Errors of Observation and their Treatment

In: Springer eBook Collection

Abstract

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.