# Data Analysis: Statistical and Computational Methods for Scientists and Engineers

Springer Science & Business Media, Nov 25, 1998 - Science - 652 pages
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.

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### Contents

 Probabilities 7 Random Variables Distributions 17 of Two Variables Conditional Probability 27 Computer Generated Random Numbers 49 Some Important Distributions and Theorems 87 Samples 133 The Method of Maximum Likelihood 187 Testing Statistical Hypotheses 212
 Time Series Analysis 427 A Matrix Calculations 441 B Combinatorics 525 The Gamma Function and Related Functions 545 E Utility Programs 558 F The Graphics Programming Package GRPACK 567 G Software Installation and Technical Hints 595 H Collection of Formulas 609

 The Method of Least Squares 248 Function Minimization 332 Analysis of Variance 396 Linear and Polynomial Regression 413
 Statistical Tables 624 Literature 636 Index 645 Copyright