The Application of Mathematical Statistics to Chemical Analysis

Publisher's Note

Preface

I. Problems of Mathematical Statistics

II. Classifications of Errors in Chemical Analysis

III. Random Variables and their Characteristics


1. Distribution of a Random Variable.


2. Mean Value of a Random Variable and Variance.

Mean Value of a Random Variable

Variance and Root Mean Square Deviation


3. Calculation of Variances from Current Measurements.


4. Law of Addition of Errors.


5. Errors of Indirect Measurements.

Absorption Spectrophotometric Analysis

Emission Spectrographic Analysis

IV. Normal Distribution


1. Normal Distribution Function.


2. Some Special Distributions Connected with Normal Distribution.

t-distribution

X2-distribution

F-distribution

r-distribution


3. Criteria for Estimating the Degree- of Proximity of the Observed Distribution to the Normal Distribution.

Estimation with the Help of the X2-criterion

Estimation with the Help of the λ-criterion

Verification of the Hypothesis of Normality from a Large Number of Small Samples

Method of Rectified Diagrams


4. Deviations from Normal Distribution in Chemical Analysis.

V. Poisson's Distribution and Binomial Distribution


1. Poisson's Distribution.


2. Evaluation of the Results of Semi-Quantitative Determinations with the Help of Poisson's Distribution.


3. Binomial Distribution.

VI. Estimation of the Results of Chemical Analysis


1. Comparison of two Means with the Help of the t-criterion.


2. Comparison of Several Variances.


3. Verification of the Hypothesis of Homogeneity of Results of Measurements. Estimation of Sharply Separated Determinations.


4. Sequential (Successive) Analysis.


5. Non-Parametric Statistics.

Verification of the Hypothesis of the Existence of a Constant Divergence in the Results of Observations

Verification of the Hypothesis Regarding the Random Nature of Fluctuations

Metrological Estimations on the Basis of Tschebyscheff's Inequality

VII. Analysis of Variance


1. Determination of Variance due to the Effect of One Factor.

Principle of the Method and Simple Examples

Analysis of Variance with Unequal Columns

Conditions in which Analysis of Variance can be Applied

An Example of Application of Analysis of Variance in the Study of Procedural Errors


2. Multi-Stage Classification.

Two-Stage Grouping

Three-Stage Grouping


3. Complex Experiment.

Two-Sided Classification

Three-Sided Classification


4. Design of An Experiment by the Latin-Square Method.


5. Efficiency of Analysis of Variance.

VIII. Statistics of Linear Relations


1. Method of Least Squares.

Determination of the Parameters of a Graduated Graph

Weighted mean of Unequally Accurate Measurements


2. Regression Analysis.

Verification of the Hypothesis of Linearity

Comparison of Parameters of Graduated Graphs with the Theoretically Expected Values

Comparison of Two Graduated Graphs

Verification of the Hypothesis of Parallel Displacement of Graduated Graphs

Estimation of the Results of Analysis Obtained with the Help of a Graduated Graph


3. Correlational Analysis.


4. Application of Complex Design of An Experiment using Different Statistical Methods of Analysis.

IX. Some Working Methods Connected with the Statistical Design of An Experiment


1. Sampling and Randomization of Experimental Conditions. Application of the Table of Random Numbers.


2. Choice of the Number of Parallel Determinations.


3. Documentation of the Material.


4. Control Diagrams.

Bibliography


1. Principal Manuals and Monographs on Mathematical Statistics and the Theory of Probability.


2. Reviews and Bibliographical Sources of Problems Relating to the Application of Mathematical Statistics to Analysis.


3. Articles on Questions Relating to the Application of Mathematical Statistics to Analysis Published in Periodicals and Symposia.


4. Miscellaneous

Appendix

Index