Chemometrics in Spectroscopy

Chapter 1 - A New Beginning

Section 1 - Elementary Matrix AlgebraChapter 2 - Elementary Matrix Algebra, Part 1Chapter 3 - Elementary Matrix Algebra, Part 2

Section 2 - Matrix Algebra and Multiple Linear RegressionChapter 4 - Matrix Algebra and Multiple Linear Regression: Part 1Chapter 5 - Matrix Algebra and Multiple Linear Regression: Part 2Chapter 6 - Matrix Algebra and Multiple Linear Regression: Part 3 - The Concept of DeterminantsChapter 7 - Matrix Algebra and Multiple Linear Regression: Part 4 - Concluding Remarks

Section 3 - Experimental DesignsChapter 8 - Experimental Designs, Part I: IntroductionChapter 9 - Experimental Designs, Part II: One-way ANOVAChapter 10 - Experimental Designs, Part III - Two-factor DesignsChapter 11 - Experimental Designs, Part IV:- Varying Parameters to Expand the DesignChapter 12 - Experimental Designs Part V: One-at-a-time DesignsChapter 13 - Experimental Designs, Part VI: Sequential designsChapter 14 - Experimental Designs, Part 7: β, the Power of a TestChapter 15 - Experimental Designs, Part 8: β, the Power of a Test (continued)Chapter 16 - Experimental Designs, Part 9: Sequential Designs concluded

Section 4 - Analytic GeometryChapter 17 - Analytic Geometry: Part 1 - The Basics in Two and Three DimensionsChapter 18 - Analytic Geometry: Part 2 - Geometric Representation of Vectors and Algebraic OperationChapter 19 - Analytic Geometry: Part 3 - Reducing DimensionalityChapter 20 - Analytic Geometry: Part 4 - The Geometry of Vectors and Matrices

Section 5 - Regression TechniquesChapter 21 - Calculating the Solution for Regression Techniques: Part 1 - Multivariate Regression Made SimpleChapter 22 - Calculating the Solution for Regression Techniques: Part 2 - Principal Component(s) Regression Made SimpleChapter 23 - Calculating the Solution for Regression Techniques: Part 3 - Partial Least Squares Made SimpleChapter 24 - Calculating the Solution for Regression Techniques: Part 4 - Singular Value Decomposition Made SimpleChapter 25 - Interlude: Looking Behind and AheadChapter 26 - A Simple QuestionChapter 27 - Challenges: Unsolved Problems in Chemometrics

Section 6 - Linearity in CalibrationChapter 28 - Linearity in Calibration, Act IChapter 29 - Linearity in Calibration - Act II Scene IChapter 30 - Linearity in Calibration - Act II Scene II: Reader ResponsesChapter 31 - Linearity in Calibration - Act II Scene IIIChapter 32 - Linearity in Calibration - Act II Scene IVChapter 33 - Linearity in Calibration - Act II Scene V

Section 7 - Collaborative Laboratory StudiesChapter 34 - Collaborative Laboratory Studies: Part 1 - A BlueprintChapter 35 - Collaborative Laboratory Studies: Part 2 - Using ANOVAChapter 36 - Collaborative Laboratory Studies: Part 3 - Testing for Systematic ErrorChapter 37 - Collaborative Laboratory Studies: Part 4 - Ranking TestChapter 38 - Collaborative Laboratory Studies: Part 5 - Efficient Comparison of Two MethodsChapter 39 - Collaborative Laboratory Studies: Part 6 - MathCAD Worksheet Text

Section 8 - Analysis of NoiseChapter 40 - Is Noise Brought by the Stork? Analysis of Noise - Part 1Chapter 41 - Analysis of Noise - Part 2Chapter 42 - Analysis of Noise - Part 3Chapter 43 - Analysis of Noise - Part 4Chapter 44 - Analysis of Noise - Part 5Chapter 45 - Analysis of Noise - Part 6Chapter 46 - Analysis of Noise - Part 7Chapter 47- Analysis of Noise - Part 8Chapter 48 - Analysis of Noise - Part 9Chapter 49 - Analysis of Noise - Part 10Chapter 50 - Analysis of Noise - Part 11Chapter 51 - Analysis of Noise - Part 12Chapter 52 - Analysis of Noise - Part 13Chapter 53 - Analysis of Noise - Part 14Chapter 54 - Analysis of Noise - Part 15

Section 9 - DerivativesChapter 55 - Derivatives in Spectroscopy, Part 1 - The Behavior of the Theoretical Derivative Chapter 56 - Derivatives in Spectroscopy, Part 2 - The "True" DerivativeChapter 57 - Derivatives in Spectroscopy, Part 3 - Computing the Derivative (the Savitzky-Golay method) Chapter 58 - Derivatives in Spectroscopy, Part 4 - Calibrating with DerivativesChapter 59 - Corrections and Discussion Regarding Derivatives

Section 10 - Goodness of Fit StatisticsChapter 60 - Comparison of Goodness-of-Fit Statistics for Linear Regression: Part 1 - IntroductionChapter 61 - Comparison of Goodness-of-Fit Statistics for Linear Regression: Part 2 - The Correlation Coefficient Chapter 62 - Comparison of Goodness-of-Fit Statistics for Linear Regression: Part 3 - Computing Confidence Limits for the Correlation CoefficientChapter 63 - Comparison of Goodness-of-Fit Statistics for Linear Regression: Part 4 - Confidence Limits for Slope and Intercept

Section 11 - More About Linearity in CalibrationChapter 64 - Linearity in Calibration, Act III Scene I: Importance of (non)LinearityChapter 65 - Linearity in Calibration, Act III Scene II: A Discussion of the Durbin-Watson Statistic, a Step in the Right DirectionChapter 66 - Linearity in Calibration, Act III Scene III: Other Tests for non-LinearityChapter 67 - Linearity in Calibration, Act III Scene IV: How Test For non-LinearityChapter 68 - Linearity in Calibration: Act III Scene V: Quantifying Non-linearityChapter 69 - Linearity in Calibration, Act III Scene VI: Quantifying Non-linearity, Part II, and a News Flash

Section 12 - Connecting Chemometrics to StatisticsChapter 70 - Connecting Chemometrics to Statistics Part 1: The Chemometrics SideChapter 71 - Connecting Chemometrics to Statistics - Part 2, the Statistics Side

Section 13 - Limitations in Analytical AccuracyChapter 72 - Limitations in Analytical Accuracy: Part 1 - Horwitz's TrumpetChapter 73 - Limitations in Analytical Accuracy: Part 2 - Theories to Describe the Limits in Analytical AccuracyChapter 74 - Limitations in Analytical Accuracy: Part 3 - Comparing Test Results for Analytical UncertaintyChapter 75 - The Statistics of Spectral SearchesChapter 76 - The Chemometrics of Imaging SpectroscopyChapter 77 - Corrections to Analysis of Noise - Part 1Chapter 78 - Corrections to Analysis of Noise - Part 2Chapter 79 - What can NIR predict?

Section 14 - Derivations of Principal ComponentsChapter 80 - The Long, Complicated, Tedious and Difficult Route to Principal Components (or, when you’re through reading this set you’ll know why it’s always done with matrices) - Part I, Introduction and ReviewChapter 81 - The Long, Complicated, Tedious and Difficult Route to Principal Components (or, when you’re through reading this set you’ll know why it’s always done with matrices) - Part II, our first attempt: univariate curve fittingChapter 82 - The Long, Complicated, Tedious and Difficult Route to Principal Components (or, when you’re through reading this set you’ll know why it’s always done with matrices) - Part III, multivariate curve fittingChapter 83 - The Long, Complicated, Tedious and Difficult Route to Principal Components (or, when you’re through reading this set you’ll know why it’s always done with matrices) - Part IV, the Lagrange MultiplierChapter 84 - The Long, Complicated, Tedious and Difficult Route to Principal Components (or, when you’re through reading this set you’ll know why it’s always done with matrices) - Part V, Solving the Equations with DeterminantsChapter 85 - The Long, Complicated, Tedious and Difficult Route to Principal Components (or, when you’re through reading this set you’ll know why it’s always done with matrices) - Part VI: Solving the Equations Without DeterminantsChapter 86 - The Long, Complicated, Tedious and Difficult Route to Principal Components (or, when you’re through reading this set you’ll know why it’s always done with matrices) - Coda: Applying Constrained Univariate Calculations

Section 15 - Clinical Data ReportingChapter 87 - Statistics and Chemometrics for Clinical Data Reporting - Part 1Chapter 88 - Statistics and Chemometrics for Clinical Data Reporting - Part 2: Using Excel for ComputationsChapter 89 - Statistics and Chemometrics for Clinical Data Reporting - Part 3: Using Excel for Data Plotting

Section 16 - Classical Least Squares (CLS)Chapter 90 - Classical Least Squares, Part 1: Mathematical theoryChapter 91 - Classical Least Squares, Part 2: Mathematical Theory ContinuedChapter 92 - Classical Least Squares, Part 3: Spectroscopic TheoryChapter 93 - Classical Least Squares, Part 4: Spectroscopic Theory ContinuedChapter 94 - Classical Least Squares, Part 5: Experimental ResultsChapter 95 - Classical Least Squares, Part 6: Spectral ResultsChapter 96 - Classical Least Squares, Part 7: Spectral Reconstruction of MixturesChapter 97 - Classical Least Squares, Part 8: Comparison of CLS Values with Known ValuesChapter 98 - Classical Least Squares, Part 9: Spectral Results from a Second LaboratoryChapter 99 - Classical Least Squares, Part 10: Numerical Results from the Second LaboratoryChapter 100 - Classical Least Squares, Part 11: Comparison of Results from the Two Laboratories Continued

Section 17 - Transfer of CalibrationsChapter 101 - Transfer of Calibrations - Part 1Chapter 102 - Chapter 102 - Calibration Transfer - Part 2: The Instrumentation AspectsChapter 103 - Calibration Transfer - Part 3: The Mathematical AspectsChapter 104 - Calibration Transfer - Part 4: Measuring the Agreement Between Instruments Following Calibration TransferChapter 105 - Calibration transfer - Part 5: The Mathematics of Wavelength Standards Used for SpectroscopyChapter 106 - Calibration transfer - Part 6: The Mathematics of Photometric Standards Used for Spectroscopy

Section 18 - The Importance of Units of MeasureChapter 107 - Units of Measure in Spectroscopy, Part 1: ... and Then The Light DawnedChapter 108 - Units of Measure in Spectroscopy, Part 2: It's the VOLUME, Folks!Chapter 109 - Units of Measure in Spectroscopy, Part 3: What Does it all MeanChapter 110 - Units of Measure in Spectroscopy, Part IV: Summary of our FindingsChapter 111 - Units of Measure in Spectroscopy, Part V: The "Mythbusters" and Spectral Reconstruction

Section 19 - The Best Calibration ModelChapter 112 - Choosing the Best Calibration ModelChapter 113 - Optimizing the Regression Bias and Slope

Section 20 - StatisticsChapter 114 - Statistics, Part I: First FoundationChapter 115 - STATISTICS, Part II – Second FoundationChapter 116 - STATISTICS, Part III: Third FoundationChapter 117 - Calibration Transfer Chemometrics, Part 1: Review of the SubjectChapter 118 - Calibration Transfer Chemometrics, Part 2: Overview

Section 21 - OutliersChapter 119 - Classical Least Squares, Part 13: What does it mean?Outliers - Part 1: What are OutliersChapter 120 - Classical Least Squares, Part 13: What does it mean?Outliers - Part 2: Pitfalls in Detecting OutliersChapter 121 - Classical Least Squares, Part 13: What does it mean?Outliers - Part 3: Dealing with Outliers

Section 22 - Spectral Transfer: Making Instruments AgreeChapter 122 - Calibration Transfer Chemometrics, Part 1: Review of the SubjectChapter 123 - Calibration Transfer Chemometrics, Part 2: Review of the Subject

Section 23 - Applying Standard Reference MaterialsChapter 124 - How to Apply Standard Reference Materials, Part 1Chapter 125 - How to Apply Standard Reference Materials, Part 2

Section 24 - More About CLSChapter 126 - More About CLS, Part 1: Expanding the ConceptChapter 127 - More About CLS, Part 2: Spectral Results & CLS (not requiring constituent values)Chapter 128 - More About CLS, Part 3: Expanding the Analysis to Include Concentration Information (PCR & PLS)