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.
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Random Variables Distributions
of Two Variables Conditional Probability
Computer Generated Random Numbers
Some Important Distributions and Theorems
The Method of Maximum Likelihood
Testing Statistical Hypotheses
Time Series Analysis
A Matrix Calculations
The Gamma Function and Related Functions
E Utility Programs
F The Graphics Programming Package GRPACK
G Software Installation and Technical Hints
H Collection of Formulas
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Data Analysis: Statistical and Computational Methods for Scientists and ...
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approximation asymmetric errors binomial distribution CALLING SEQUENCE characteristic function Cholesky decomposition coefficients computes confidence limits confidence region coordinates corresponding covariance ellipse covariance matrix data points defined degrees of freedom Demonstrate Subprogram determined DIMENSION distribution function DOUBLE PRECISION A-H.O-Z DOUBLE PRECISION FUNCTION END IF END equations estimator example programs expectation value FORTRAN function value Gaussian distribution given graphics histogram hypothesis IMPLICIT DOUBLE PRECISION INPUT ARGUMENTS interval least-squares likelihood function linear m x n matrix Main Program measured values measurement errors method minimization Monte Carlo method n-vector NSTEP number of degrees obtain orthogonal OUTPUT ARGUMENTS parameters plot Poisson distribution polyline polynomial probability density problem procedure quantile quantities random numbers random variable result routines sample Sect singular value decomposition solution standard deviation standard normal distribution subdirectory Subroutine sum of squares symmetric transformation uniform distribution USERFN vector width window workstation x2-distribution x2-test zero