## Statistics in SpectroscopyThis tutorial offers a basic hands-on approach to statistical analysis for chemists and spectroscopists. Without involving complicated mathematics, this book is designed to provide the reader with the basic principles underlying the use of common mathematical and statistical tools. Particular emphasis has been given to problem-solving applications and the proper use and interpretation of spectroscopic data. With exercises throughout, this book is also suitable for use as a textbook in analytical chemistry, instrumental analysis, and statistics in chemistry courses. Key Features * Serves as a primer for all chemists who need to know more about statistical analysis * Explains the effect of error on data and how to make the correct interpretation * Written in a readable style with minimal mathematics * Developed from the popular series of the same name first published in Spectroscropy magazine |

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### Contents

1 | |

7 | |

17 | |

Chapter 4 DEGREES OF FREEDOM | 25 |

Chapter 5 INTRODUCTION TO DISTRIBUTIONS AND PROBABILITY SAMPLING | 35 |

Chapter 6 THE NORMAL DISTRIBUTION | 45 |

Chapter 7 ALTERNATIVE WAYS TO CALCULATE STANDARD DEVIATION | 57 |

Chapter 8 THE CENTRAL LIMIT THEOREM | 69 |

Chapter 21 HOW TO COUNT | 169 |

Chapter 22 AND STILL COUNTING | 175 |

Chapter 23 CONTINGENCY TABLES | 181 |

Chapter 24 WHAT DO YOU MEAN RANDOM? | 189 |

Chapter 25 THE F STATISTIC | 199 |

INTRODUCTION TO ANALYSIS OF VARIANCE | 207 |

Chapter 27 ANALYSIS OF VARIANCE AND STATISTICAL DESIGN OF EXPERIMENTS | 217 |

Chapter 28 CROSSED AND NESTED EXPERIMENTS | 229 |

Chapter 9 SYNTHESIS OF VARIANCE | 79 |

Chapter 10 WHERE ARE WE AND WHERE ARE WE GOING? | 87 |

Chapter 11 MORE AND DIFFERENT STATISTICS | 93 |

Chapter 12 THE T STATISTIC | 103 |

Chapter 13 DISTRIBUTION OF MEANS | 113 |

Chapter 14 ONE AND TWOTAILED TESTS | 121 |

Chapter 15 PHILOSOPHICAL INTERLUDE | 131 |

Chapter 16 BIASED AND UNBIASED ESTIMATORS | 135 |

Chapter 17 THE VARIANCE OF VARIANCE | 141 |

Chapter 18 HYPOTHESIS TESTING OF CHISQUARE | 149 |

Chapter 19 MORE HYPOTHESIS TESTING | 155 |

Chapter 20 STATISTICAL INFERENCES | 161 |

Chapter 29 MISCELLANEOUS CONSIDERATIONS REGARDING ANALYSIS OF VARIANCE | 239 |

Chapter 30 PITFALLS OF STATISTICS | 247 |

Chapter 31 PITFALLS OF STATISTICS CONTINUED | 255 |

Chapter 32 CALIBRATION IN SPECTROSCOPY | 263 |

LINEAR REGRESSION AS A STATISTICAL TECHNIQUE | 271 |

ERROR SOURCES IN CALIBRATION | 277 |

SELECTING THE CALIBRATION SAMPLES | 283 |

DEVELOPING THE CALIBRATION MODEL | 287 |

AUXILIARY STATISTICS FOR THE CALIBRATION MODEL | 293 |

Chapter 38 THE BEGINNING | 303 |

309 | |

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### Common terms and phrases

actually algorithm analysis of variance analyte ANOVA ANOVA table apply assumption average bution calculated calibration model calibration set Central Limit Theorem Chapter chemometrics coefﬁcient column computed concentration conﬁdence interval conﬁdence level conﬁdence limit corresponding critical values data points deﬁned deﬁnition degrees of freedom determine discussion distri effect equal error sources estimate example expected value experiment experimental design F statistic fact factors Figure ﬁnd ﬁnite ﬁrst ﬁt ﬁve formula given important included inﬁnite instrument integers mathematical mean square nn nn nn noise level Normal distribution null hypothesis number of degrees obtained outlier parameter performing hypothesis tests population mean population value probability levels problem properties question random numbers random samples range reader readings reﬂectance regression relationship represents residuals sample mean selected signiﬁcant situation speciﬁed spectra spectroscopic spectroscopy standard deviation statisticians sum of squares techniques term test statistic tion unbiased variability variation wavelength wavenumbers zero