Statistics and Chemometrics for Analytical Chemistry

TLDR: In this article, the authors present a set of confidence limits of the geometric mean for a log-normal distribution for a given value and the confidence limits for a large sample for a small sample.

Abstract: 1 Introduction 11 Analytical problems 12 Errors in qunatitative analysis 13 Types of error 14 Random and systematic errors in titrimetric analysis 15 Handling systematic errors 16 Planning and design of experiments 17 Calculators and computers in statistical calculations 2 Statistics of Repeated Measurements 21 Mean and standard deviation 22 The distribution of repeated measurements 23 Log-normal distribution 24 Definition of a 'sample' 25 The sampling distribution of the mean 26 Confidence limits of the mean for large samples 27 Confidence limits of the mean for small samples 28 Presentation of results 29 Other uses of confidence limits 210 Confidence limits of the geometric mean for a log-normal distribution 211 Propagation of random errors 212 Propagation of systematic errors 3 Significance Tests 31 Introduction 32 Comparison of an experimental mean with a known value 33 Comparison of two experimental means 34 Paired t-test 35 One-sided and two-sided tests 36 F-test for the comparison of standard deviations 37 Outliers 38 Analysis of variance 39 Comparison of several means 310 The arithmetic of ANOVA calculations 311 The chi-squared test 312 Testing for normality of distribution 313 Conclusions from significance tests 314 Bayesian Statistics 4 The Quality of Analytical Measurements 41 Introduction 42 Sampling 43 Separation and estimation of variances using ANOVA 44 Sampling strategy 45 Quality control methods - Introduction 46 Stewhart charts for mean values 47 Stewhart charts for ranges 48 Establishing the process capability 49 Average run length: cusum charts 410 Zone control charts (J-charts) 411 Proficiency testing schemes 412 Method performance studies (collaborative trials) 413 Uncertainty 414 Acceptable sampling 415 Method validation 5 Calibration Methods in Instumental Analysis 51 Introduction: instrumentational analysis 52 Calibration graphs in instrumental analysis 53 The product-moment correlation coefficient 54 The line of regression of y on x 55 Errors in the slope and intercept of the regression line 56 Calculation of a concentration and its random error 57 Limits of detection 58 The method of standard additions 59 Use of regression lines for comparing analytical methods 510 Weighted regression lines 511 Intersection of two straight lines 512 ANOVA and regression calculations 513 Curvilinear regression methods - Introduction 514 Curve fitting 515 Outliers in regression 6 Non-parametric and Robust Methods 61 Introduction 62 The median: initial data analysis 63 The sign test 64 The Wald-Wolfowitz runs test 65 The Wilcoxon signed rank test 66 Simple tests for two independent samples 67 Non-parametric tests for more than two samples 68 Rank correlation 69 Non-parametric regression methods 610 Robust methods: introduction 611 Simple robust methods: trimming and winsorization 612 Further robust estimates of location and spread 613 Robust ANOVA 614 Robust regression methods 615 Re-sampling statistics 616 Conclusions 7 Experiimental Design and Optimization 71 Introduction 72 Randomization and blocking 73 Two-way ANOVA 74 Latin squares and other designs 75 Interactions 76 Identifying the important factors: factorial designs 77 Fractional factorial designs 78 Optimization: basic principles and univariate methods 79 Optimization using the alternating variable search method 710 The method of steepest ascent 711 Simplex optimization 712 Simulated annealing 8 Multivariate Analysis 81 Introduction 82 Initial analysis 83 Prinicipal component analysis 84 Cluster analysis 85 Discriminant analysis 86 K-nearest neighbour method 87 Disjoint class modelling 88 Regression methods 89 Multiple linear regression 810 Principal component regression 811 Partial least squares regression 812 Natural computation methods artificial neural networks 813 Conclusions Solutions to Exercises Appendix 1 Commonly used statistical significance tests Appendix 2 Statistical tables Index