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Table of contents
- Table of Contentsvii
- Prefacexi
- Note to Readersxiii
- Chapter 1. A New Beginning . . .1
- THE MULTIVARIATE NORMAL DISTRIBUTION3
- REFERENCES7
- Chapter 2. Elementary Matrix Algebra: Part 19
- MATRIX OPERATIONS10
- ELEMENTARY OPERATIONS FOR LINEAR EQUATIONS12
- SUMMARY15
- REFERENCES15
- Chapter 3. Elementary Matrix Algebra: Part 217
- ELEMENTARY MATRIX OPERATIONS17
- CALCULATING THE INVERSE OF A MATRIX19
- SUMMARY20
- REFERENCES21
- Chapter 4. Matrix Algebra and Multiple Linear Regression: Part 123
- QUASI-ALGEBRAIC OPERATIONS25
- MULTIPLE LINEAR REGRESSION28
- THE LEAST SQUARES METHOD29
- REFERENCES32
- Chapter 5. Matrix Algebra and Multiple Linear Regression: Part 233
- THE POWER OF MATRIX MATHEMATICS38
- REFERENCES41
- Chapter 6. Matrix Algebra and Multiple Linear Regression: Part 3 – The Concept of Determinants43
- REFERENCES45
- Chapter 7. Matrix Algebra and Multiple Linear Regression: Part 4 – Concluding Remarks47
- A WORD OF CAUTION48
- REFERENCE49
- Chapter 8. Experimental Designs: Part 151
- REFERENCES55
- Chapter 9. Experimental Designs: Part 257
- REFERENCES62
- Chapter 10. Experimental Designs: Part 363
- Chapter 11. Analytic Geometry: Part 1 – The Basics in Two and Three Dimensions71
- THE DISTANCE FORMULA71
- DIRECTION NOTATION72
- THE COSINE FUNCTION72
- DIRECTION IN 3-D SPACE74
- DEFINING SLOPE IN TWO DIMENSIONS75
- RECOMMENDED READING76
- Chapter 12. Analytic Geometry: Part 2 – Geometric Representation of Vectors and Algebraic Operatio77
- VECTOR MULTIPLICATION (SCALAR × VECTOR)77
- VECTOR DIVISION (VECTOR ÷ SCALAR)78
- VECTOR ADDITION (VECTOR + VECTOR)78
- VECTOR SUBTRACTION (VECTOR Š VECTOR)79
- Chapter 13. Analytic Geometry: Part 3 – Reducing Dimensionality81
- REDUCING DIMENSIONALITY81
- 3-D TO 2-D BY PROJECTION81
- 2-D INTO 1-D BY ROTATION84
- Chapter 14. Analytic Geometry: Part 4 – The Geometry of Vectors and Matrices85
- ROW VECTORS IN COLUMN SPACE85
- COLUMN VECTORS IN ROW SPACE85
- PRINCIPAL COMPONENTS FOR REGRESSION VECTORS86
- RECOMMENDED READING88
- Chapter 15. Experimental Designs: Part 4 – Varying Parameters to Expand the Design89
- REFERENCES90
- Chapter 16. Experimental Designs: Part 5 – One-at-a-time Designs91
- REFERENCES92
- Chapter 17. Experimental Designs: Part 6 – Sequential Designs93
- REFERENCES95
- Chapter 18. Experimental Designs: Part 7 – β, the Power of a Test97
- REFERENCES99
- Chapter 19. Experimental Designs: Part 8 – β, the Power of a Test (Continued)101
- REFERENCES102
- Chapter 20. Experimental Designs: Part 9 – Sequential Designs Concluded103
- REFERENCES105
- Chapter 21. Calculating the Solution for Regression Techniques: Part 1 – Multivariate Regression M107
- REFERENCES108
- Chapter 22. Calculating the Solution for Regression Techniques: Part 2 – Principal Component(s) Re109
- REFERENCES111
- Chapter 23. Calculating the Solution for Regression Techniques: Part 3 – Partial Least Squares Reg113
- REFERENCES116
- Chapter 24. Looking Behind and Ahead: Interlude117
- Chapter 25. A Simple Question: The Meaning of Chemometrics Pondered119
- REFERENCES125
- Chapter 26. Calculating the Solution for Regression Techniques: Part 4 – Singular Value Decomposit127
- REFERENCES129
- Chapter 27. Linearity in Calibration131
- REFERENCE134
- Chapter 28. Challenges: Unsolved Problems in Chemometrics135
- REFERENCE139
- Chapter 29. Linearity in Calibration: Act II Scene I141
- REFERENCES144
- Chapter 30. Linearity in Calibration: Act II Scene II – Reader’s Comments . . .145
- REFERENCES148
- Chapter 31. Linearity in Calibration: Act II Scene III149
- REFERENCES157
- Chapter 32. Linearity in Calibration: Act II Scene IV159
- REFERENCES162
- Chapter 33. Linearity in Calibration: Act II Scene V163
- REFERENCES166
- Chapter 34. Collaborative Laboratory Studies: Part 1 – A Blueprint167
- EXPERIMENTAL DESIGN168
- ANALYTICAL METHODS173
- METHOD A and B analysis173
- RESULTS AND DATA ANALYSIS173
- REFERENCES177
- Chapter 35. Collaborative Laboratory Studies: Part 2 – using ANOVA179
- ANOVA TEST COMPARISONS FOR LABORATORIES AND METHODS (ANOVA_s4 WORKSHEET)179
- ANOVA test comparisons (using ANOVA_s2 worksheet)180
- REFERENCES181
- Chapter 36. Collaborative Laboratory Studies: Part 3 – Testing for Systematic Error183
- TESTING FOR SYSTEMATIC ERROR IN A METHOD: COMPARISON TEST FOR A SET OF MEASUREMENTS VERSUS TRUE VALU183
- REFERENCES184
- Chapter 37. Collaborative Laboratory Studies: Part 4 – Ranking Test185
- RANKING TEST FOR LABORATORIES AND METHODS (MANUAL COMPUTATIONS)185
- REFERENCE186
- Chapter 38. Collaborative Laboratory Studies: Part 5 – Efficient Comparison of Two Methods187
- COMPUTATIONS FOR EFFICIENT COMPARISON OF TWO METHODS (COMP_METH WORKSHEET)187
- SUMMARY192
- ACKNOWLEDGEMENT192
- REFERENCES192
- Chapter 39. Collaborative Laboratory Studies: Part 6 – MathCad Worksheet Text193
- REFERENCES222
- Chapter 40. Is Noise Brought by the Stork? Analysis of Noise: Part 1223
- REFERENCES226
- Chapter 41. Analysis of Noise: Part 2227
- APPENDIX232
- REFERENCES233
- Chapter 42. Analysis of Noise: Part 3235
- REFERENCES242
- Chapter 43. Analysis of Noise: Part 4243
- REFERENCES252
- Chapter 44. Analysis of Noise: Part 5253
- ALTERNATE ANALYSIS258
- ABSORBANCE NOISE IN THE “HIGH NOISE” REGIME266
- REFERENCES268
- Chapter 45. Analysis of Noise: Part 6271
- REFERENCES276
- Chapter 46. Analysis of Noise: Part 7277
- EFFECT OF NOISE ON COMPUTED TRANSMITTANCE279
- COMPUTED TRANSMITTANCE NOISE281
- REFERENCES283
- Chapter 47. Analysis of Noise: Part 8285
- REFERENCES292
- Chapter 48. Analysis of Noise: Part 9293
- REFERENCES298
- Chapter 49. Analysis of Noise: Part 10299
- DISCUSSION308
- REFERENCES311
- Chapter 50. Analysis of Noise: Part 11313
- REFERENCES315
- Chapter 51. Analysis of Noise: Part 12317
- REFERENCES321
- Chapter 52. Analysis of Noise: Part 13323
- REFERENCES327
- Chapter 53. Analysis of Noise: Part 14329
- PRELIMINARY STEPS332
- EVALUATION OF THE FUNCTION335
- REFERENCES337
- Chapter 54. Derivatives in Spectroscopy: Part 1 – The Behavior of the Derivative339
- THE BEHAVIOR OF THEORETICAL DERIVATIVES339
- THE BEHAVIOR OF COMPUTED DERIVATIVES344
- REFERENCES350
- Chapter 55. Derivatives in Spectroscopy: Part 2 The TrueŽ Derivative351
- BETTER DERIVATIVE APPROXIMATIONS352
- REFERENCES357
- Chapter 56. Derivatives in Spectroscopy: Part 3 – Computing the Derivative359
- METHODS OF COMPUTING THE DERIVATIVE360
- LIMITATIONS OF THE SAVITZKY–GOLAY METHOD363
- EXTENSIONS TO THE SAVITZKY–GOLAY METHOD365
- REFERENCES369
- Chapter 57. Derivatives in Spectroscopy: Part 4 – Calibrating with Derivatives371
- ACKNOWLEDGEMENT378
- REFERENCES378
- Chapter 58. Comparison of Goodness of Fit Statistics for Linear Regression: Part 1 – Introduction379
- REFERENCE384
- Chapter 59. Comparison of Goodness of Fit Statistics for Linear Regression: Part 2 – The Correlati385
- REFERENCES391
- Chapter 60. Comparison of Goodness of Fit Statistics for Linear Regression: Part 3 – Computing Con393
- TESTING CORRELATION FOR DIFFERENT SIZE POPULATIONS396
- REFERENCES397
- Chapter 61. Comparison of Goodness of Fit Statistics for Linear Regression: Part 4 – Confidence Li399
- REFERENCES401
- Supplement402
- MathCad Worksheets for Correlation, Slope and Intercept402
- REFERENCES412
- Chapter 62. Correction and Discussion Regarding Derivatives413
- REFERENCES419
- Chapter 63. Linearity in Calibration: Act III Scene I – Importance of Nonlinearity421
- WHY IS NONLINEARITY IMPORTANT?421
- REFERENCES426
- Chapter 64. Linearity in Calibration: Act III Scene II – A Discussion of the Durbin-Watson Statist427
- REFERENCES434
- Chapter 65. Linearity in Calibration: Act III Scene III – Other Tests for Nonlinearity435
- F -TEST435
- NORMALITY OF RESIDUALS437
- Chapter 66. Linearity in Calibration: Act III Scene IV – How to Test for Nonlinearity439
- CONCLUSION445
- APPENDIX A: DERIVATION AND DISCUSSION OF THE FORMULA IN EQUATION 66–11447
- REFERENCES449
- Chapter 67. Linearity in Calibration: Act III Scene V – Quantifying Nonlinearity451
- REFERENCES458
- Chapter 68. Linearity in Calibration: Act III Scene VI – Quantifying Nonlinearity, Part II, and a459
- NEWS FLASH!!463
- REFERENCES468
- Chapter 69. Connecting Chemometrics to Statistics: Part 1 – The Chemometrics Side471
- REFERENCES475
- Chapter 70. Connecting Chemometrics to Statistics: Part 2 – The Statistics Side477
- MULTIVARIATE ANOVA477
- REFERENCES480
- Chapter 71. Limitations in Analytical Accuracy: Part 1 – Horwitz’s Trumpet481
- REFERENCES485
- Chapter 72. Limitations in Analytical Accuracy: Part 2 – Theories to Describe the Limits in Analyt487
- DETECTION LIMIT FOR CONCENTRATIONS NEAR ZERO488
- REFERENCES489
- Chapter 73. Limitations in Analytical Accuracy: Part 3 – Comparing Test Results for Analytical Unc491
- UNCERTAINTY IN AN ANALYTICAL MEASUREMENT491
- COMPARISON TEST FOR A SINGLE SET OF MEASUREMENTS VERSUS A TRUE ANALYTICAL RESULT491
- COMPARISON TEST FOR A TWO SETS OF MEASUREMENTS492
- CALCULATING THE NUMBER OF MEASUREMENTS REQUIRED TO ESTABLISH A MEAN VALUE (OR ANALYTICAL RESULT) WIT493
- THE Q-TEST FOR OUTLIERS [1–3]494
- SUMMATION OF VARIANCE FROM SEVERAL DATA SETS494
- REFERENCES495
- Chapter 74. The Statistics of Spectral Searches497
- COMMON SPECTRAL MATCHING APPROACHES497
- MAHALANOBIS DISTANCE MEASUREMENTS497
- EUCLIDEAN DISTANCE499
- COMMON SPECTRAL MATCHING (CORRELATION OR DOT PRODUCT)499
- REFERENCES500
- Chapter 75. The Chemometrics of Imaging Spectroscopy503
- IMAGE PROJECTION OF SPECTROSCOPIC DATA503
- REFERENCES507
- Glossary of Terms509
- Index513
- COLOUR PLATE SECTION527
Book details
- Vendor Elsevier S & T
- SKU 9780123740243
- ISBN-13 9780080548388
- Author Mark, Howard; Workman, Jerry, Jr.
- Category Science
- Subject Spectroscopy & Spectrum Analysis
Do you have questions about this book?
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
* 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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