The Correlation Coefficient: An Overview

REFERENCES

• Warren , W. G. 1971 . Correlation or regression: bias or precision . Applied Statistic , 20 : 148 – 164 . [CSA]
   Web of Science ®Google Scholar
• Moore , B. A. 1980 . Correlation and regression analysis: applications to the analysis of chemical data . Analytical Proceedings , 17 : 124 – 127 . [CSA]
   Google Scholar
• Aknazarova , S. and Kafarov , V. 1982 . Experiment Optimization in Chemistry and Chemical Engineering , 123 – 127 . Moscow : Mir Publishers .
   Google Scholar
• Galton , F. 1888 . Co-relations and their measurement, chiefly from anthropometric data . Proceedings of the Royal Society of London , 45 : 135 – 145 . [CSA]
   Google Scholar
• Rodgers , J. L. and Nicewander , W. A. 1998 . Thirteen ways to look at the correlation coefficient . The American Statistician , 42 : 59 – 66 . [CSA]
   Web of Science ®Google Scholar
• Nadkarni , R. A. 1991 . The quest for quality in the laboratory . Analytical Chemistry , 63 : 675A – 682A . [CSA]
   Web of Science ®Google Scholar
• ISO 9004-4:1993 . 1993 . Quality Management and Quality System Elements. Part 4: Guidelines for Quality Improvement , Geneva : ISO .
   Google Scholar
• 1997 . IUPAC Compendium of Chemical Terminology, , 2nd ed.
   Google Scholar
• Leach , A. R. and Gillet , V. J. 2003 . An Introduction to Chemoinformatics , 79 Dordrecht : Kluwer .
   Google Scholar
• Draper , N. and Smith , H. 1998 . Applied Regression Analysis, , 3th ed. , New York : Wiley .
   Google Scholar
• Deming , S. N. and Morgan , S. L. 1987 . Experimental Design, a Chemometric Approach , 143 – 145 . Amsterdam : Elsevier .
   Google Scholar
• de Maesschalck , R. , Jouan-Rimbaud , D. and Massart , D. L. 2000 . The Mahalanobis distance . Chemometrics and Intelligent Laboratory Systems , 50 : 1 – 18 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Auf der Heyde , T. P. E. 1990 . Analyzing chemical data in more than two dimensions. A tutorial on factor and cluster analysis . Journal of Chemical Education , 67 : 461 – 469 . [CSA]
   Web of Science ®Google Scholar
• Yafle , R. A. 2003 . Common correlation and reliability analysis with SPSS for Windows ⟨http://www.nyu.edu/its/socsci/Docs/correlate.html⟩
   Google Scholar
• Weihs , C. 1993 . Multivariate exploratory data-analysis and graphics—a tutorial . Journal of Chemometrics , 7 : 305 – 340 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Cook , R. D. and Weisberg , S. 1994 . An Introduction to Regression Graphics , 10 – 12 . New York : Wiley .
   Google Scholar
• Tomassone , R. , Lesquoy , E. and Millier , C. 1983 . La Regression, Nouveaux regards sur une ancienne méthode statistique , 21 – 23 . Paris : Masson .
   Google Scholar
• Ouchi , G. I. 1987 . Personal Computers for Scientists, A Byte at a Time , 111 Washingon : American Chemical Society .
   Google Scholar
• Sayago , A. , Boccio , M. and Asuero , A. G. 2004 . Fitting straight lines with replicated observations by linear regression: the least squares postulates . CRC Critical Reviews in Analytical Chemistry , 34 : 39 – 50 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Asuero , A. G. and González , A. G. 1989 . Some observations on fitting a straight line to data . Microchemical Journal , 40 : 216 – 225 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• de Levie , R. 1986 . When, why, and how to use weighted least squares . Journal of Chemical Education , 63 : 10 – 15 . [CSA]
   Web of Science ®Google Scholar
• Exner , O. 1997 . How to get wrong results from good experimental data: a survey of incorrect applications of regression . Journal of Physical Organic Chemistry , 10 : 797 – 813 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Riu , J. and Rius , F. X. 1995 . Univariate regression models with error in both axes . Journal of Chemometrics , 9 : 343 – 362 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Castillo , M. A. and Castells , R. C. 2001 . Initial evaluation of quantitative performance of chromatographic methods using replicates at multiple concentrations . Journal of Chromatography A , 921 : 121 – 133 . [PUBMED] [INFOTRIEVE] [CROSSREF] [CSA]
   PubMed Web of Science ®Google Scholar
• Baumann , K. 1997 . Regression and calibration for analytical separation techniques, Part II Validation, weighted and robust calibration . Process Control Quality , 10 : 75 – 112 . [CSA]
   Google Scholar
• Kelkar , S. N. and Bzik , J. J. 2000 . Calibration of analytical instruments. Impact of nonconstant variance in calibration data . Analytical Chemistry , 72 : 4762 – 4765 . [CROSSREF] [CSA]
   PubMed Web of Science ®Google Scholar
• Bayne , C. K. and Rubin , I. B. 1986 . Practical Experimental Designs and Optimization Methods for Chemistry , Deerfield Beach , FL : VCR Publishers .
   Google Scholar
• Rousseeuw , P. J. and Leroy , A. M. 1987 . Robust Regression and Outlier Detection , 42 New York : Wiley .
   Google Scholar
• Exner , O. and Zvára , K. 1999 . Coefficient of determination in some atypical situations: use in chemical correlation analysis . Journal of Physical Organic Chemistry , 12 : 151 – 156 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Kvalseth , T. O. 1985 . Cautionary note about R2 . The American Statistician , 39 : 279 – 285 . [CSA]
   Web of Science ®Google Scholar
• Asuero , A. G. , González , G. , de Pablos , F. and Gómez Ariza , J. L. 1988 . Determination of the optimum working range in spectrophotometric procedures . Talanta , 35 : 531 – 537 . [CROSSREF] [CSA]
   PubMed Web of Science ®Google Scholar
• Taylor , J. R. 1982 . “ An introduction to error analysis ” . In The study of uncertainties in physical measurements , 185 – 186 . Oxford : University Science Books .
   Google Scholar
• Brownlee , K. A. 1984 . Statistical Methodology in Science and Engineering, , 3th ed. , 77 – 80 . Malabar , Fl : Robert G. Krieger Publishing Co. .
   Google Scholar
• Bremser , W. and Hässelbarth , W. 1998 . Shall we consider covariance? . Accreditation and Qualily Assurance , 3 : 106 – 110 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Salter , C. 2000 . Error using the variance-covariance matrix . Journal of Chemical Education , 57 : 1239 – 1243 . [CSA]
   Google Scholar
• Bruce , G. R. and Gill , P. S.P.S. 1999 . Estimates of precision in a standard addition analysis . Journal of Chemical Education , 76 : 805 – 807 . [CSA]
   Web of Science ®Google Scholar
• Meyer , E. F. 1997 . A note on covariance in propagation of uncertainty . Journal of Chemical Education , 74 : 1339 – 1340 . [CSA]
   Web of Science ®Google Scholar
• de Levie , R. 2004 . Advanced Excel for Scientific Data Analysis , 91 – 92 . Oxford : Oxford University Press .
   Google Scholar
• Bookbinder , M. and Panosian , K. J. 1987 . Using the coefficient of correlation in method-comparison studies . Clinical Chemistry , 33 : 1170 – 1176 . [PUBMED] [INFOTRIEVE] [CSA]
   PubMed Web of Science ®Google Scholar
• Johnson , R. A. and Wichern , D. W. 1992 . Applied Multivariate Statistical Analysis, , 3rd ed. , 11 – 12 . Englewood Cliffs , NJ : Prentice-Hall .
   Google Scholar
• Sands , D. E. 1977 . Correlation and covariance . Journal of Chemical Education , 54 : 90 – 94 . [CSA]
   Web of Science ®Google Scholar
• Gad , S. C. 1999 . Statistics and Experimental Design for Toxicologists , 49 – 51 . Boca Raton , FL : CRC Press . 119
   Google Scholar
• Garson , G. D. 1999 . Correlation ⟨http://www2.chass.ncsu.edu/garson/pa765/correl.htm⟩
   Google Scholar
• Wilcox , R. R. 2001 . Fundamentals of Modern Statistical Methods , New York : Springer-Verlag .
   Google Scholar
• Hopkins , W. G. 2004 . A new view of statistics, correlation coefficient ⟨http://www.sportsci.org/resource/stats/correl.html⟩
   Google Scholar
• Zady , M. F. October 2000 . Correlation and simple least squares regression October , ⟨http://www.westgard.com/lesson44.htm⟩
   Google Scholar
• Lawson , J. and Erjavec , J. 2000 . Modern Statistics for Engineering and Quality Improvement , New York : Brooks Cole .
   Google Scholar
• Phillippe , J. 1967 . Les Méthodes Statistiques en Pharmacie et en Chimie , Paris : Masson .
   Google Scholar
• Dallal , G. E. 2003 . Correlation coefficient ⟨http://www.tufts.edu/~gdallal/corr.htm⟩
   Google Scholar
• Armstrong , N. A. and James , K. C. 1996 . Pharmaceutical Experimental Design and Interpretation , 59 London : Taylor and Francis .
   Google Scholar
• Stoeppler , M. , Valenta , P. and Nürnberg , H. W. 1979 . Application of independent methods and standard materials–effective approach to relible trace and ultratrace analysis of metals and metalloids in environment and biological studies . Fresenius Zeitschrif für analytische Chemie. Anal. Chem , 297 : 22 – 34 . [CSA]
   Google Scholar
• Cox , M. G. and Harris , P. M. 1999 . Design and use of reference data sets for testing scientific software . Analytical Chimica Acta , 380 : 339 – 351 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Wanek , P. M. , Whippe , R. E. , Fickies , T. E. and Grant , P. M. 1982 . Inaccuracies in the calculation of standard-deviation with electronic calculators . Analytical Chemistry , 54 : 1877 – 1878 . [CSA]
   Web of Science ®Google Scholar
• McCullough , B. D. and Wilson , B. 1999 . On the accuracy of statistical procedures in Microsoft Excel 97 . Computational Statistical Data Analysis , 31 : 27 – 37 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Miller , J. N. 1991 . Basic statistical methods for analytical chemistry. Part 2. Calibration and regression methods. A review . Analyst , 116 : 3 – 14 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Meier , P. C. and Zünd , R. E. 2000 . Statistical Methods in Analytical Chemistry, , 2nd ed. , 92 – 94 . New York : Wiley .
   Google Scholar
• Johnson , N. L. and Leone , F. C. 1977 . Statistics and Experimental Design in Engineering and the Physical Sciences, , 2nd ed. , Vol. I , 455 – 456 . New York : Wiley .
   Google Scholar
• Koch , G. G. 1985 . A basic demonstration of the [−1, 1] range for the correlation coefficient . The American Statistician , 39 : 201 – 202 . [CSA]
   Web of Science ®Google Scholar
• Kvalseth , T. O. 1985 . Cautionary note about R2 . The American Statistician , 30 : 279 – 285 . [CSA]
   Google Scholar
• Neter , J. , Wasserman , W. and Kutner , M. H. 1989 . Applied Linear Models, , 2nd ed. , 102 Homewood , II : Richard D. Irving .
   Google Scholar
• Havilcek , L. L. and Crain , R. D. 1988 . Practical Statistics for the Physical Sciences , 91 – 92 . Washington , DC : ACS .
   Google Scholar
• Meloun , M. , Militki , J. and Forina , F. 1994 . Chemometrics for Analytical Chemistry , PC-Aaided Regression and Related Methods Volume 2 , 197 – 198 . New York : Ellis Horwood .
   Google Scholar
• Lee , J. D. and Lee , T. D. 1982 . Statistics and Computer Methods in BASIC , 81 – 83 . New York : Van Nostrand Reinhold .
   Google Scholar
• Mandel , J. 1964 . The Statistical Analysis of Experimental Data , New York : Wiley-Interscience .
   Google Scholar
• Reed , A. H. 1972 . Misleading correlations in clinical application . Clinica Chimica Acta , 40 : 266 – 268 . [CROSSREF] [CSA]
   PubMed Web of Science ®Google Scholar
• Westgard , J. O. and Hunt , M. R. 1973 . Use and interpretation of common statistical tests in method comparison studies . Clinical Chemistry , 19 : 49 – 57 . [PUBMED] [INFOTRIEVE] [CSA]
   PubMed Web of Science ®Google Scholar
• Auget , J. L. and Maccario , J. 1981 . Mesusages du coefficient de correlation lineaire dans la comparaison de deux methods . European Reviews of Biomedical Technology , 3 : 187 – 192 . [CSA]
   Google Scholar
• Bolton , S. 1994 . Pharmaceutical Statistics, Practical and Clinical Applications, , 3rd ed. , 252 New York : Marcel Dekker .
   Google Scholar
• Fisher , R. A. 1958 . Lung cancer and cigarettes . Nature , 182 : 108 – 109 . [PUBMED] [INFOTRIEVE] [CSA]
   PubMed Web of Science ®Google Scholar
• Fisher , R. A. 1958 . Cancer and smooking . Nature , 182 : 596 – 597 . [PUBMED] [INFOTRIEVE] [CSA]
   PubMed Web of Science ®Google Scholar
• Analytical Methods Committee . 1994 . Is my calibration linear? . Analyst , 119 : 2363 – 2366 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Boque , R. , Rius , F. X. and Massart , D. L. 1993 . Straight line calibration—something more than slopes, intercepts and correlation coefficients . Journal of Chemical Education , 70 : 230 – 232 . [CSA]
   Google Scholar
• Loco , J. V. , Elskens , M. , Croux , C. and Beernaert , H. 2002 . Linearity and calibration curves: use and misuse of the correlation coefficient . Accreditation and Quality Assurance , 7 : 281 – 285 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Belloto , J. R. J. and Sokolovski , T. D. 1985 . Residual analysis in regression . American Journal of Pharmaceutical Education , 49 : 295 – 303 . [CSA]
   Web of Science ®Google Scholar
• Thompson , M. 1982 . Regression methods in the comparison of accuracy . Analyst , 107 : 1169 – 1180 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Mulholland , M. and Hibert , P. B. 1997 . Linearity and the limitations of least squares calibration . Journal of Chromatography A , 762 : 73 – 82 . [PUBMED] [INFOTRIEVE] [CROSSREF] [CSA]
   PubMed Web of Science ®Google Scholar
• MacTaggart , D. L. and Farwell , S. O. 1992 . Analytical uses of linear regression. Part I. Regression procedures for calibration and quantitation . Journal of the Association of Official Analytical Chemists , 75 : 594 – 607 . [CSA]
   Google Scholar
• Noggle , J. H. 1993 . Practical Curve Fitting and Data Analysis , 34 – 36 . Englewood Cliffs , NJ : Prentice-Hall .
   Google Scholar
• 1961 . Matheson Gas Data Book , East Rutherford , NJ : The Matheson Co. .
   Google Scholar
• Currie , L. A. 1978 . “ Approach to accuracy in analytical chemistry ” . In Treatise on Analytical Chemistry, , 2nd ed. , Edited by: Kolthoff , I. M. and Elving , P. J. Vol. 1 , 95 – 242 . New York : Wiley . Part 1
   Google Scholar
• Green , J. M. 1996 . A practical guide to analytical method validation . Analytical Chemistry , 66 : 305A – 309A . [CSA]
   Google Scholar
• Crocker , D. C. 1990 . How to Use Regression Analysis in Quality Control , 21 Milwaukee : ASQC .
   Google Scholar
• Kennedy , J. B. and Neville , A. M. 1976 . Basic Statistical Methods for Engineers and Scientists, , 2nd ed. , 301 New York : Harper .
   Google Scholar
• Bartlett , R. F. 1993 . Linear modelling of Pearson's product moment correlation coefficient: An application of Fisher's z-transformation . The Statistician , 42 : 43 – 53 . [CSA]
   Google Scholar
• Hoaglin , D. C. , Mosteller , F. and Tukey , J. W. 2000 . Understanding Robust and Exploratory Data Analysis , 276 – 277 . New York : Wiley Classic Library Edition .
   Google Scholar
• Bond , C. F. and Richardson , K. 2004 . Seeing the Fischer z-transformation . Psychometrika , 69 : 291 – 304 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Harley , B. I. 1956 . Some properties of an angular transformation for the correlation coefficient . Biometrika , 43 : 219 – 224 . [CSA]
   Web of Science ®Google Scholar
• Günther , W. C. 1977 . Desk calculation of probabilities for the distribution of the sample correlation coefficient . The American Statistician , 31 : 45 – 48 . [CSA]
   Web of Science ®Google Scholar
• Crystal Ball . 2002 . Decisioneering, Inc. . Standard edition, ⟨http://www.crystallball.com⟩
   Google Scholar
• Henderson , A. R. 1993 . Chemistry with confidence: should clinical chemists require confidence intervals for analytical and other data? . Clinical Chemistry , 39 : 929 – 935 . [PUBMED] [INFOTRIEVE] [CSA]
   PubMed Web of Science ®Google Scholar
• Workman , J. and Mark , H. 2004 . Comparison of goodness of fit statistics for linear regression, Part I . Spectroscopy , 19 ( 9 ) : 38 – 41 . [CSA]
   Google Scholar
• Lü , J.-X. , Shen , Q. , Jiang , J.-H. , Shen , G.-L. and Yu , R.-Q. 2004 . QASR analysis of cyclooxygenase inhibitor using particle swarm optimisation and multiple linear regression . Journal of Pharmaceutical and Biomedical Analysis , 35 : 679 – 687 . [CSA]
   PubMed Web of Science ®Google Scholar
• Miller , J. N. II . 1991 . Is it a straight line? . Spectroscopy International , 3 ( 4 ) : 41 – 43 . [CSA]
   Google Scholar
• Cornell , J. A. 1990 . How to Apply Response Surface Methodology , 41 Milwaukee : American Society for Quality Control, ASQC .
   Google Scholar
• Lyons , L. 1986 . Statistics for Nuclear and Particle Physicist , 61 Cambridge : Cambridge University Press .
   Google Scholar
• Chatfield , C. and Collins , A. J. 1980 . Introduction to Multivariate Analysis , 26 London : Chapman and Hall .
   Google Scholar
• Massart , D. L. and Kaufman , L. 1983 . The Interpretation of Analytical Chemistry Data by the Use of Cluster Analysis , 15 – 17 . New York : Wiley .
   Google Scholar
• Chambers , J. M. , Cleveland , W. S. , Kleiner , B. and Tukey , P. A. 1983 . Graphical Methods for Data Analysis , 77 – 79 . Belmont , CA : Wadsworth International Group .
   Google Scholar
• Anscombe , J. L. 1973 . Graphs in statistical analysis . The Statistician , 27 : 17 – 21 . [CSA]
   Google Scholar
• Brillinger , D. R. 2001 . Does anyone know when the correlation coefficient is useful? A study of the times of extreme river flows . Technometrics , 43 : 266 – 273 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Rummel , R. J. 1976 . Understanding Correlation , 1 Honolulu : University of Hawaii . Chapter 1, ⟨http://www.mega.nu:8080/ampp/rummel/uc.htm⟩
   Google Scholar
• Press , W. H. , Teukolsky , S. A. , Vetterling , W. T. and Flannery , B. P. 1999 . Numerical Recipes in C. The Art of Scientific Computing, , 2nd ed. , 636 – 639 . Cambridge : Cambridge University Press .
   Google Scholar
• Statistica . 1998 . General Conventions & Statistics I, , 2nd ed. , Volume I , 1450 – 1453 . Tulsa , OK : StatSoft .
   Google Scholar
• Natrella , M. G. 1963 . Experimental Statistics, NBS Handbook , Vol. 91 , 5 – 6 . Washington , DC : NBS, U.S. Government Printing Office .
   Google Scholar
• Hunter , J. S. 1981 . Calibration and the straight line: Current statistical practices . Journal of Association of Official Analytical Chemists , 64 : 574 – 583 . [CSA]
   Google Scholar
• de Levie , R. 2003 . Two linear correlation coefficients . Journal of Chemical Education , 80 : 1030 – 1032 . [CSA]
   Web of Science ®Google Scholar
• Plesch , R. 1982 . Der Korrelations Koeffizient—Prügröber der Analytik? . GIT Fachz. Lab. , 26 : 1040 – 1044 . [CSA]
   Google Scholar
• VanArendonk , M. D. , Skogerboe , R. K. and Grant , C. L. 1981 . Correlation coefficients for evaluation of analytical calibration curves . Analytical Chemistry , 53 : 2349 – 2350 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Tiley , P. F. 1985 . The misuse of correlation coefficients . Chemistry in Britain , 21 : 162 – 163 . [CSA]
   Google Scholar
• Hancock , C. K. 1965 . Some misconceptions of regression analysis in physical organic chemistry . Journal of Chemical Education , 42 : 608 – 609 . [CSA]
   Web of Science ®Google Scholar
• Davies , W. H. and Pryor , W. A. 1976 . Measures of goodness of fit in linear free energy relationships . Journal of Chemical Education , 53 : 285 – 287 . [CSA]
   Web of Science ®Google Scholar
• Analytical Methods Committee . 1988 . Uses (proper and improper) of correlation coefficients . Analyst , 113 : 1469 – 1471 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Huber , W. 2004 . On the use of the correlation coefficient r for testing the linearity of calibration functions . Accreditation and Quality Assurance , 9 : 726 – 727 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar