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Ph. D. ThesisPh. D. Thesis 2. Theory – Fundamentals of the Multivariate Data Analysis 2. Theory – Fundamentals of the Multivariate Data Analysis 2.9. Measures of Error and Validation2.9. Measures of Error and Validation
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Ph. D. Thesis
  Table of Contents
  1. Introduction
  2. Theory – Fundamentals of the Multivariate Data Analysis
    2.1. Overview of the Multivariate Quantitative Data Analysis
    2.2. Experimental Design
    2.3. Data Preprocessing
    2.4. Data Splitting and Validation
    2.5. Calibration of Linear Relationships
    2.6. Calibration of Nonlinear Relationships
    2.7. Neural Networks – Universal Calibration Tools
    2.8. Too Much Information Deteriorates Calibration
    2.9. Measures of Error and Validation
  3. Theory – Quantification of the Refrigerants R22 and R134a: Part I
  4. Experiments, Setups and Data Sets
  5. Results – Kinetic Measurements
  6. Results – Multivariate Calibrations
  7. Results – Genetic Algorithm Framework
  8. Results – Growing Neural Network Framework
  9. Results – All Data Sets
  10. Results – Various Aspects of the Frameworks and Measurements
  11. Summary and Outlook
  12. References
  13. Acknowledgements
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2.9.   Measures of Error and Validation

Besides of the true-predicted plots, which will be introduced in section 3.4, the root mean square errors (RMSE) are used for the validation of the models in this work as it is one of the most common measures for the quality of calibrations and predictions in chemometrics:


Thereby  is the predicted concentration of the sample, yi is the true concentration of the sample and N is the total number of samples. The RMSE, which has the dimension and units of the concentrations predicted, is a strict measure of the error as it penalizes poor predictions by a quadratic term. For a relative measure of the error, the relative RMSE, which is also sometimes misnamed standard error of prediction (SEP) [41],[153],[154], is used in this work:

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