Costas Christodoulides

The Statistical Analysis of Experimental Results

The way in which the results of experimental measurements can be best used in the extraction of conclusions relating to the magnitude measured is presented. The understanding of the concepts and methods presented in this chapter possibly constitute the main benefit the reader may derive from studying this book.

The Presentation of Numerical Results

The way in which numerical results should be presented are discussed. The S.I. system of units is also presented, as well as the basic rules that must be followed in its use for the presentation of experimental results.

The Three Basic Probability Distributions

The three basic probability distributions, Binomial or Bernoulli, Poisson and Normal or Gaussian, are briefly examined.

The Written Report of the Results of an Experiment

The presentation of the results of an experiment in written form is examined. The basic rules of this presentation for a report of the results of an experiment in an educational laboratory are given. An example of the written report of an actual experiment is presented.

The Method of Least Squares

The method of least squares is developed. The application of the method in the fitting of the best straight line or curve to a series of experimental results, with the aim of determining the relationship existing between two variables. The method is also used in finding the optimal solutions of systems of overdetermined linear equations.

Comparison and Rejection of Measurements

The matter of the rejection of a measurement is examined. Criteria, such as Chauvenet’s criterion for the rejection of data are discussed.

The Statistics of Radioactivity

The laws of Statistics find applications in the phenomenon of radioactivity. The disintegration of a nucleus is a random event which is not affected by the history of the nucleus or the conditions external to the nucleus. The probabilities that govern radioactive decay are evaluated.

Elements from the Theory of Errors

The general principles of the Theory of Errors are examined. This chapter provides new theoretical tools which may be used in the development of techniques in the analysis of experimental results.

The Propagation of Errors

Quite often, it is necessary to calculate the value of a quantity that was not measured directly but is expressed on terms of one or more quantities which have been measured and whose means and standard deviations are known. The evaluation of the standard deviation of this quantity is done taking into account the so-called propagation of errors from the quantities that have been measured to the derived quantity.

Basic Statistical Concepts

In order to understand the theory of errors, as well as the methods of analysis and presentation of experimental results, knowledge of the basic concepts of Probability Theory and Statistics is required. The purpose of this chapter is the concise presentation of the basic concepts from these fields that will be used in the book.