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Preface

Notation

Chapter I. The Origin and Presentation of Chemical Data

1.1 The Origin and Nature of Quantitative Data

1.2 Operation of a Scale of Measurement

1.3 Measuring and Counting

1.4 Units, Fixed Points and Relationship between Scales

1.5 Dimensions

1.6 The Presentation of Quantitative Data

1.7 Tabular Presentation

1.8 Graphical Presentation

1.9 Graphical Representation of More than Two Variables

1.10 Alignment Charts

1.11 Empirical Equations

Chapter II. Measurements of a Single Variable

2.1 The Provenance of Frequency Data

2.2 Classification of Data—The Frequency Distribution

2.3 Types of Frequency Distribution

(1) Normal

(2) Non-Normal Unimodal

(3) J-Shaped, U-Shaped and Rectangular

(4) Irregular

2.4 Condensation of Data—The Sample Estimates

(1) Measures of Central Tendency

(2) Measures of Dispersion or Variability

(3) Measures of Skewness and Kurtosis

2.5 Computation of the Estimates from Sample Data

(1) Small Sample Methods

(2) Grouping Methods

(3) Graphical Methods

Notation of Chapter II

Chapter III. Errors, Probability and Tests of Significance

3.1 The Nature of Error in Experimental Science

3.2 Probability and Random Errors

3.3 Probability and Physico-chemical Processes

3.4 Sampling Distributions

3.5 Tests of Significance and Confidence Intervals

(1) Tests Involving a Known Standard Error

(2) Tests Involving Estimated Standard Errors

(3) The Comparison of Several Samples

(4) Some Tests on Frequencies and Proportions

3.6 The Expression, Combination and Manipulation of Experimental Results

(1) Expression of Results

(2) Testing of Suspected Observations

(3) The Weighted Mean and its Confidence Limits

(4) Propagation of Error

(5) Tolerance Limits

Notation of Chapter III

Chapter IV. The Relationship between Two Variables—Simple Linear Relationships

4.1 Regression, Correlation and Confluence

4.2 The Simple Regression Line

4.3 Fitting the Least Squares Line

(1) General Method

(2) Summation Method

(3) Graphic Method

4.4 Confidence Intervals for the Parameters of the Simple Linear Model

(1) Tests and Confidence Intervals for Slope and Intercept

(2) A Joint Confidence Region for Slope and Intercept

(3) Interval-Estimates for Points on the True Line

4.5 Predictions Based on a Fitted Line

4.6 Constrained Models and their Comparison with the Simple Regression Model

4.7 Computations in Simple Regression with Replication

4.8 The Comparison of Several Regression Lines

4.9 The Intersection of Two Regression Lines

4.10 The Correlation Model

4.11 Tests of Significance Involving the Correlation Coefficient

4.12 The Approximate Treatment of Associated Data

(1) The Grouping Method

(2) Three-Group Analysis

(3) The Ranking Method

(4) A Control Chart Method

Notation of Chapter IV

Chapter V. The Relationship between Two or More Variables—Multiple, Non-linear and Other Relationships

5.1 Multiple Linear Correlation and Regression

5.2 The Fitting of Polynomials. Statistical Methods

5.3 The Fitting of Polynomials. Non-statistical Methods

5.4 Departures from the Simple Regression Model

(1) Varying Incidence of Random Error

(2) Cumulative Values

(3) Errors in Both Variables

5.5 Rectification

5.6 Miscellaneous Curvilinear Relationships

(1) Hyperbolic Equations

(2) Exponential and Asymptotic Regression

5.7 Frequency and Distribution Curves

(1) Fitting the Gaussian Function

(2) Resolving Normal Distributions

(3) Other Frequency Functions

5.8 A Least Squares Solution of Simultaneous Equations

Notation of Chapter V

Chapter VI. Smoothing, Interpolation, Differentiation and Integration

6.1 The Smoothing of Data

(1) Direct Methods

(2) Difference Methods

(3) Least Squares Method for Equally Spaced Values

(4) Other Methods

6.2 Interpolation and Extrapolation

(1) Direct Methods

(2) Proportional Parts and Three-point Interpolation

(3) The Gregory-Newton Method

(4) The Newton Method

(5) Interpolation with Two Independent Variables

(6) Other Methods and Applications

6.3 Graphical and Tabular Differentiation

(1) Direct Methods

(2) Difference Methods

(3) A Semi-graphical Method

6.4 Graphical and Tabular Integration

(1) The Graphical Method

(2) The Equation Method

(3) The Trapezoidal Rule and Simpson's Rules

Notation of Chapter VI

Chapter VII. Dimensional Analysis in Physico-chemical Problems

7.1 Units

7.2 Systems of Units

7.3 Dimensions

7.4 Dimensional Homogeneity

7.5 Systems of Dimensions

7.6 Some Discussion of the Length Dimension

7.7 Dimensionless Ratios or Numerics

7.8 Applications of Dimensional Theory

7.9 The Principle of Similarity

7.10 Partial Similarity

7.11 Chemical Similarity

Notation of Chapter VII

Appendix: Tables of Statistical Functions

Sources and References

Table I Ordinates and Areas of the Gaussian Curve

Table II Percentage Points of the Distributions of t, χ2 and r

Table III Percentage Points of the Distribution of F

Table IV Percentage Points of the Distribution of M

Table V Control Chart Factors

Table VI Percentage Points of Dixon's r

Table VII Percentage Points of the Distribution of q

Table VIII Two-sided Tolerance Limit Factors, l

Table IX The Reduction in ΣY2 for Significance at the 5% Level

Table X The Transformation of r to z and z to r

Table XI Critical Values of Σd2 for Rank Correlation

Table XII Orthogonal Polynomials

Table XIII Summary of Tests of Significance

Exercises

References

General Bibliography

Index

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1st Edition - January 1, 1968

Authors: P. D. Lark, B. R. Craven, R. C. L. Bosworth

Language: EnglisheBook ISBN:

9 7 8 - 1 - 4 8 3 1 - 4 6 1 5 - 7

The Handling of Chemical Data deals with how measurements, such as those arrived at from chemical experimentation, are handled. The book discusses the different kinds of… Read more

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The Handling of Chemical Data deals with how measurements, such as those arrived at from chemical experimentation, are handled. The book discusses the different kinds of measurements and their specific dimensional characteristics by starting with the origin and presentation of chemical data. The text explains the units, fixed points, and relationships found between scales, the concept of dimensions, the presentation of quantitative data (whether in a tabular or graphical form), and some uses of empirical equations. The book also explains the relationship between two variables, and how equations such as fitting the least square lines can be applied. The text explains how the simple regression and the correlations models can be modified in three ways depending on the complexities present while studying experimental data. When data are reduced to equation form, ancillary operations — interpolation, integration, and differentiation — become useful for more precise presentation and understanding of the experimental data. The book notes the importance of smoothing or adjustment as a procedure to eliminate the effects of random error through application of the direct methods, difference methods, and the least squares method for equally space values. The text then addresses the dimensional analysis in physico-chemical problems and discusses the different dimensions (time, mass, force, energy, and temperature) that can affect systems. Researchers who are time-constrained or equipped with only fundamental training and knowledge of statistical analysis will find this book helpful. It can also be read by students of advanced mathematics and statistical analysis.

Preface

Notation

Chapter I. The Origin and Presentation of Chemical Data

1.1 The Origin and Nature of Quantitative Data

1.2 Operation of a Scale of Measurement

1.3 Measuring and Counting

1.4 Units, Fixed Points and Relationship between Scales

1.5 Dimensions

1.6 The Presentation of Quantitative Data

1.7 Tabular Presentation

1.8 Graphical Presentation

1.9 Graphical Representation of More than Two Variables

1.10 Alignment Charts

1.11 Empirical Equations

Chapter II. Measurements of a Single Variable

2.1 The Provenance of Frequency Data

2.2 Classification of Data—The Frequency Distribution

2.3 Types of Frequency Distribution

(1) Normal

(2) Non-Normal Unimodal

(3) J-Shaped, U-Shaped and Rectangular

(4) Irregular

2.4 Condensation of Data—The Sample Estimates

(1) Measures of Central Tendency

(2) Measures of Dispersion or Variability

(3) Measures of Skewness and Kurtosis

2.5 Computation of the Estimates from Sample Data

(1) Small Sample Methods

(2) Grouping Methods

(3) Graphical Methods

Notation of Chapter II

Chapter III. Errors, Probability and Tests of Significance

3.1 The Nature of Error in Experimental Science

3.2 Probability and Random Errors

3.3 Probability and Physico-chemical Processes

3.4 Sampling Distributions

3.5 Tests of Significance and Confidence Intervals

(1) Tests Involving a Known Standard Error

(2) Tests Involving Estimated Standard Errors

(3) The Comparison of Several Samples

(4) Some Tests on Frequencies and Proportions

3.6 The Expression, Combination and Manipulation of Experimental Results

(1) Expression of Results

(2) Testing of Suspected Observations

(3) The Weighted Mean and its Confidence Limits

(4) Propagation of Error

(5) Tolerance Limits

Notation of Chapter III

Chapter IV. The Relationship between Two Variables—Simple Linear Relationships

4.1 Regression, Correlation and Confluence

4.2 The Simple Regression Line

4.3 Fitting the Least Squares Line

(1) General Method

(2) Summation Method

(3) Graphic Method

4.4 Confidence Intervals for the Parameters of the Simple Linear Model

(1) Tests and Confidence Intervals for Slope and Intercept

(2) A Joint Confidence Region for Slope and Intercept

(3) Interval-Estimates for Points on the True Line

4.5 Predictions Based on a Fitted Line

4.6 Constrained Models and their Comparison with the Simple Regression Model

4.7 Computations in Simple Regression with Replication

4.8 The Comparison of Several Regression Lines

4.9 The Intersection of Two Regression Lines

4.10 The Correlation Model

4.11 Tests of Significance Involving the Correlation Coefficient

4.12 The Approximate Treatment of Associated Data

(1) The Grouping Method

(2) Three-Group Analysis

(3) The Ranking Method

(4) A Control Chart Method

Notation of Chapter IV

Chapter V. The Relationship between Two or More Variables—Multiple, Non-linear and Other Relationships

5.1 Multiple Linear Correlation and Regression

5.2 The Fitting of Polynomials. Statistical Methods

5.3 The Fitting of Polynomials. Non-statistical Methods

5.4 Departures from the Simple Regression Model

(1) Varying Incidence of Random Error

(2) Cumulative Values

(3) Errors in Both Variables

5.5 Rectification

5.6 Miscellaneous Curvilinear Relationships

(1) Hyperbolic Equations

(2) Exponential and Asymptotic Regression

5.7 Frequency and Distribution Curves

(1) Fitting the Gaussian Function

(2) Resolving Normal Distributions

(3) Other Frequency Functions

5.8 A Least Squares Solution of Simultaneous Equations

Notation of Chapter V

Chapter VI. Smoothing, Interpolation, Differentiation and Integration

6.1 The Smoothing of Data

(1) Direct Methods

(2) Difference Methods

(3) Least Squares Method for Equally Spaced Values

(4) Other Methods

6.2 Interpolation and Extrapolation

(1) Direct Methods

(2) Proportional Parts and Three-point Interpolation

(3) The Gregory-Newton Method

(4) The Newton Method

(5) Interpolation with Two Independent Variables

(6) Other Methods and Applications

6.3 Graphical and Tabular Differentiation

(1) Direct Methods

(2) Difference Methods

(3) A Semi-graphical Method

6.4 Graphical and Tabular Integration

(1) The Graphical Method

(2) The Equation Method

(3) The Trapezoidal Rule and Simpson's Rules

Notation of Chapter VI

Chapter VII. Dimensional Analysis in Physico-chemical Problems

7.1 Units

7.2 Systems of Units

7.3 Dimensions

7.4 Dimensional Homogeneity

7.5 Systems of Dimensions

7.6 Some Discussion of the Length Dimension

7.7 Dimensionless Ratios or Numerics

7.8 Applications of Dimensional Theory

7.9 The Principle of Similarity

7.10 Partial Similarity

7.11 Chemical Similarity

Notation of Chapter VII

Appendix: Tables of Statistical Functions

Sources and References

Table I Ordinates and Areas of the Gaussian Curve

Table II Percentage Points of the Distributions of t, χ2 and r

Table III Percentage Points of the Distribution of F

Table IV Percentage Points of the Distribution of M

Table V Control Chart Factors

Table VI Percentage Points of Dixon's r

Table VII Percentage Points of the Distribution of q

Table VIII Two-sided Tolerance Limit Factors, l

Table IX The Reduction in ΣY2 for Significance at the 5% Level

Table X The Transformation of r to z and z to r

Table XI Critical Values of Σd2 for Rank Correlation

Table XII Orthogonal Polynomials

Table XIII Summary of Tests of Significance

Exercises

References

General Bibliography

Index

- No. of pages: 392
- Language: English
- Edition: 1
- Published: January 1, 1968
- Imprint: Pergamon
- eBook ISBN: 9781483146157

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