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Published in:
Principles of Identification Read chapter Read first chapter

2011 | OriginalPaper | Chapter

3. Probability, Statistics, and Related Methods

Author : Boris L. Milman

Published in: Chemical Identification and its Quality Assurance

Publisher: Springer Berlin Heidelberg

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Abstract

The probability/statistical methods used for identification purposes are briefly considered. The basic statement is that many phenomena and procedures included in qualitative analysis are of a probabilistic nature. The probability of yes/no responses in target detection is described by binomial distribution. Values of quantities required for identification, such as retention times in chromatography, wavelengths and frequencies in optical spectroscopy, masses in mass spectrometry, intensities (heights, areas) of any analytical signals, are considered as normally distributed (including t-distributed) ones over probabilities. Parameters of the distributions are used in calculations incorporated into procedures of detection and identification. Multivariate statistics connected with chemometrics is essential for classification/authentication of samples, i.e., qualitative analysis II. Bayesian statistics takes into account a prior probability that an analyte is present in a sample.
In the second part of this chapter, operations of setting up, testing, and screening of hypotheses as the core processes of qualitative analysis, are considered. The simplest are hypotheses for a detection operation, e.g., ‘\( {H_0} \): an analyte is absent in the sample’. In identification, analogous hypotheses: ‘\( {H_0} \): the analyte is compound A’, and ‘\( {\overline H_0} \): the analyte is not compound A’ are set up and tested. Identification hypotheses are transformed into experimental and statistical ones to be accepted or rejected on the basis of corresponding criteria, both range/tolerance and statistical criteria. False acceptance or rejection of hypotheses leads to false positive/negative results of identification or detection, the probability of which can be estimated.

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previous chapter Techniques and Methods of Identification
next chapter Reliability and Errors of Identification
Footnotes
1
In this book, two similar but not the same meanings of sample occur. They are “a part of something to be tested” (this case) and “a subset of random values selected from a population” (statistical issues).
 
2
In the case of a large number of replicate measurements, the population standard deviation σ can be estimated by the sample parameter s.
 
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Metadata
Title
Probability, Statistics, and Related Methods
Author
Boris L. Milman
Copyright Year
2011
Publisher
Springer Berlin Heidelberg
Book
Chemical Identification and its Quality Assurance

Print ISBN: 978-3-642-15360-0

Electronic ISBN: 978-3-642-15361-7

Copyright Year: 2011

DOI
https://doi.org/10.1007/978-3-642-15361-7_3

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