with user-specified significance level (0.1, 0.5, 1.0, 5.0, 10.0, and 25.0%). A Hotelling´s T2 ellipse can be drawn on a 2-D scores plot in The Unscrambler® X using this icon with the significance level set using the dropdown next to it (default is 5%).
Further plots of Samples vs. Hotelling´s T2 as a line plot are available as one of the standard PLS regression plots. The limit serves as the outlier limts for newly measured samples and those exceeding the limits are deemed outliers. Such samples are well explained by the model but represent extreme variation and are far from the model center. They should be further investigated and a determination made on whether to remove them from a model. During prediction and process monitoring outlier statistics are powerful tools for identifying if samples are different to those used in the calibration set. Such outlier statistics are used for detecting process deviations, potential process upsets or measurement issues.
The plots for this are available as one of the outputs in the Predict function in The Unscrambler® X. The Hotelling´s T2 limit is calculated based on the calibration samples, and a Contribution plot for the Hotelling´s T2 plot can aid in finding the root cause of an outlying sample. The contribution values for prediction are computed, and available in the Results Folder for plotting.