Outlier analysis of the modified Gompertz model used in fitting the growth of sludge microbes on PEG 600

Main Article Content

Mohd Izuan Effendi Halmi Mohd Shukri Shukor Noor Azlina Masdor Nor Aripin Shamaan Mohd Yunus Shukor


Polyethylene glycols (PEGs) are employed in numerous sectors. PEGs are nephrotoxic and their biodegradation by microbes could be a potential tool for bioremediation. Numerous bacterial growth studies neglect primary modelling even though modelling exercises can reveal important parameters. Previously, we have utilized several growth models to model the growth of sludge microbes on PEG 600. We discovered that the modified Gompertz model via nonlinear regression utilizing the least square method was the best model to describe the growth curve. However, the use of statistical tests to choose the best model relies heavily on the residuals of the curve to be statistically robust. More often than not, the residuals must be tested for the presence of outliers (at 95 or 99% of confidence). In this work, the Grubb’s test to detect the presence of outlier in the growth model was carried out. The test detected an outlier. This datum point will be removed in all future statistical tests such as normality, runs test, tests for homoscedasticity and presence of autocorrelation. In addition, remodeling of the data using the modified Gompertz model will be carried out.

Article Details

How to Cite
HALMI, Mohd Izuan Effendi et al. Outlier analysis of the modified Gompertz model used in fitting the growth of sludge microbes on PEG 600. Journal of Environmental Microbiology and Toxicology, [S.l.], v. 3, n. 1, p. 12-14, july 2015. ISSN 2289-5906. Available at: <http://journal.hibiscuspublisher.com/index.php/JEMAT/article/view/241>. Date accessed: 19 feb. 2018.
Polyethylene Glycol; modified Gompertz; sludge microbes; ordinary least squares method; Grubbs test


[1] Herold DA, Rodeheaver GT, Bellamy WT, Fitton LA, Bruns DE, Edlich RF. Toxicity of topical polyethylene glycol. Toxicol Appl Pharmacol. 1982;65(2):329–335.
[2] Watanabe M, Kawai F. Study on biodegradation process of polyethylene glycol with exponential growth of microbial population. 2010;145-157.
[3] Payne WJ, Williams JP, Mayberry WR. Primary alcohol sulfatase in a Pseudomonas species. Appl Microbiol. 1965;13(5):698–701.
[4] Halmi MIE, Shukor MS, Johari WLW, Shukor MY. Evaluation of several mathematical models for fitting the growth of the algae Dunaliella tertiolecta. Asian J Plant Biol. 2014;2(1):1–6.
[5] Zwietering MH, Jongenburger I, Rombouts FM, Van’t Riet K. Modeling of the bacterial growth curve. Appl Environ Microbiol. 1990;56(6):1875–1881.
[6] Ahmad SA, Ahamad KNEK, Johari WLW, Halmi MIE, Shukor MY, Yusof MT. Kinetics of diesel degradation by an acrylamide-degrading bacterium. Rendiconti Lincei. 2014;25(4):505–512.
[7] Rohatgi, A. WebPlotDigitizer. http://arohatgi.info/WebPlotDigitizer/app/ Accessed June 2 2014.
[8] Huang Y-L, Li Q-B, Deng X, Lu Y-H, Liao X-K, Hong M-Y, et al. Aerobic and anaerobic biodegradation of polyethylene glycols using sludge microbes. Process Biochem. 2005;40(1):207–211.
[9] Grubbs F. Procedures for detecting outlying observations in samples. Technometrics. 1969;11(1):1–21.
[10] López S, Prieto M, Dijkstra J, Dhanoa MS, France J. Statistical evaluation of mathematical models for microbial growth. Int J Food Microbiol. 2004;96(3):289–300.
[11] Barnett V, Lewis T. Outliers in Statistical Data. 3rd ed. Chichester ; New York: Wiley; 1994. 604.
[12] Rosner B. Fundamentals of biostatistics. 7th ed. Boston: Brooks/Cole; 2011.