No More Crying About Your Stats Class and Cry1Ab: An Application of the Coefficient of Variation

Lots of times students complain that either their statistics classes used silly examples that were too simple to ever be realistic, or that their course was too complicated and thus they leave the class without the capability of  any practical application.  A recent study looking at the safety of GMO corn provides a great case study for the practical application of the coefficient of variation (CV). 

In ‘Maternal and fetal exposure to pesticides associated to genetically modified Foods in Eastern Townships of Quebec, Canada’ the authors claim to have identified the toxin Cry1Ab in the blood of pregnant women.  Cry1Ab is a protein produced by the bacteria Bacillus thuringiensis (Bt) that is toxic to certain insect pests. Cry1Ab is just one version (event) of this Bt toxin.  Bt toxins have been used extensively by organic farmers and biotechnology has enabled seed companies to develop corn plants that express Cry1Ab proteins giving them a built in defense mechanism against insects susceptible to the toxin, while preserving the biodiversity of friendly insects.  Bt genetics have also been incorporated into cotton. The economic, environmental, safety, and health benefits have made this a very popular  tool used by the majority of family farmers. 

One of the major criticisms of the article was the use of the test used to identify the Cry1Ab protein. In the article the authors state:

‘Cry1Ab protein levels were determined in blood using a commercially available double antibody sandwich(DAS)enzyme-linked immune sorbent assay.’

In previous research, the enzyme-linked immunosorbent assay or ELISA test has been shown to be one of the most unreliable tests for detecting Cry1Ab proteins.  Recall, the CV is relative measure of variation measuring the standard deviation relative to the mean.   It can be used as a metric for risk and reliability (such a consistent yield performance or stock returns).  In the article ‘Comparison and Validation of Methods To Quantify Cry1Ab Toxin from Bacillus thuringiensis for Standardization of Insect Bioassays’ the authors investigate procedures commonly used to identify Cry1Ab.  The authors explain:

“We compared three methods of quantification on three different toxin preparations from independent sources: enzyme-linked immunosorbent assay (ELISA), sodium dodecyl sulfate-polyacrylamide gel electrophoresis and densitometry (SDS-PAGE/densitometry), and the Bradford assay for total protein....The Bradford method resulted in statistically higher estimates than either ELISA or SDSPAGE/ densitometry but also provided the lowest coefficients of variation (CVs) for estimates of the Cry1Ab concentration (from 2.4 to 5.4%). The CV of estimates obtained by ELISA ranged from 12.8 to 26.5%, whereas  the CV of estimates obtained by SDS-PAGE/densitometry ranged from 0.2 to 15.4%....we conclude that standardization of Cry1Ab production and quantification by SDS-PAGE/densitometry may improve data consistency.”

If we look at their reported statistics, we can see for ourselves just how high the CV is on the ELISA test (and therefore how unreliable it is as a method for quantifying Cry1Ab)  compared to other proven methods of quantification.

 

So there you have it. A practical example of an application of a very basic statistic, the coefficient of variation.

References:

Maternal and fetal exposure to pesticides associated to genetically modified foods in Eastern Townships of Quebec, Canada. Reprod Toxicol. 2011 May;31(4):528-33. Epub 2011 Feb 18.

Aris A, Leblanc S.

Comparison and Validation of Methods To Quantify Cry1Ab Toxin from Bacillus thuringiensis for Standardization of Insect Bioassays. Andre´ L. B. Crespo,1 Terence A. Spencer,1 Emily Nekl,2 Marianne Pusztai-Carey,3 William J. Moar,4 and Blair D. Siegfried1* APPLIED AND ENVIRONMENTAL MICROBIOLOGY, Jan. 2008, p. 130–135 Vol. 74, No. 1

A Meta-Analysis of Effects of Bt Cotton and Maize on Nontarget Invertebrates. Michelle Marvier, Chanel McCreedy, James Regetz, Peter Kareiva Science 8 June 2007: Vol. 316. no. 5830, pp. 1475 – 1477

Comparison of Fumonisin Concentrations in Kernels of Transgenic Bt Maize Hybrids and Nontransgenic Hybrids. Munkvold, G.P. et al . Plant Disease 83, 130-138 1999.

Indirect Reduction of Ear Molds and Associated Mycotoxins in Bacillus thuringiensis Corn Under Controlled and Open Field Conditions: Utility and Limitations. Dowd, J. Economic Entomology. 93 1669-1679 2000.

Impact of Bt cotton on pesticide poisoning in smallholder agriculture: A panel data analysis. Shahzad Kouser, Matin Qaim. Ecological Economics

Volume 70, Issue 11, 15 September 2011, Pages 2105–2113

Communal Benefits of Transgenic Corn. Bruce E. Tabashnik  Science 8 October 2010:Vol. 330. no. 6001, pp. 189 - 190DOI: 10.1126/science.1196864

The Coefficient of Variation

Coefficient of Variation: A relative measure of variation measuring the standard deviation relative to the mean.  

Recall the standard deviation is the square root of variance.

CV = (standard deviation / mean) * 100

This metric is useful for comparing variables that have different standard deviations and different means.

For instance, let’s assume we have two corn hybrids that average 150 bushels an acre, and hybrid A’s yield has a standard deviation of 10 bushels per acre, while hybrid B’s yield has a standard deviation of 50 bushels an acre.  If we are about to plant one of these hybrids, we know that hybrid A is going to provide us more certainty about our expected yields in the fall.  The empirical rule tells us that about 95% of the time if we plant hybrid A, our yields will be between 130 and 170 bu/acre. If we plant hybrid B, 95% of the time yields will be between 50 and 250 bu/acre.

So, with two hybrids with the same average yield, we know that the one with the lower standard deviation will perform more consistently. But what if they both have different yields and different standard deviations?

Hybrid A:  mean 185 bu;/acre  std dev: 5 bu/acre

Hybrid B: mean: 200 bu/acre std dev: 30 bu/acre

Choosing the most reliably yielding hybrid in this case is not quite so easy. But the CV helps us make the comparison:

Hybrid A: CV = (5/185) *100 = 2.7%

Hybrid B: CV =  (30/200)*100 = 15%

We can see by the CV that hybrid A, even though it yields on average less than hybrid B,  will deliver more consistent results.
 

In the context of finance, we can think of the CV as a measure of relative dispersion that can be used to compare the risks of assets  that have different mean (expected )returns.

Reference: Principles of Managerial Finance.  11^th Edition. Lawrence J. Gitman.

Empirical Studies Related to Gender Wage Gap

Albelda, R. P. (1986, April) Occupational segregation by race and gender, 1958-1981. Industrial and Labor Relations, 39(3):404-411.

Amuedo-Dorantes, C. & Mach, T. (2003) Performance pay and fringe benefits. International Journal of Manpower, 24(6):672-698.

Anderson, D. J., Binder, M., & Krause, K. (2003, January) The motherhood wage penalty revisited: Experience, heterogeneity, work effort, and work-schedule flexibility. Industrial and Labor Relations Review, 56(2):273-294.

Bauer, T. & Zimmermann, K.F. (1999) Overtime work and overtime compensation in Germany. Scottish Journal of Political Economy, 46:419-436.

Bayard, K., Hellerstein, J., Neumark, D., & Troske, K. (2003) New evidence on sex segregation and sex differences in wages from matched employee-employer data. Journal of Labor Economics, 21(4):887-921.

Bell, D.N.F. & Hart, R.A. (1999). Unpaid work. Economica, 66:271-290.

Bell, D.N.F., Hart, R.A., Hubler, O. & Schwerdt, W. (2000, March), Paid and unpaid overtime working in Germany and the UK, IZA Discussion Paper Number 133, Bonn, Germany: The Institute for the Study of Labor (IZA).

Blau, F. and DeVaro, J. (2006, April) New evidence on gender differences in promotion rates: An empirical analysis of a sample of new hires. Working paper. Princeton, NJ: Princeton University.

Blau, F.D., Ferber, M.A., & Winkler, A.E. (2007) The economics of women, men, and work. (5th ed.) Upper Saddle River, NJ: Pearson Education, Inc.

Blau, F.D. & Kahn, L.M. (2006, June) The U.S. gender pay gap in the 1990s: Slowing convergence. Discussion paper 2176, Bonn, Germany: Institute for the Study of Labor (published in: Industrial and Labor Relations Review, 2006, 60 (1):45-66) .

Blau, F. D. & Kahn. L.M. (2000) Gender differences in pay. Journal of Economic Perspectives, 14(4):75-99.

Boraas, S. & Rodgers, W.M. III. (2003, March) How does gender play a role in the earnings gap? An update. Monthly Labor Review, 9-15.

Bowler, M. (1999, December) Women's earnings: An overview. Monthly Labor Review, 13-21.

Brooks, P. (1999, June) Compensation inequality. Washington, DC: Bureau of Labor Statistics.

Budig, M. J. and England, P. (2001, April) The wage penalty for motherhood. American Sociological Review, 66(2):204-225.

Correll, S. J, Benard, S. & Paik, I. (2007, March) Getting a job: Is there a motherhood penalty? American Journal of Sociology, 112(5):1297-1338.

Cortes, P. & Tessada, J. (2008, May) Cheap maids and nannies: How low-skilled immigration is changing the labor supply of high-skilled American women. Working paper. Chicago, IL: University of Chicago and Cambridge:MA: Massachusetts Institute of Technology.

Costa, D.L. (2000) Hours of work and the Fair Labor Standards Act: A study of retail and wholesale trade, 1938-1950. Industrial and Labor Relations Review, 53(4):648-664.

Dey, J.G. & Hill, C. (2007, April) Behind the pay gap. Washington, DC: American Association of University Women Educational Foundation.

DiNatale, M. & Boraas, S. (2002, March) The labor force experience of women from "Generation X". Monthly Labor Review, 3-15.

Even, W.E. & Macpherson, D.A. (1990) The gender gap in pensions and wages. Review of Economics and Statistics, 72(2):259-265.

Fields, J. & Wolff, E. (1995, October) Interindustry wage differentials and the gender wage gap. Industrial and Labor Relations Review, 49(1):105-120.

Gabriel, P.E. (2005, July) The effects of differences in year-round, full-time labor market experience on gender wage levels in the United States. International Review of Applied Economics, 19(3):369-377.

Groshen, E. (1991) The structure of the female/male wage differential: Is it who you are, what you do, or where you work? Journal of Human Resources, 26(3):457-472.

Gruber, J. (1994, June) The incidence of mandated maternity benefits. American Economic Review, 84(3):622-641.

Hamermesh, D.S. & Trejo, S.J. (2000, February) The demand for hours of labor: Direct evidence from California. The Review of Economics and Statistics, 82(1):38-47.

Hartmann, H., Sorokina, O. & Williams, E. (2006, December) The best and worst state economies for women. Washington, DC: Institute for Women's Policy Research.

Johnson, G. & Solon, G. (1986, December) Estimates of the direct effects of comparable worth policy. American Economic Review, 76:1117-1125.

Johnson, T.D. (2008, February) Maternity leave and employment patterns of first-time mothers: 1961- 2003. Household Economic Studies. Washington, DC: U.S. Census Bureau.

Joy, L. (2006, April) Occupational differences between recent male and female college graduates. Economics of Education Review, 25(2):221-231.

Levine, L. (2003, April) The gender wage gap and pay equity: Is comparable worth the next step? Washington, DC: Congressional Research Service.

 

Light, A. & Ureta, M. (1995) Early-career work experience and gender wage differentials. Journal of Labor Economics, 13(1):121-154.

Lowen, A. & Sicilian, P. (2008) "Family-friendly" fringe benefits and the gender wage gap. Journal of Labor Research. Online publication date: March 12, 2008.

Mandel, H. & Semyonov. M. (2005, December) Family policies, wage structures, and gender gaps: Sources of earnings inequality in 20 countries. American Sociological Review, 70:949-967.

McCrate, E. (2005, March) Flexible hours, workplace authority, and compensating wage differentials in the US. Feminist Economics, 11(1):11-39.

Morrisey, M. (2001, September) Why do employers do what they do? Compensating differentials. International Journal of Health Care Finance and Economics, 1(3-4): 195-201.

Mulligan, C.B. & Rubinstein, Y. (2008, August) Selection, investment, and women's relative wages over time. Quarterly Journal of Economics, 123(3):1061-1110.

Oaxaca, R. (1973, October) Male-female wage differentials in urban labor markets. International Economic Review, 14(3):693-708.

Olson, C. (2002) Do workers accept lower wages in exchange for health benefits? Journal of Labor Economics, 20(2):91-114.

Pannenberg, M. (2002, October), Long-term effects of unpaid overtime: Evidence for West Germany, IZA Discussion Paper Number 614, Bonn, Germany: The Institute for the Study of Labor (IZA).

Phelps, E. (1972, September) The statistical theory of racism and sexism. American Economic Review, 62(4):659-661.

Plasman, R. & Sissoko, S. (2004, December). Comparing apples with oranges: Revisiting the gender wage gap in an international perspective. Discussion Paper Series, Brussels, Belgium: Institute for the Study of Labor.

Rhine, S. L.W. (1987, December) The determinants of fringe benefits: Additional evidence. Journal of Risk and Insurance, 54(4):790-799.

Rose, S & Hartmann, H. (2004) Still a man's labor market: The long-term earnings gap. Washington, DC: Institute for Women's Policy Research.

Sanborn, H. (1964, July) Pay differences between men and women. Industrial and Labor Relations Review, 17(4):534-550.

Sheiner, L. (1999, April) Health care costs, wages, and aging. Washington, DC: Federal Reserve Board of Governors.

Solberg, E. & Laughlin, T. (1995, July) The gender pay gap, fringe benefits, and occupational crowding. Industrial and Labor Relations Review, 48(4):692-708.

 

Spivey, C. (2005, October) Time off at what price? The effects of career interruptions on earnings. Industrial and Labor Relations Review, 59(1):119-140.

Trejo, S.J. (2003, April), Does the statutory overtime premium discourage long workweeks?, Industrial and Labor Relations Review, 56(3):530-551.

Trejo, S.J. (1993) Overtime pay, overtime hours, and labor unions. Journal of Labor Economics, 11(2):253-278.

Trejo, S.J. (1991, September) The effects of overtime pay regulation on worker compensation. American Economic Review, 81(4):719-740.

U. S. Department of Labor, Bureau of Labor Statistics (2008, October) Highlights of Women's Earnings in 2007, Report 1008.

U. S. General Accounting Office (2003, October) Women's earnings: Work patterns partially explain difference between men's and women's earnings. Washington, DC: General Accounting Office.

Weinberg, D. (2007, July/August) Earnings by gender: Evidence from Census 2000. Monthly Labor Review: 25-34.

WFD Consulting. (2006, October) Workplace flexibility for lower wage workers. Washington, DC: Corporate Voices for Working Families. 

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