# Chemometrics in Spectroscopy

**By**

- Howard Mark, Mark Electronics, Suffern, New York, U.S.A.
- Jerome Workman, Thermo Electron Corporation, Molecular Spectroscopy and Microanalysis, Madison, U.S.A.

**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.

View full description### Audience

For graduate students and above and for the practicing analyst or theoretician. Chemometricians, bioinformaticians, econometricians, psychometricians, statisticians, scientists, spectroscopists, analysts, clinicians, researchers, computer scientists, information specialists, and students in the natural sciences will all find the short descriptive chapters both helpful and full of valuable insight for mathematical and philosophical methods and approaches common to all these fields.

### Table of Contents

1. A New Beginning

2. Elementary Matrix Algebra, Part 1

3. Elementary Matrix Algebra, Part 2

4. Matrix Algebra and Multiple Linear Regression, Part 1

5. Matrix Algebra and Multiple Linear Regression, Part 2

6. Matrix Algebra and Multiple Linear Regression, Part 3

7. Matrix Algebra and Multiple Linear Regression: Conclusion

8. Experimental Designs - Part 1

9. Experimental Designs - Part 2

10. Experimental Designs - Part 3

11. Analytic Geometry, Part I

12. Analytic Geometry, Part II

13. Analytic Geometry, Part III

14. Analytic Geometry, Part IV

15. Experimental Designs Part IV - Varying Parameters to Expand the Design

16. Experimental Designs Part V - One-at-a-time Designs

17. Experimental Designs Part VI - Sequential Designs

18. Experimental Designs Part VII, The Power of a Test

19. Experimental Designs Part VIII, The Power of a Test (Continued)

20. Experimental Designs Part IX - Sequential Designs Concluded

21. Calculating the Solution for Regression Techniques - Part I: Multivariate Regression Made Simple

22. Calculating the Solution for Regression Techniques - Part II: Principal Component(s) Regression Made Simple

23. Calculating the Solution for Regression Techniques - Part III: Partial Least Squares Regression Made Simple

24. Looking Ahead and Behind

25. A Simple Question

26. Calculating the Solution for Regression Techniques - Part IV: Singular Value Decomposition

27. Linearity in Calibration

28. Challenges: Unsolved Problems in Chemometrics

29. Linearity in Calibration - Act II Scene I

30. Linearity in Calibration - Act II Scene II

31. Linearity in Calibration - Act II Scene III

32. Linearity in Calibration - Act II Scene IV

33. Linearity in Calibration - Act II Scene V

34. A Blueprint for Collaborative Laboratory Studies

35. Using ANOVA for Collaborative Laboratory Studies, Part Two

36. Testing for Systematic Error in Collaborative Laboratory Studies, Part Three

37. Ranking Test for Collaborative Studies, Part Four

38. Efficient Comparison of Two Methods for Collaborative Laboratory Studies

39. More About Collaborative Laboratory Studies, a Brief Recap and Additional Resources, Part Five

40. Is Noise Brought by the Stork?: Analysis of Noise, Part 1

41. Analysis of Noise, Part 2

42. Analysis of Noise, Part 3

43. Analysis of Noise, Part 4

44. Analysis of Noise, Part 5

45. Analysis of Noise, Part 6

46. Analysis of Noise, Part 7

47. Analysis of Noise, Part 8

48. Analysis of Noise, Part 9

49. Analysis of Noise, Part 10

50. Analysis of Noise, Part 11

51. Analysis of Noise, Part 12

52. Analysis of Noise, Part 13

53. Analysis of Noise, Part 14

54. Derivatives in Spectroscopy, Part 1: The Behaviour of Derivatives

55. Derivatives in Spectroscopy, Part 2: The True Derivative

56. Derivatives in Spectroscopy, Part 3: Computing the Derivative

57. Derivatives in Spectroscopy, Part 4: Calibrating with Derivatives

58. Comparison of Goodness of Fit Statistics, Part I

59. Comparison of Goodness of Fit Statistics, Part II

60. Comparison of Goodness of Fit Statistics, Part III

61. Comparison of Goodness of Fit Statistics, Part IV

62. Derivatives in Spectroscopy - Update

63. Linearity in Calibration, Act III, Scene I: The Importance of Non-Linearity

64. Linearity in Calibration, Act III, Scene II: The Durbin-Watson Statistic

65. Linearity in Calibration, Act III, Scene III: Other Tests for Non-Linearity

66. Linearity in Calibration, Act III Scene IV: How To Test For non-Linearity

67. Linearity in Calibration, Act III Scene V: Quantifying Non-linearity

68. Linearity in Calibration, Act III Scene VI: Quantifying Non-linearity, Part II, and a News Flash

69. Connecting Chemometrics to Statistics - Part 1, the Chemometrics Side

70. Connecting Chemometrics to Statistics - Part 2, the Statistics Side

71. Limitations in Analytical Accuracy – Part 1

72. Limitations in Analytical Accuracy – Part 2

73. Limitations in Analytical Accuracy – Part 3

74. The Statistics of Spectral Searches

75. The Chemometrics of Imaging Spectroscopy