Data Analysis

1. Front Matter

   Pages i-xxxiv

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2. Introduction

   • Siegmund Brandt

   Pages 1-6

3. Probabilities

   • Siegmund Brandt

   Pages 7-16

4. Random Variables. Distributions

   • Siegmund Brandt

   Pages 17-48

5. Computer Generated Random Numbers. The Monte Carlo Method

   • Siegmund Brandt

   Pages 49-86

6. Some Important Distributions and Theorems

   • Siegmund Brandt

   Pages 87-132

7. Samples

   • Siegmund Brandt

   Pages 133-186

8. The Method of Maximum Likelihood

   • Siegmund Brandt

   Pages 187-211

9. Testing Statistical Hypotheses

   • Siegmund Brandt

   Pages 212-247

10. The Method of Least Squares

    • Siegmund Brandt

    Pages 248-331

11. Function Minimization

    • Siegmund Brandt

    Pages 332-395

12. Analysis of Variance

    • Siegmund Brandt

    Pages 396-412

13. Linear and Polynomial Regression

    • Siegmund Brandt

    Pages 413-426

14. Time Series Analysis

    • Siegmund Brandt

    Pages 427-440

15. Back Matter

    Pages 441-652

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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.

• Analysis of variance
• Experiment
• Monte Carlo method
• Normal distribution
• Random variable
• algorithms
• data analysis

From the reviews:

"The book is concise, but gives a sufficiently rigorous mathematical treatment of practical statistical methods for data analysis¿It can be of great use to all who are involved with data analysis." Physicalia

"... Serves as a nice reference guide for any scientist interested in the fundamentals of data analysis on the computer." The American Statistician

• Physics Department, University of Siegen, Siegen, Germany

  Siegmund Brandt

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