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Chemometrics in Spectroscopy.

By: Contributor(s): Publisher: San Diego : Elsevier Science & Technology, 2007Copyright date: ©2007Description: 1 online resource (559 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780080548388
Subject(s): Genre/Form: Additional physical formats: Print version:: Chemometrics in SpectroscopyDDC classification:
  • 543.5
LOC classification:
  • QD95.5.S72M37 2007
Online resources:
Contents:
Front Cover -- Chemometrics in Spectroscopy -- Copyright page -- Table of Contents -- Preface -- Note to Readers -- Chapter 1. A New Beginning . . . -- THE MULTIVARIATE NORMAL DISTRIBUTION -- REFERENCES -- Chapter 2. Elementary Matrix Algebra: Part 1 -- MATRIX OPERATIONS -- ELEMENTARY OPERATIONS FOR LINEAR EQUATIONS -- SUMMARY -- REFERENCES -- Chapter 3. Elementary Matrix Algebra: Part 2 -- ELEMENTARY MATRIX OPERATIONS -- CALCULATING THE INVERSE OF A MATRIX -- SUMMARY -- REFERENCES -- Chapter 4. Matrix Algebra and Multiple Linear Regression: Part 1 -- QUASI-ALGEBRAIC OPERATIONS -- MULTIPLE LINEAR REGRESSION -- THE LEAST SQUARES METHOD -- REFERENCES -- Chapter 5. Matrix Algebra and Multiple Linear Regression: Part 2 -- THE POWER OF MATRIX MATHEMATICS -- REFERENCES -- Chapter 6. Matrix Algebra and Multiple Linear Regression: Part 3 - The Concept of Determinants -- REFERENCES -- Chapter 7. Matrix Algebra and Multiple Linear Regression: Part 4 - Concluding Remarks -- A WORD OF CAUTION -- REFERENCE -- Chapter 8. Experimental Designs: Part 1 -- REFERENCES -- Chapter 9. Experimental Designs: Part 2 -- REFERENCES -- Chapter 10. Experimental Designs: Part 3 -- Chapter 11. Analytic Geometry: Part 1 - The Basics in Two and Three Dimensions -- THE DISTANCE FORMULA -- DIRECTION NOTATION -- THE COSINE FUNCTION -- DIRECTION IN 3-D SPACE -- DEFINING SLOPE IN TWO DIMENSIONS -- RECOMMENDED READING -- Chapter 12. Analytic Geometry: Part 2 - Geometric Representation of Vectors and Algebraic Operations -- VECTOR MULTIPLICATION (SCALAR × VECTOR) -- VECTOR DIVISION (VECTOR ÷ SCALAR) -- VECTOR ADDITION (VECTOR + VECTOR) -- VECTOR SUBTRACTION (VECTOR − VECTOR) -- Chapter 13. Analytic Geometry: Part 3 - Reducing Dimensionality -- REDUCING DIMENSIONALITY -- 3-D TO 2-D BY PROJECTION -- 2-D INTO 1-D BY ROTATION.
Chapter 14. Analytic Geometry: Part 4 - The Geometry of Vectors and Matrices -- ROW VECTORS IN COLUMN SPACE -- COLUMN VECTORS IN ROW SPACE -- PRINCIPAL COMPONENTS FOR REGRESSION VECTORS -- RECOMMENDED READING -- Chapter 15. Experimental Designs: Part 4 - Varying Parameters to Expand the Design -- REFERENCES -- Chapter 16. Experimental Designs: Part 5 - One-at-a-time Designs -- REFERENCES -- Chapter 17. Experimental Designs: Part 6 - Sequential Designs -- REFERENCES -- Chapter 18. Experimental Designs: Part 7 - β, the Power of a Test -- REFERENCES -- Chapter 19. Experimental Designs: Part 8 - β, the Power of a Test (Continued) -- REFERENCES -- Chapter 20. Experimental Designs: Part 9 - Sequential Designs Concluded -- REFERENCES -- Chapter 21. Calculating the Solution for Regression Techniques: Part 1 - Multivariate Regression Made Simple -- REFERENCES -- Chapter 22. Calculating the Solution for Regression Techniques: Part 2 - Principal Component(s) Regression Made Simple -- REFERENCES -- Chapter 23. Calculating the Solution for Regression Techniques: Part 3 - Partial Least Squares Regression Made Simple -- REFERENCES -- Chapter 24. Looking Behind and Ahead: Interlude -- Chapter 25. A Simple Question: The Meaning of Chemometrics Pondered -- REFERENCES -- Chapter 26. Calculating the Solution for Regression Techniques: Part 4 - Singular Value Decomposition -- REFERENCES -- Chapter 27. Linearity in Calibration -- REFERENCE -- Chapter 28. Challenges: Unsolved Problems in Chemometrics -- REFERENCE -- Chapter 29. Linearity in Calibration: Act II Scene I -- REFERENCES -- Chapter 30. Linearity in Calibration: Act II Scene II - Reader's Comments . . . -- REFERENCES -- Chapter 31. Linearity in Calibration: Act II Scene III -- REFERENCES -- Chapter 32. Linearity in Calibration: Act II Scene IV -- REFERENCES -- Chapter 33. Linearity in Calibration: Act II Scene V.
REFERENCES -- Chapter 34. Collaborative Laboratory Studies: Part 1 - A Blueprint -- EXPERIMENTAL DESIGN -- ANALYTICAL METHODS -- METHOD A and B analysis -- RESULTS AND DATA ANALYSIS -- REFERENCES -- Chapter 35. Collaborative Laboratory Studies: Part 2 - using ANOVA -- ANOVA TEST COMPARISONS FOR LABORATORIES AND METHODS (ANOVA_s4 WORKSHEET) -- ANOVA test comparisons (using ANOVA_s2 worksheet) -- REFERENCES -- Chapter 36. Collaborative Laboratory Studies: Part 3 - Testing for Systematic Error -- TESTING FOR SYSTEMATIC ERROR IN A METHOD: COMPARISON TEST FOR A SET OF MEASUREMENTS VERSUS TRUE VALUE - SPIKED RECOVERY METHOD (COMPARET WORKSHEET) -- REFERENCES -- Chapter 37. Collaborative Laboratory Studies: Part 4 - Ranking Test -- RANKING TEST FOR LABORATORIES AND METHODS (MANUAL COMPUTATIONS) -- REFERENCE -- Chapter 38. Collaborative Laboratory Studies: Part 5 - Efficient Comparison of Two Methods -- COMPUTATIONS FOR EFFICIENT COMPARISON OF TWO METHODS (COMP_METH WORKSHEET) -- SUMMARY -- ACKNOWLEDGEMENT -- REFERENCES -- Chapter 39. Collaborative Laboratory Studies: Part 6 - MathCad Worksheet Text -- REFERENCES -- Chapter 40. Is Noise Brought by the Stork? Analysis of Noise: Part 1 -- REFERENCES -- Chapter 41. Analysis of Noise: Part 2 -- APPENDIX -- REFERENCES -- Chapter 42. Analysis of Noise: Part 3 -- REFERENCES -- Chapter 43. Analysis of Noise: Part 4 -- REFERENCES -- Chapter 44. Analysis of Noise: Part 5 -- ALTERNATE ANALYSIS -- ABSORBANCE NOISE IN THE "HIGH NOISE" REGIME -- REFERENCES -- Chapter 45. Analysis of Noise: Part 6 -- REFERENCES -- Chapter 46. Analysis of Noise: Part 7 -- EFFECT OF NOISE ON COMPUTED TRANSMITTANCE -- COMPUTED TRANSMITTANCE NOISE -- REFERENCES -- Chapter 47. Analysis of Noise: Part 8 -- REFERENCES -- Chapter 48. Analysis of Noise: Part 9 -- REFERENCES -- Chapter 49. Analysis of Noise: Part 10 -- DISCUSSION -- REFERENCES.
Chapter 50. Analysis of Noise: Part 11 -- REFERENCES -- Chapter 51. Analysis of Noise: Part 12 -- REFERENCES -- Chapter 52. Analysis of Noise: Part 13 -- REFERENCES -- Chapter 53. Analysis of Noise: Part 14 -- PRELIMINARY STEPS -- EVALUATION OF THE FUNCTION -- REFERENCES -- Chapter 54. Derivatives in Spectroscopy: Part 1 - The Behavior of the Derivative -- THE BEHAVIOR OF THEORETICAL DERIVATIVES -- THE BEHAVIOR OF COMPUTED DERIVATIVES -- REFERENCES -- Chapter 55. Derivatives in Spectroscopy: Part 2 - The "True" Derivative -- BETTER DERIVATIVE APPROXIMATIONS -- REFERENCES -- Chapter 56. Derivatives in Spectroscopy: Part 3 - Computing the Derivative -- METHODS OF COMPUTING THE DERIVATIVE -- LIMITATIONS OF THE SAVITZKY-GOLAY METHOD -- EXTENSIONS TO THE SAVITZKY-GOLAY METHOD -- REFERENCES -- Chapter 57. Derivatives in Spectroscopy: Part 4 - Calibrating with Derivatives -- ACKNOWLEDGEMENT -- REFERENCES -- Chapter 58. Comparison of Goodness of Fit Statistics for Linear Regression: Part 1 - Introduction -- REFERENCE -- Chapter 59. Comparison of Goodness of Fit Statistics for Linear Regression: Part 2 - The Correlation Coefficient -- REFERENCES -- Chapter 60. Comparison of Goodness of Fit Statistics for Linear Regression: Part 3 - Computing Confidence Limits for the Correlation Coefficient -- TESTING CORRELATION FOR DIFFERENT SIZE POPULATIONS -- REFERENCES -- Chapter 61. Comparison of Goodness of Fit Statistics for Linear Regression: Part 4 - Confidence Limits for Slope and Intercept -- REFERENCES -- Supplement -- MathCad Worksheets for Correlation, Slope and Intercept -- REFERENCES -- Chapter 62. Correction and Discussion Regarding Derivatives -- REFERENCES -- Chapter 63. Linearity in Calibration: Act III Scene I - Importance of Nonlinearity -- WHY IS NONLINEARITY IMPORTANT? -- REFERENCES.
Chapter 64. Linearity in Calibration: Act III Scene II - A Discussion of the Durbin-Watson Statistic, a Step in the Right Direction -- REFERENCES -- Chapter 65. Linearity in Calibration: Act III Scene III - Other Tests for Nonlinearity -- F -TEST -- NORMALITY OF RESIDUALS -- Chapter 66. Linearity in Calibration: Act III Scene IV - How to Test for Nonlinearity -- CONCLUSION -- APPENDIX A: DERIVATION AND DISCUSSION OF THE FORMULA IN EQUATION 66-11 -- REFERENCES -- Chapter 67. Linearity in Calibration: Act III Scene V - Quantifying Nonlinearity -- REFERENCES -- Chapter 68. Linearity in Calibration: Act III Scene VI - Quantifying Nonlinearity, Part II, and a News Flash -- NEWS FLASH!! -- REFERENCES -- Chapter 69. Connecting Chemometrics to Statistics: Part 1 - The Chemometrics Side -- REFERENCES -- Chapter 70. Connecting Chemometrics to Statistics: Part 2 - The Statistics Side -- MULTIVARIATE ANOVA -- REFERENCES -- Chapter 71. Limitations in Analytical Accuracy: Part 1 - Horwitz's Trumpet -- REFERENCES -- Chapter 72. Limitations in Analytical Accuracy: Part 2 - Theories to Describe the Limits in Analytical Accuracy -- DETECTION LIMIT FOR CONCENTRATIONS NEAR ZERO -- REFERENCES -- Chapter 73. Limitations in Analytical Accuracy: Part 3 - Comparing Test Results for Analytical Uncertainty -- UNCERTAINTY IN AN ANALYTICAL MEASUREMENT -- COMPARISON TEST FOR A SINGLE SET OF MEASUREMENTS VERSUS A TRUE ANALYTICAL RESULT -- COMPARISON TEST FOR A TWO SETS OF MEASUREMENTS -- CALCULATING THE NUMBER OF MEASUREMENTS REQUIRED TO ESTABLISH A MEAN VALUE (OR ANALYTICAL RESULT) WITH A PRESCRIBED UNCERTAINTY (ACCURACY) -- THE Q-TEST FOR OUTLIERS [1-3] -- SUMMATION OF VARIANCE FROM SEVERAL DATA SETS -- REFERENCES -- Chapter 74. The Statistics of Spectral Searches -- COMMON SPECTRAL MATCHING APPROACHES -- MAHALANOBIS DISTANCE MEASUREMENTS -- EUCLIDEAN DISTANCE.
COMMON SPECTRAL MATCHING (CORRELATION OR DOT PRODUCT).
Summary: Chemometrics in Spectroscopy builds upon the statistical information covered in other books written by these leading authors in the field by providing a broader range of mathematics and progressing into the fundamentals of multivariate and experimental data analysis. Subjects covered in this work include: matrix algebra, analytic geometry, experimental design, calibration regression, linearity, design of collaborative laboratory studies, comparing analytical methods, noise analysis, use of derivatives, analytical accuracy, analysis of variance, and much more are all part of this chemometrics compendium. Developed in the form of a tutorial offering a basic hands-on approach to chemometric and statistical analysis for analytical scientists, experimentalists, and spectroscopists. Without using complicated mathematics, Chemometrics in Spectroscopy demonstrates the basic principles underlying the use of common experimental, chemometric, and statistical tools. Emphasis has been given to problem-solving applications and the proper use and interpretation of data used for scientific research. * Offers basic hands-on approach to chemometric and statistical analysis for analytical scientists, experimentalists, and spectroscopists. * Useful for analysts in their daily problem solving, as well as detailed insights into subjects often considered difficult to thoroughly grasp by non-specialists. * Provides mathematical proofs and derivations for the student or rigorously-minded specialist.
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Front Cover -- Chemometrics in Spectroscopy -- Copyright page -- Table of Contents -- Preface -- Note to Readers -- Chapter 1. A New Beginning . . . -- THE MULTIVARIATE NORMAL DISTRIBUTION -- REFERENCES -- Chapter 2. Elementary Matrix Algebra: Part 1 -- MATRIX OPERATIONS -- ELEMENTARY OPERATIONS FOR LINEAR EQUATIONS -- SUMMARY -- REFERENCES -- Chapter 3. Elementary Matrix Algebra: Part 2 -- ELEMENTARY MATRIX OPERATIONS -- CALCULATING THE INVERSE OF A MATRIX -- SUMMARY -- REFERENCES -- Chapter 4. Matrix Algebra and Multiple Linear Regression: Part 1 -- QUASI-ALGEBRAIC OPERATIONS -- MULTIPLE LINEAR REGRESSION -- THE LEAST SQUARES METHOD -- REFERENCES -- Chapter 5. Matrix Algebra and Multiple Linear Regression: Part 2 -- THE POWER OF MATRIX MATHEMATICS -- REFERENCES -- Chapter 6. Matrix Algebra and Multiple Linear Regression: Part 3 - The Concept of Determinants -- REFERENCES -- Chapter 7. Matrix Algebra and Multiple Linear Regression: Part 4 - Concluding Remarks -- A WORD OF CAUTION -- REFERENCE -- Chapter 8. Experimental Designs: Part 1 -- REFERENCES -- Chapter 9. Experimental Designs: Part 2 -- REFERENCES -- Chapter 10. Experimental Designs: Part 3 -- Chapter 11. Analytic Geometry: Part 1 - The Basics in Two and Three Dimensions -- THE DISTANCE FORMULA -- DIRECTION NOTATION -- THE COSINE FUNCTION -- DIRECTION IN 3-D SPACE -- DEFINING SLOPE IN TWO DIMENSIONS -- RECOMMENDED READING -- Chapter 12. Analytic Geometry: Part 2 - Geometric Representation of Vectors and Algebraic Operations -- VECTOR MULTIPLICATION (SCALAR × VECTOR) -- VECTOR DIVISION (VECTOR ÷ SCALAR) -- VECTOR ADDITION (VECTOR + VECTOR) -- VECTOR SUBTRACTION (VECTOR − VECTOR) -- Chapter 13. Analytic Geometry: Part 3 - Reducing Dimensionality -- REDUCING DIMENSIONALITY -- 3-D TO 2-D BY PROJECTION -- 2-D INTO 1-D BY ROTATION.

Chapter 14. Analytic Geometry: Part 4 - The Geometry of Vectors and Matrices -- ROW VECTORS IN COLUMN SPACE -- COLUMN VECTORS IN ROW SPACE -- PRINCIPAL COMPONENTS FOR REGRESSION VECTORS -- RECOMMENDED READING -- Chapter 15. Experimental Designs: Part 4 - Varying Parameters to Expand the Design -- REFERENCES -- Chapter 16. Experimental Designs: Part 5 - One-at-a-time Designs -- REFERENCES -- Chapter 17. Experimental Designs: Part 6 - Sequential Designs -- REFERENCES -- Chapter 18. Experimental Designs: Part 7 - β, the Power of a Test -- REFERENCES -- Chapter 19. Experimental Designs: Part 8 - β, the Power of a Test (Continued) -- REFERENCES -- Chapter 20. Experimental Designs: Part 9 - Sequential Designs Concluded -- REFERENCES -- Chapter 21. Calculating the Solution for Regression Techniques: Part 1 - Multivariate Regression Made Simple -- REFERENCES -- Chapter 22. Calculating the Solution for Regression Techniques: Part 2 - Principal Component(s) Regression Made Simple -- REFERENCES -- Chapter 23. Calculating the Solution for Regression Techniques: Part 3 - Partial Least Squares Regression Made Simple -- REFERENCES -- Chapter 24. Looking Behind and Ahead: Interlude -- Chapter 25. A Simple Question: The Meaning of Chemometrics Pondered -- REFERENCES -- Chapter 26. Calculating the Solution for Regression Techniques: Part 4 - Singular Value Decomposition -- REFERENCES -- Chapter 27. Linearity in Calibration -- REFERENCE -- Chapter 28. Challenges: Unsolved Problems in Chemometrics -- REFERENCE -- Chapter 29. Linearity in Calibration: Act II Scene I -- REFERENCES -- Chapter 30. Linearity in Calibration: Act II Scene II - Reader's Comments . . . -- REFERENCES -- Chapter 31. Linearity in Calibration: Act II Scene III -- REFERENCES -- Chapter 32. Linearity in Calibration: Act II Scene IV -- REFERENCES -- Chapter 33. Linearity in Calibration: Act II Scene V.

REFERENCES -- Chapter 34. Collaborative Laboratory Studies: Part 1 - A Blueprint -- EXPERIMENTAL DESIGN -- ANALYTICAL METHODS -- METHOD A and B analysis -- RESULTS AND DATA ANALYSIS -- REFERENCES -- Chapter 35. Collaborative Laboratory Studies: Part 2 - using ANOVA -- ANOVA TEST COMPARISONS FOR LABORATORIES AND METHODS (ANOVA_s4 WORKSHEET) -- ANOVA test comparisons (using ANOVA_s2 worksheet) -- REFERENCES -- Chapter 36. Collaborative Laboratory Studies: Part 3 - Testing for Systematic Error -- TESTING FOR SYSTEMATIC ERROR IN A METHOD: COMPARISON TEST FOR A SET OF MEASUREMENTS VERSUS TRUE VALUE - SPIKED RECOVERY METHOD (COMPARET WORKSHEET) -- REFERENCES -- Chapter 37. Collaborative Laboratory Studies: Part 4 - Ranking Test -- RANKING TEST FOR LABORATORIES AND METHODS (MANUAL COMPUTATIONS) -- REFERENCE -- Chapter 38. Collaborative Laboratory Studies: Part 5 - Efficient Comparison of Two Methods -- COMPUTATIONS FOR EFFICIENT COMPARISON OF TWO METHODS (COMP_METH WORKSHEET) -- SUMMARY -- ACKNOWLEDGEMENT -- REFERENCES -- Chapter 39. Collaborative Laboratory Studies: Part 6 - MathCad Worksheet Text -- REFERENCES -- Chapter 40. Is Noise Brought by the Stork? Analysis of Noise: Part 1 -- REFERENCES -- Chapter 41. Analysis of Noise: Part 2 -- APPENDIX -- REFERENCES -- Chapter 42. Analysis of Noise: Part 3 -- REFERENCES -- Chapter 43. Analysis of Noise: Part 4 -- REFERENCES -- Chapter 44. Analysis of Noise: Part 5 -- ALTERNATE ANALYSIS -- ABSORBANCE NOISE IN THE "HIGH NOISE" REGIME -- REFERENCES -- Chapter 45. Analysis of Noise: Part 6 -- REFERENCES -- Chapter 46. Analysis of Noise: Part 7 -- EFFECT OF NOISE ON COMPUTED TRANSMITTANCE -- COMPUTED TRANSMITTANCE NOISE -- REFERENCES -- Chapter 47. Analysis of Noise: Part 8 -- REFERENCES -- Chapter 48. Analysis of Noise: Part 9 -- REFERENCES -- Chapter 49. Analysis of Noise: Part 10 -- DISCUSSION -- REFERENCES.

Chapter 50. Analysis of Noise: Part 11 -- REFERENCES -- Chapter 51. Analysis of Noise: Part 12 -- REFERENCES -- Chapter 52. Analysis of Noise: Part 13 -- REFERENCES -- Chapter 53. Analysis of Noise: Part 14 -- PRELIMINARY STEPS -- EVALUATION OF THE FUNCTION -- REFERENCES -- Chapter 54. Derivatives in Spectroscopy: Part 1 - The Behavior of the Derivative -- THE BEHAVIOR OF THEORETICAL DERIVATIVES -- THE BEHAVIOR OF COMPUTED DERIVATIVES -- REFERENCES -- Chapter 55. Derivatives in Spectroscopy: Part 2 - The "True" Derivative -- BETTER DERIVATIVE APPROXIMATIONS -- REFERENCES -- Chapter 56. Derivatives in Spectroscopy: Part 3 - Computing the Derivative -- METHODS OF COMPUTING THE DERIVATIVE -- LIMITATIONS OF THE SAVITZKY-GOLAY METHOD -- EXTENSIONS TO THE SAVITZKY-GOLAY METHOD -- REFERENCES -- Chapter 57. Derivatives in Spectroscopy: Part 4 - Calibrating with Derivatives -- ACKNOWLEDGEMENT -- REFERENCES -- Chapter 58. Comparison of Goodness of Fit Statistics for Linear Regression: Part 1 - Introduction -- REFERENCE -- Chapter 59. Comparison of Goodness of Fit Statistics for Linear Regression: Part 2 - The Correlation Coefficient -- REFERENCES -- Chapter 60. Comparison of Goodness of Fit Statistics for Linear Regression: Part 3 - Computing Confidence Limits for the Correlation Coefficient -- TESTING CORRELATION FOR DIFFERENT SIZE POPULATIONS -- REFERENCES -- Chapter 61. Comparison of Goodness of Fit Statistics for Linear Regression: Part 4 - Confidence Limits for Slope and Intercept -- REFERENCES -- Supplement -- MathCad Worksheets for Correlation, Slope and Intercept -- REFERENCES -- Chapter 62. Correction and Discussion Regarding Derivatives -- REFERENCES -- Chapter 63. Linearity in Calibration: Act III Scene I - Importance of Nonlinearity -- WHY IS NONLINEARITY IMPORTANT? -- REFERENCES.

Chapter 64. Linearity in Calibration: Act III Scene II - A Discussion of the Durbin-Watson Statistic, a Step in the Right Direction -- REFERENCES -- Chapter 65. Linearity in Calibration: Act III Scene III - Other Tests for Nonlinearity -- F -TEST -- NORMALITY OF RESIDUALS -- Chapter 66. Linearity in Calibration: Act III Scene IV - How to Test for Nonlinearity -- CONCLUSION -- APPENDIX A: DERIVATION AND DISCUSSION OF THE FORMULA IN EQUATION 66-11 -- REFERENCES -- Chapter 67. Linearity in Calibration: Act III Scene V - Quantifying Nonlinearity -- REFERENCES -- Chapter 68. Linearity in Calibration: Act III Scene VI - Quantifying Nonlinearity, Part II, and a News Flash -- NEWS FLASH!! -- REFERENCES -- Chapter 69. Connecting Chemometrics to Statistics: Part 1 - The Chemometrics Side -- REFERENCES -- Chapter 70. Connecting Chemometrics to Statistics: Part 2 - The Statistics Side -- MULTIVARIATE ANOVA -- REFERENCES -- Chapter 71. Limitations in Analytical Accuracy: Part 1 - Horwitz's Trumpet -- REFERENCES -- Chapter 72. Limitations in Analytical Accuracy: Part 2 - Theories to Describe the Limits in Analytical Accuracy -- DETECTION LIMIT FOR CONCENTRATIONS NEAR ZERO -- REFERENCES -- Chapter 73. Limitations in Analytical Accuracy: Part 3 - Comparing Test Results for Analytical Uncertainty -- UNCERTAINTY IN AN ANALYTICAL MEASUREMENT -- COMPARISON TEST FOR A SINGLE SET OF MEASUREMENTS VERSUS A TRUE ANALYTICAL RESULT -- COMPARISON TEST FOR A TWO SETS OF MEASUREMENTS -- CALCULATING THE NUMBER OF MEASUREMENTS REQUIRED TO ESTABLISH A MEAN VALUE (OR ANALYTICAL RESULT) WITH A PRESCRIBED UNCERTAINTY (ACCURACY) -- THE Q-TEST FOR OUTLIERS [1-3] -- SUMMATION OF VARIANCE FROM SEVERAL DATA SETS -- REFERENCES -- Chapter 74. The Statistics of Spectral Searches -- COMMON SPECTRAL MATCHING APPROACHES -- MAHALANOBIS DISTANCE MEASUREMENTS -- EUCLIDEAN DISTANCE.

COMMON SPECTRAL MATCHING (CORRELATION OR DOT PRODUCT).

Chemometrics in Spectroscopy builds upon the statistical information covered in other books written by these leading authors in the field by providing a broader range of mathematics and progressing into the fundamentals of multivariate and experimental data analysis. Subjects covered in this work include: matrix algebra, analytic geometry, experimental design, calibration regression, linearity, design of collaborative laboratory studies, comparing analytical methods, noise analysis, use of derivatives, analytical accuracy, analysis of variance, and much more are all part of this chemometrics compendium. Developed in the form of a tutorial offering a basic hands-on approach to chemometric and statistical analysis for analytical scientists, experimentalists, and spectroscopists. Without using complicated mathematics, Chemometrics in Spectroscopy demonstrates the basic principles underlying the use of common experimental, chemometric, and statistical tools. Emphasis has been given to problem-solving applications and the proper use and interpretation of data used for scientific research. * Offers basic hands-on approach to chemometric and statistical analysis for analytical scientists, experimentalists, and spectroscopists. * Useful for analysts in their daily problem solving, as well as detailed insights into subjects often considered difficult to thoroughly grasp by non-specialists. * Provides mathematical proofs and derivations for the student or rigorously-minded specialist.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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