Mehr zum Titel: | 1. Errors of Observation1 Accidental and systematic errors -- 2 Errors and fractional errors -- 3 Estimate of error -- 4 Estimate of the error in compound quantities -- 5 Error in a product -- 6 Error in a quotient -- 7 Use of the calculus -- 8 Error in a sum or difference -- 2. Some Statistical Ideas -- 9 Frequency distributions -- 10 The mean -- 11 Relative frequency -- 12 The median -- 13 Frequency curves -- 14 Measures of dispersion -- 15 The range -- 16 The mean deviation -- 17 The standard deviation -- 18 Evaluation of standard deviation, ? -- 19 Sheppard’s correction -- 20 Charlier’s checks -- 21 The mean and standard deviation of a sum -- 22 Certain special frequency distributions -- 23 The binomial distribution -- 24 The Poisson distribution -- 25 The normal distribution -- 26 Relation between a normal and a binomial distribution -- 27 The mean deviation of a normal distribution -- 28 Area under the normal error curve -- 29 Sampling, standard error of the mean -- 30 Bessel’s formulae -- 31 Peters’ formulae -- 32 Fitting of a normal curve -- 33 Other frequency distributions -- 3. Theory of Errors -- 34 The normal or Gaussian law of error -- 35 Applicability of the normal law of error -- 36 Normal error distributions -- 37 Standard error of a sum or difference -- 38 Standard error of a product -- 39 Standard error of a compound quantity -- 40 Method of least squares -- 41 Weighted mean -- 42 Standard error of weighted mean -- 43 Internal and external consistency -- 44 Other applications of the method of least squares, solution of linear equations -- 45 Solution of linear equations involving observed quantities -- 46 Curve fitting -- 47 Line of regression -- 48 Accuracy of coefficients -- 49 Other curves -- References. |
Inhalt: | 1. Errors of Observation -- 1 Accidental and systematic errors -- 2 Errors and fractional errors -- 3 Estimate of error -- 4 Estimate of the error in compound quantities -- 5 Error in a product -- 6 Error in a quotient -- 7 Use of the calculus -- 8 Error in a sum or difference -- 2. Some Statistical Ideas -- 9 Frequency distributions -- 10 The mean -- 11 Relative frequency -- 12 The median -- 13 Frequency curves -- 14 Measures of dispersion -- 15 The range -- 16 The mean deviation -- 17 The standard deviation -- 18 Evaluation of standard deviation, ? -- 19 Sheppard’s correction -- 20 Charlier’s checks -- 21 The mean and standard deviation of a sum -- 22 Certain special frequency distributions -- 23 The binomial distribution -- 24 The Poisson distribution -- 25 The normal distribution -- 26 Relation between a normal and a binomial distribution -- 27 The mean deviation of a normal distribution -- 28 Area under the normal error curve -- 29 Sampling, standard error of the mean -- 30 Bessel’s formulae -- 31 Peters’ formulae -- 32 Fitting of a normal curve -- 33 Other frequency distributions -- 3. Theory of Errors -- 34 The normal or Gaussian law of error -- 35 Applicability of the normal law of error -- 36 Normal error distributions -- 37 Standard error of a sum or difference -- 38 Standard error of a product -- 39 Standard error of a compound quantity -- 40 Method of least squares -- 41 Weighted mean -- 42 Standard error of weighted mean -- 43 Internal and external consistency -- 44 Other applications of the method of least squares, solution of linear equations -- 45 Solution of linear equations involving observed quantities -- 46 Curve fitting -- 47 Line of regression -- 48 Accuracy of coefficients -- 49 Other curves -- References. This little book is written in the first place for students in technical colleges taking the National Certificate Courses in Applied Physics; it is hoped it will appeal also to students of physics, and pernaps chemistry, in the sixth forms of grammar schools and in the universltIes. For wherever experimental work in physics, or in science generally, is undertakcn the degree of accuracy of the measurements, and of the res,!lts of the experiments, must be of the first importance. Every teacher of experimental physics knows how "results" given to three or four decimal plaees are often in error in the first place; students suffer from "delusions of accuracy. " At a higher level too, more experieneed workers sometimes claim a degree of accuracy which cannot be justified. Perhaps a considera tion of the topics discussed in this monograph will stimulate in students an attitude to experimental results at onee more modest and more profound. The mathematical treatment throughout has been kept as simple as possible. It has seemed advisable, however, to explain the statistical concepts at the basis of the main considerations, and it is hoped that Chapter 2 contains as elementary an account of the leading statistical ideas involved as is possible in such small compass. It is a necessary link between the simple introduction to the nature and estimation of errors given in Chapter 1, and the theory of errors discussed in Chapter 3. |
