Spectroscopy - June 2009 - (Page 20) 20 Spectroscopy 24(6) June 2009 w w w. s p e c t r o s c o p y o n l i n e . c o m is the alikeness of x to y including their respective differences ratioed to the dispersion (standard deviation) of the dataset. So the same error between x and y computes to a higher correlation when the data is more disperse or has a wider range. Therefore to compare correlation between experiments one should use the same data distribution for both. A high correlation does not mean smaller error unless the spread of the data used in the experiments is equivalent. The correlation coefficient computed using a standard summation notation is defined as: n n⋅ m0 = n i =1 (yi ⋅ x i ) n i =1 n i =1 n i =1 yi ⋅ n i =1 xi n⋅ ( y i2 ) (y i ) 2 = n ⋅sum(y ⋅ x) sum(y ) sum(x ) n ⋅ sum(y 2 ) (sum y )2 [7] y-Intercept (i) The y-intercept is the point on the yaxis where the regression line crosses the 0 reference (x) value. It is not the bias which has already been defined as Parameter #3. In summation notation the intercept is computed as follows: n (2) r= i =1 n i =1 [(x i i xi ⋅ y i xi )( ⋅ yi i )] yi i= y i2 ⋅ n xi n i =1 yi ⋅ n i =1 n i =1 (y i ⋅ x i ) i =1 (x ) 2 n i =1 (y ) = 2 n⋅ i =1 n i =1 ( y i2 ) (y i )2 = (3) sum(y 2 ) ⋅ sum(x ) sum (y ) ⋅ sum(y ⋅ x ) n ⋅ sum(y 2 ) (sum y ) 2 (4) sum[(x sum(x x)⋅( y x ) 2 ⋅ sum(y y )] y )2 [8] [6] Coefficient of Determination (R 2) The Coefficient of Determination, R 2, is the square of the Pearson product-moment correlation coefficient. This statistic represents the amount of variation in the data that is modeled by linear fit of the test and comparative data pairs as a fraction of 1.0. Note: For a multivariate calibration, this statistic is often termed the coefficient of multiple determination. It specifically reports the total amount of variation in the data that is fully modeled by the calibration equation as a total fraction of 1.0. If the R 2 is 1.00 then 100% of the variation is modeled in the calibration; similarly, an R 2 of 0.80 indicates 80% of the variation has been modeled using the mathematics selected. Acknowledgment The column editors would like to thank Drs. Bill Patterson, Shonn Hendee, Stephen Vanslyke, and David Abookasis of Luminous Medical for their multidisciplinary contributions in authorship, review, and editing for this discussion of statistical methods suitable for clinical data presentation when comparing different methods of analysis. (5) (6) • CLSI Document EP9-A2, Method Comparison and Bias Estimation using Patient Samples; Approved Guideline — Second Edition. • CLSI Document EP10-A2, Preliminary Evaluation of Quantitative Clinical Laboratory Methods; Approved Guideline — Second Edition. • CLSI Document EP15-A2, User Verification of Precision and Trueness; Approved Guideline — Second Edition. ASTM Standard Practice E1655-00, “Standard Practices for Infrared, Multivariate, Quantitative Analysis,” American Society for Testing and Materials International, Barr Harbor Dr., West Conshohocken, PA 19428. N.M. Faber, F.H. Schreutelkamp, and H.W. Vedder, Spectroscopy Europe 16(1), 17–20 (2004). W.J. Youden and E.H. Steiner, Statistical Manual of the AOAC, 1st Ed. (Association of Official Analytical Chemists, Washington, D.C., 1975). J.C. Miller and J.N. Miller, Statistics for Analytical Chemistry, 2nd Ed. (Ellis Horwood, New York, 1992). H. Mark and J. Workman, Chemometrics in Spectroscopy (Elsevier/Academic Press, Boston, 2007), chapters 58–61. Howard Mark serves References Many references are available. These have been selected as they are specifically related to the use of data for spectroscopy, and for comparison of general analytical methods. (1) Clinical and Laboratory Standards Institute (CLSI) guidelines: Q300-001, Terminology for standard definitions. For more details on statistical estimation and verification see: • CLSI Document EP5-A2, Evaluation of Precision Performance of Quantitative Measurement Methods; Approved Guideline — Second Edition. • CLSI Document EP10-A2, Preliminary Evaluation of Quantitative Clinical Laboratory Methods; Approved Guideline — Second Edition. • CLSI Document EP15-A2, User Verification of Precision and Trueness; Approved Guideline — Second Edition. on the Editorial Advisory Board of Spectroscopy and runs a consulting service, Mark Electronics (Suffern, NY). He can be reached via e-mail: hlmark@prodigy.net Slope (m0) Jerome Workman, Jr. serves on the Editorial Advisory Board of Spectroscopy and is currently with Luminous Medical, Inc., a company dedicated to providing automated glucose management systems to empower health care professionals. This is the slope of the regression line between x and y paired values. A slope of 1.00 indicates perfect agreement between a change in reference value magnitude and a change in test value magnitude. This slope value does not indicate the magnitude of the bias or of the intercept of the regression line between x and y values. It is computed as follows (summation notation is indicated): For more information on this topic, please visit: www.spectroscopyonline.com/mark http://www.spectroscopyonline.com http://www.spectroscopyonline.com/mark Table of Contents for the Digital Edition of Spectroscopy - June 2009 Spectroscopy - June 2009 Contents News Spectrum Auger Spectroscopy Statistics and Chemometrics for Clinical Data Reporting, Part 1 Understanding and Interpreting the New GAMP 5 Software Categories Current Status of Standoff LIBS Security Applications at the United States Army Research Laboratory Spectral Studies on the Interaction of [Ru(bpy)2(BTIP)]2+ with DNA and Determination of Nucleic Acids at Nanogram Levels Product Resources Calendar Ad Index Spectroscopy - June 2009 Spectroscopy - June 2009 - (Page BB1) Spectroscopy - June 2009 - (Page BB2) Spectroscopy - June 2009 - Spectroscopy - June 2009 (Page Cover1) Spectroscopy - June 2009 - Spectroscopy - June 2009 (Page Cover2) Spectroscopy - June 2009 - Spectroscopy - June 2009 (Page 3) Spectroscopy - June 2009 - Spectroscopy - June 2009 (Page 4) Spectroscopy - June 2009 - Spectroscopy - June 2009 (Page 5) Spectroscopy - June 2009 - Spectroscopy - June 2009 (Page 6) Spectroscopy - June 2009 - Spectroscopy - June 2009 (Page 7) Spectroscopy - June 2009 - Contents (Page 8) Spectroscopy - June 2009 - Contents (Page 9) Spectroscopy - June 2009 - Contents (Page 10) Spectroscopy - June 2009 - Contents (Page 11) Spectroscopy - June 2009 - News Spectrum (Page 12) Spectroscopy - June 2009 - News Spectrum (Page 13) Spectroscopy - June 2009 - Auger Spectroscopy (Page 14) Spectroscopy - June 2009 - Auger Spectroscopy (Page 15) Spectroscopy - June 2009 - Auger Spectroscopy (Page 16) Spectroscopy - June 2009 - Auger Spectroscopy (Page 17) Spectroscopy - June 2009 - Statistics and Chemometrics for Clinical Data Reporting, Part 1 (Page 18) Spectroscopy - June 2009 - Statistics and Chemometrics for Clinical Data Reporting, Part 1 (Page 19) Spectroscopy - June 2009 - Statistics and Chemometrics for Clinical Data Reporting, Part 1 (Page 20) Spectroscopy - June 2009 - Statistics and Chemometrics for Clinical Data Reporting, Part 1 (Page 21) Spectroscopy - June 2009 - Understanding and Interpreting the New GAMP 5 Software Categories (Page 22) Spectroscopy - June 2009 - Understanding and Interpreting the New GAMP 5 Software Categories (Page 23) Spectroscopy - June 2009 - Understanding and Interpreting the New GAMP 5 Software Categories (Page 24) Spectroscopy - June 2009 - Understanding and Interpreting the New GAMP 5 Software Categories (Page 25) Spectroscopy - June 2009 - Understanding and Interpreting the New GAMP 5 Software Categories (Page 26) Spectroscopy - June 2009 - Understanding and Interpreting the New GAMP 5 Software Categories (Page 27) Spectroscopy - June 2009 - Understanding and Interpreting the New GAMP 5 Software Categories (Page 28) Spectroscopy - June 2009 - Understanding and Interpreting the New GAMP 5 Software Categories (Page 29) Spectroscopy - June 2009 - Understanding and Interpreting the New GAMP 5 Software Categories (Page 30) Spectroscopy - June 2009 - Understanding and Interpreting the New GAMP 5 Software Categories (Page 31) Spectroscopy - June 2009 - Current Status of Standoff LIBS Security Applications at the United States Army Research Laboratory (Page 32) Spectroscopy - June 2009 - Current Status of Standoff LIBS Security Applications at the United States Army Research Laboratory (Page 33) Spectroscopy - June 2009 - Current Status of Standoff LIBS Security Applications at the United States Army Research Laboratory (Page 34) Spectroscopy - June 2009 - Current Status of Standoff LIBS Security Applications at the United States Army Research Laboratory (Page 35) Spectroscopy - June 2009 - Current Status of Standoff LIBS Security Applications at the United States Army Research Laboratory (Page 36) Spectroscopy - June 2009 - Current Status of Standoff LIBS Security Applications at the United States Army Research Laboratory (Page 37) Spectroscopy - June 2009 - Current Status of Standoff LIBS Security Applications at the United States Army Research Laboratory (Page 38) Spectroscopy - June 2009 - Spectral Studies on the Interaction of [Ru(bpy)2(BTIP)]2+ with DNA and Determination of Nucleic Acids at Nanogram Levels (Page 39) Spectroscopy - June 2009 - Spectral Studies on the Interaction of [Ru(bpy)2(BTIP)]2+ with DNA and Determination of Nucleic Acids at Nanogram Levels (Page 40) Spectroscopy - June 2009 - Spectral Studies on the Interaction of [Ru(bpy)2(BTIP)]2+ with DNA and Determination of Nucleic Acids at Nanogram Levels (Page 41) Spectroscopy - June 2009 - Spectral Studies on the Interaction of [Ru(bpy)2(BTIP)]2+ with DNA and Determination of Nucleic Acids at Nanogram Levels (Page 42) Spectroscopy - June 2009 - Spectral Studies on the Interaction of [Ru(bpy)2(BTIP)]2+ with DNA and Determination of Nucleic Acids at Nanogram Levels (Page 43) Spectroscopy - June 2009 - Spectral Studies on the Interaction of [Ru(bpy)2(BTIP)]2+ with DNA and Determination of Nucleic Acids at Nanogram Levels (Page 44) Spectroscopy - June 2009 - Product Resources (Page 45) Spectroscopy - June 2009 - Product Resources (Page 46) Spectroscopy - June 2009 - Product Resources (Page 47) Spectroscopy - June 2009 - Calendar (Page 48) Spectroscopy - June 2009 - Calendar (Page 49) Spectroscopy - June 2009 - Ad Index (Page 50) Spectroscopy - June 2009 - Ad Index (Page Cover3) Spectroscopy - June 2009 - Ad Index (Page Cover4) http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0810_bg http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0810_supp http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0710 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0610 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0510 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0410 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0310 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0210 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0110 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy1209 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy1109 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy1009 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0909 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0809 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0709 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0609 http://digital.findanalytichem.com/nxtbooks/advanstar/spectroscopy0509 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0409 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0309 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0209 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0109 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy1208 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy1108 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy1008 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0908 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0808 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0708 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0608 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0508 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0308 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0208 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0108 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy1207 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy1107 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy1007 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0907 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0807 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0707 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0607 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0507 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0407 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0307 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0207 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0107 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy1106 http://www.nxtbook.com/nxtbooks/advanstar/spectroscopy0906 http://www.nxtbookMEDIA.com
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