Chapter 13
Statistical Techniques for the Interpretation
of Analytical Data
Pedro J. Mart ́ın-Alvarez ́
Contents
13.1 UnivariateStatisticalTechniques ............................................. 677
13.1.1 StatisticalTreatmentforOnlyOneSample.............................. 678
13.1.2 StatisticalTreatmenttoCompareTwoIndependent Samples ............... 680
13.1.3 StatisticalTreatmenttoCompareTwoRelatedSamples ................... 681
13.1.4 StatisticalTreatmenttoCompareMorethanTwoIndependentSamples...... 682
13.2 BivariateStatisticalTechniques .............................................. 688
13.2.1 CorrelationAnalysis ................................................ 688
13.2.2 SimpleLinearRegressionAnalysis .................................... 689
13.3 MultivariateStatisticalTechniques............................................ 692
13.3.1 Introduction................ ........................................ 692
13.3.2 MultivariateStatisticalNonSupervisedTechniques....................... 693
13.3.3 MultivariateStatisticalSupervisedTechniques........................... 699
13.3.4 MultivariateStatisticalTechniquestoStudyDependence .................. 706
References ............................................................... 710
In this chapter, I will try to explain some of the statistical methods (univariate, bivari-
ate and multivariate) most used by our group, in the hope that it will be useful and
accessible for the majority of readers, given that the emphasis is on comprehension
of the principles of the methods, their applications and interpretation of the results
obtained.
13.1 Univariate Statistical Techniques
In this first section, we will consider the statistical methods to process data, originat-
ing in the observation ofa single continuous random variable. We will distinguish
three possible situations, with one, two or more than two data sets of the observed
variable. In the last case, we will present the Analysis of Variance (ANOVA) for one
or more factors.
P. J. M a r t ́ın-Alvarez ( ́ B)
Instituto de Fermentaciones Industriales, Consejo Superior de Investigaciones Cient ́ıficas (CSIC),
C/Juan de la Cierva 3, 28006 Madrid, Spain
e-mail: [email protected]
M.V. Moreno-Arribas, M.C. Polo (eds.),Wine Chemistry and Biochemistry,
DOI 10.1007/978-0-387-74118-525,©CSpringer Science+Business Media, LLC 2009
677