6.1.1. Wald-Wolfowitz Runs Test (Dr. Frank Dieterle)

Frank Dieterle

Ph. D. Thesis

6. Results – Multivariate Calibrations

6.1. PLS Calibration

6.1.1. Wald-Wolfowitz Runs Test

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Ph. D. Thesis
	Abstract
	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
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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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