Statistics and chemometrics for analytical chemistry
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1. Introduction 1.1 Analytical problems 1.2 Errors in quantitative analysis 1.3 Types of error 1.4 Random and systematic errors in titrimetric analysis 1.5 Handling systematic errors 1.6 Planning and design of experiments 1.7 Calculators and computers in statistical calculations 2. Statistics of Repeated Measurements 2.1 Mean and standard deviation 2.2 The distribution of repeated measurements 2.3 Log-normal distribution 2.4 Definition of a 'sample' 2.5 The sampling distribution of the mean 2.6 Confidence limits of the mean for large samples 2.7 Confidence limits of the mean for small samples 2.8 Presentation of results 2.9 Other uses of confidence limits 2.10 Confidence limits of the geometric mean for a log-normal distribution 2.11 Propagation of random errors 2.12 Propagation of systematic errors 3. Significance Tests 3.1 Introduction 3.2 Comparison of an experimental mean with a known value 3.3 Comparison of two experimental means 3.4 Paired t-test 3.5 One-sided and two-sided tests 3.6 F-test for the comparison of standard deviations 3.7 Outliers 3.8 Analysis of variance 3.9 Comparison of several means 3.10 The arithmetic of ANOVA calculations 3.11 The chi-squared test 3.12 Testing for normality of distribution 3.13 Conclusions from significance tests 3.14 Bayesian Statistics 4. The Quality of Analytical Measurements 4.1 Introduction 4.2 Sampling 4.3 Separation and estimation of variances using ANOVA 4.4 Sampling strategy 4.5 Quality control methods - Introduction 4.6 Stewhart charts for mean values 4.7 Stewhart charts for ranges 4.8 Establishing the process capability 4.9 Average run length: cusum charts 4.10 Zone control charts (J-charts)