Explorations in statistics: The analysis of ratios and normalized data

American Journal of Physiology - Advances in Physiology Education

Volumn 37, Issue 3, 2013, Pages 213-219

  Curran Everett, Douglas ^a,b  

^a DEPARTMENT OF MEDICINE   (United States)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

Analysis of covariance; Model II regression; Ordinary least squares regression

Indexed keywords

ANALYSIS OF COVARIANCE; ARTICLE; BIOLOGICAL MODEL; HUMAN; MODEL II REGRESSION; ORDINARY LEAST-SQUARES REGRESSION; REGRESSION ANALYSIS; STATISTICAL MODEL;

ANALYSIS OF COVARIANCE; MODEL II REGRESSION; ORDINARY LEAST-SQUARES REGRESSION;

HUMANS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; REGRESSION ANALYSIS;

EID: 84885935040     PISSN: 10434046     EISSN: 15221229     Source Type: Journal    
DOI: 10.1152/advan.00053.2013     Document Type: Article

References (61)

1. Allison DB, Paultre F, Goran MI, Poehlman ET, Heymsfield SB. Statistical considerations regarding the use of ratios to adjust data. Int J Obesity 19: 644-652, 1995.
2. Atchley WR. Ratios, regression intercepts, and the scaling of data. Syst Zool 27: 78-83, 1978.
3. Atchley WR, Gaskins CT, Anderson D. Statistical properties of ratios. I. Empirical results. Syst Zool 25: 137-148, 1976.
4. Atchley WR, Anderson D. Ratios and the statistical analysis of biological data. Syst Zool 27: 71-78, 1978.
5. Atkinson G, Batterham AM, Black MA, Cable NT, Hopkins ND, Dawson EA, Thijssen DH, Jones H, Tinken TM, Green DJ. Is the ratio of flow-mediated dilation and shear rate a statistically sound approach to normalization in cross-sectional studies on endothelial function? J Appl Physiol 107: 1893-1899, 2009.
6. Beaupre SJ. Ratio representations of specific dynamic action (massspecific SDA and SDA coefficient) do not standardize for body mass and meal size. Physiol Biochem Zool 78: 126-131, 2005.
7. Beaupre SJ, Dunham AE. A comparison of ratio-based and covariance analyses of a nutritional data set. Funct Ecol 9: 876-880, 1995.
8. Bollen KA, Ward S. Ratio variables in aggregate data analysis: their uses, problems, and alternatives. Sociol Methods Res 7: 431-450, 1979.
9. Brown RH, Pearse DB, Pyrgos G, Liu MC, Togias A, Permutt S. The structural basis of airways hyperresponsiveness in asthma. J Appl Physiol 101: 30-39, 2006.
10. Carroll RJ, Ruppert D, Stefanski LA. Measurement Error in Nonlinear Models. New York: Chapman & Hall, 1995, p. 21-23.
11. Chon D, Beck KC, Larsen RL, Shikata H, Hoffman EA. Regional pulmonary blood flow in dogs by 4D-X-ray CT. J Appl Physiol 101: 1451-1465, 2006.
12. Cochran WG. Analysis of covariance: its nature and uses. Biometrics 13: 261-280, 1957.
13. Curran-Everett D. Explorations in statistics: standard deviations and standard errors. Adv Physiol Educ 32: 203-208, 2008.
14. Curran-Everett D. Explorations in statistics: confidence intervals. Adv Physiol Educ 33: 87-90, 2009.
15. Curran-Everett D. Explorations in statistics: hypothesis tests and P values. Adv Physiol Educ 33: 81-86, 2009.
16. Curran-Everett D. Explorations in statistics: the bootstrap. Adv Physiol Educ 33: 286-292, 2009.
17. Curran-Everett D. Explorations in statistics: correlation. Adv Physiol Educ 34: 186-191, 2010.
18. Curran-Everett D. Explorations in statistics: power. Adv Physiol Educ 34: 41-43, 2010.
19. Curran-Everett D. Explorations in statistics: regression. Adv Physiol Educ 35: 347-352, 2011.
20. Curran-Everett D. Explorations in statistics: permutation methods. Adv Physiol Educ 36: 181-187, 2012.
21. Curran-Everett D, Benos DJ. Guidelines for reporting statistics in journals published by the American Physiological Society. Adv Physiol Educ 28: 85-87, 2004.
22. Dejours P, Garey WF, Rahn H. Comparison of ventilatory and circulatory flow rates between animals in various physiological conditions. Respir Physiol 9: 108-117, 1970.
23. Dempsey JA, Wagner PD. Exercise-induced arterial hypoxemia. J Appl Physiol 87: 1997-2006, 1999.
24. Eliasson P, Andersson T, Aspenberg P. Influence of a single loading episode on gene expression in healing rat Achilles tendons. J Appl Physiol 112: 279-288, 2012.
25. Federer WT. Experimental Design: Theory and Application. New York: Macmillan, 1955, p. 483-522.
26. Fisher RA. Statistical Methods for Research Workers (5th ed.). London: Oliver and Boyd, 1934, p. 257-272.
27. Fisher RA. The analysis of covariance method for the relation between a part and the whole. Biometrics 3: 65-68, 1947.
28. Gröger M, Öter S, Simkova V, Bolten M, Koch A, WarninghoffV, GeorgieffM, Muth CM, Speit G, Radermacher P. DNA damage after long-term repetitive hyperbaric oxygen exposure. J Appl Physiol 106: 311-315, 2009.
29. Haddad F, Adams GR. Aging-sensitive cellular and molecular mechanisms associated with skeletal muscle hypertrophy. J Appl Physiol 100: 1188-1203, 2006.
30. Harris RA, Padilla J. Proper normalization of flow-mediated dilation for shear. J Appl Physiol 103: 1108, 2007.
31. Heinemeier KM, Olesen JL, Haddad F, Schjerling P, Baldwin KM, Kjaer M. Effect of unloading followed by reloading on expression of collagen and related growth factors in rat tendon and muscle. J Appl Physiol 106: 178-186, 2009.
32. Hlastala MP, Lamm WJ, Karp A, Polissar NL, Starr IR, Glenny RW. Spatial distribution of hypoxic pulmonary vasoconstriction in the supine pig. J Appl Physiol 96: 1589-1599, 2004.
33. Howlett RA, Kirkton SD, Gonzalez NC, Wagner HE, Britton SL, Koch LG, Wagner PD. Peripheral oxygen transport and utilization in rats following continued selective breeding for endurance running capacity. J Appl Physiol 106: 1819-1825, 2009.
34. Inbar O, Morris N, Epstein Y, Gass G. Comparison of thermoregulatory responses to exercise in dry heat among prepubertal boys, young adults and older males. Exp Physiol 89: 691-700, 2004.
35. Jasieński M, Bazzaz FA. The fallacy of ratios and the testability of models in biology. Oikos 84: 321-326, 1999.
36. Jeal H, Draper A, Harris J, Newman Taylor A, Cullinan P, Jones M. Modified Th2 responses at high-dose exposures to allergen using an occupational model. Am J Respir Crit Care Med 174: 21-25, 2006.
37. Kronmal RA. Spurious correlation and the fallacy of the ratio standard revisited. J R Stat Soc Ser A 156: 379-392, 1993.
38. Ludbrook J. A primer for biomedical scientists on how to execute Model II linear regression analysis. Clin Exp Pharmacol Physiol 39: 329-335, 2012.
39. Moon RE, Cherry AD, Stolp BW, Camporesi EM. Pulmonary gas exchange in diving. J Appl Physiol 106: 668-677, 2009.
40. Neter J, Wasserman W, Kutner MH. Applied Linear Statistical Models. Homewood, IL: Irwin, 1985.
41. Nishiyama SK, Wray DW, Richardson RS. Aging affects vascular structure and function in a limb-specific manner. J Appl Physiol 105: 1661-1670, 2008.
42. Packard GC, Boardman TJ. The misuse of ratios, indices, and percentages in ecophysiological research. Physiol Zool 61: 1-9, 1988.
43. Packard GC, Boardman TJ. The use of percentages and size-specific indices to normalize physiological data for variation in body size: wasted time, wasted effort? Comp Biochem Physiol A 122: 37-44, 1999.
44. Pearce WJ, Williams JM, White CR, Lincoln TM. Effects of chronic hypoxia on soluble guanylate cyclase activity in fetal and adult ovine cerebral arteries. J Appl Physiol 107: 192-199, 2009.
45. Pyke KE, Tschakovsky ME. Peak vs. total reactive hyperemia: which determines the magnitude of flow-mediated dilation? J Appl Physiol 102: 1510-1519,2007.
46. R Development Core Team. R: a Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing, 2012; http://www.R-project.org.
47. Rakobowchuk M, McGowan CL, de Groot PC, Hartman JW, Phillips SM, MacDonald MJ. Endothelial function of young healthy males following whole body resistance training. J Appl Physiol 98: 2185-2190, 2005.
48. Raubenheimer D. Problems with ratio analysis in nutritional studies. Funct Ecol 9: 21-29, 1995.
49. Raubenheimer D, Simpson SJ. Analysis of covariance: an alternative to nutritional indices. Entomol Exp Appl 62: 221-231, 1992.
50. Rodríguez-Roisin R, Drakulovic M, Rodríguez DA, Roca J, Barberá JA, Wagner PD. Ventilation-perfusion imbalance and chronic obstructive pulmonary disease staging severity. J Appl Physiol 106: 1902-1908, 2009.
51. Searle SR. Linear Models. New York: Wiley, 1971, p. 340-361.
52. Secher NH, Seifert T, Van Lieshout JJ. Cerebral blood flow and metabolism during exercise: implications for fatigue. J Appl Physiol 104: 306-314, 2008.
53. Shepherd AP, Granger HJ, Smith EE, Guyton AC. Local control of tissue oxygen delivery and its contribution to the regulation of cardiac output. Am J Physiol 225: 747-755, 1973.
54. Snedecor GW. Statistical Methods (4th ed.). Ames, IA: Iowa State College Press, 1946, p. 134-136.
55. Sokal RR, Rohlf FJ. Biometry. New York: Freeman, 1995, p. 541-549.
56. Sorkness RL, Bleecker ER, Busse WW, Calhoun WJ, Castro M, Chung KF, Curran-Everett D, Erzurum SC, Gaston BM, Israel E, Jarjour NN, Moore WC, Peters SP, Teague WG, Wenzel SE; National Heart, Lung, and Blood Institute Severe Asthma Research Program. Lung function in adults with stable but severe asthma: air trapping and incomplete reversal of obstruction with bronchodilation. J Appl Physiol 104: 394-403, 2008.
57. Tanner JM. Fallacy of per-weight and per-surface area standards, and their relation to spurious correlation. J Appl Physiol 2: 1-15, 1949.
58. Thijssen DH, Bullens LM, van Bemmel MM, Dawson EA, Hopkins N, Tinken TM, Black MA, Hopman MT, Cable NT, Green DJ. Does arterial shear explain the magnitude of flow-mediated dilation?: a comparison between young and older humans. Am J Physiol Heart Circ Physiol 296: H57-H64, 2009.
59. 2 data. J Appl Physiol 75: 2288-2292, 1993.
60. Warton DI, Duursma RA, Falster DS, Taskinen S. SMATR 3: an R package for estimation and inference about allometric lines. Methods Ecol Evol 3: 257-259, 2012.
61. Warton DI, Wright IJ, Falster DS, Westoby M. Bivariate line-fitting methods for allometry. Biol Rev 81: 259-291, 2006.