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Ph. D. ThesisPh. D. Thesis 6. Results  Multivariate Calibrations6. Results Multivariate Calibrations 6.1. PLS Calibration6.1. PLS Calibration 6.1.1. Wald-Wolfowitz Runs Test6.1.1. Wald-Wolfowitz Runs Test
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Ph. D. Thesis
  Table of Contents
  1. Introduction
  2. Theory Fundamentals of the Multivariate Data Analysis
  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
    6.1. PLS Calibration
      6.1.1. Wald-Wolfowitz Runs Test
      6.1.2. Durbin-Watson Statistics
      6.1.3. Results of Statistical Tests
    6.2. Box-Cox Transformation + PLS
    6.3. INLR
    6.4. QPLS
    6.5. CART
    6.6. Model Trees
    6.7. MARS
    6.8. Neural Networks
    6.9. PCA-NN
    6.10. Neural Networks and Pruning
    6.11. Conclusions
  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
Research Tutorials
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6.1.1.   Wald-Wolfowitz Runs Test

A good calibration of a relationship results in a random sequence of the positive and negative residuals of prediction. Calibrations with systematic errors show longer sequences of positive and negative residuals. For example, in figure 29 the mean residuals of R22 show only 3 sequences, first with negative signs, then with positive signs and finally with negative signs again. These sequences are also known as runs. The Wald-Wolfowitz method tests whether the number of runs is small enough or big enough for the null hypothesis of a random distribution of the signs to be rejected [232]. Thereby the number of positive and negative runs is compared with the tabulated value for the number of observations and for a given error level [233].

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