Data Analysis Statistical and Computational Methods for Scientists and Engineers

1. 1 Typical Problems of Data Analysis Every branch of experimental science, after passing through an early stage of qualitative description, concerns itself with quantitative studies of the phe­ nomena of interest, i. e. , measurements. In addition to designing and carrying out the experiment, an importal1t task is the accurate evaluation and complete exploitation of the data obtained. Let us list a few typical problems. 1. A study is made of the weight of laboratory animals under the influence of various drugs. After the application of drug A to 25 animals, an average increase of 5 % is observed. Drug B, used on 10 animals, yields a 3 % increase. Is drug A more effective? The averages 5 % and 3 % give practically no answer to this question, since the lower value may have been caused by a single animal that lost weight for some unrelated reason. One must therefore study the distribution of individual weights and their spread around the average value. Moreover, one has to decide whether the number of test animals used will enable one to differentiate with a certain accuracy between the effects of the two drugs. 2. In experiments on crystal growth it is essential to maintain exactly the ratios of the different components. From a total of 500 crystals, a sample of 20 is selected and analyzed.

1. Introduction; 2. Probabilities; 3. Random Variables; 4. Computer- Generated Random Numbers: The Monte Carlo Method; 5. Some Important Distributions and Theorems; 6. Samples; 7. The Method of Maximum Likelihood; 8. Testing Statistical Hypotheses; 9. The Method of Least Squares; 10. Function Minimization; 11. Analysis of variance; 12. Linear and Polynomial Regression; 13. Time-Series Analysis; Appendix A: Matrix Calculation; Appendix B: Combinatorics; Appendix C: Formulas and Programs for Statistical Functions; Appendix D: The Gamma Function and Related Functions. methods and Programs for Their Computation; Appendix E: Utility Programs; Appendix F: The Graphics Programming Package GRPACK; Appendix G: Software Installation and technical Hints; Appendix H: Collection of Formulas; Appendix I: Statistical Tables; Literature; List of Computer Programs; Register.