Statistics in Spectroscopy (eBook)

Cover 1
Contents 8
Preface 12
Chapter 1. Introduction: Why This Book? 16
Chapter 2. Important Concepts from Probability Theory 22
Chapter 3. Populations and Samples: The Meaning of "Statistics" 32
Chapter 4. Degrees of Freedom 40
Chapter 5. Introduction to Distributions and Probability Sampling 50
Chapter 6. The Normal Distribution 62
Chapter 7. Alternative Ways to Calculate Standard Deviation 74
Chapter 8. The Central Limit Theorem 86
Chapter 9. Synthesis of Variance 96
Chapter 10. Where Are We and Where Are We Going? 106
Chapter 11. More and Different Statistics 112
Chapter 12. The T Statistic 122
Chapter 13. Distribution of Means 132
Chapter 14. One- and Two-Tailed Tests 140
Chapter 15. Philosophical Interlude 150
Chapter 16. Biased and Unbiased Estimators 156
Chapter 17. The Variance of Variance 162
Chapter 18. Hypothesis Testing of Chi-Square 170
Chapter 19. More Hypothesis Testing 176
Chapter 20. Statistical Inferences 182
Chapter 21. How to Count 190
Chapter 22. And Still Counting 196
Chapter 23. Contingency Tables 202
Chapter 24. What Do You Mean: Random? 210
Chapter 25. The F Statistic 220
Chapter 26. Precision and Accuracy: Introduction to Analysis of Variance 228
Chapter 27. Analysis of Variance and Statistical Design of Experiments 238
Chapter 28. Crossed and Nested Experiments 248
Chapter 29. Miscellaneous Considerations Regarding Analysis of Variance 262
Chapter 30. Pitfalls of Statistics 270
Chapter 31. Pitfalls of Statistics Continued 278
Chapter 32. Calibration in Spectroscopy 286
Chapter 33. Calibration: Linear Regression as a Statistical Technique 294
Chapter 34. Calibration: Error Sources in Calibration 302
Chapter 35. Calibration: Selecting the Calibration Samples 308
Chapter 36. Calibration: Developing the Calibration Model 312
Chapter 37. Calibration: Auxiliary Statistics for the Calibration Model 318
Chapter 38. The Beginning 328
Index 334