Data Analysis: Statistical and Computational Methods for Scientists and Engineers

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