Statistical Trend Analysis of Residential Water Demand in Kisumu City, Kenya

Robert Nyamao Nyabwanga; Edgar Ouko Otumba; Fredrick Onyango; Simeyo Otieno

doi:doi:10.11648/j.ajtas.20150403.16

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Statistical Trend Analysis of Residential Water Demand in Kisumu City, Kenya

Robert Nyamao Nyabwanga, Edgar Ouko Otumba, Fredrick Onyango, Simeyo Otieno

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 3)

Received: 30 March 2015 Accepted: 9 April 2015 Published: 18 April 2015

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Abstract

This study sought to analyse trend in the monthly water demand data series in Kisumu city at both seasonal and non-seasonal levels using the parametric method of Ordinary Least Squares (OLS) and non-parametric methods of Mann-Kendall tau and Sen's T test. Sen’s test was applied to validate the Mann Kendall trend test and to estimate the magnitude of the trend and its direction. The significance of the slope of the OLS equation was tested using the F-Test based on the Analysis of Variance (ANOVA). Secondary monthly water consumption data obtained from KIWASCO for the period January 2004 to December 2013 were used. Using logarithmically transformed data, the study established by OLS that residential water demand in Kisumu City had a significant increasing trend (FCalc=(105.13) > F(1;119)(α=0:05)=(5.15)). Kendall's tau test corroborated the OLS results of a significant increasing trend. The Sens T test indicated that most of the months registered significant upward trend with Sen’s slope estimates showing positive rates of change in residential water demand for these months.

Published in	American Journal of Theoretical and Applied Statistics (Volume 4, Issue 3)
DOI	10.11648/j.ajtas.20150403.16
Page(s)	112-117
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Trend, Kendall’s Tau, OLS, Sen’s T, Residential Water Demand

References

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[2]	Kahya, E. and S. Kalayci, 2004. Trend analysis of stream flow in Turkey. J. Hydrol., 289: 128-144. DOI:10.1016/j.jhydrol.2003.11.006.
[3]	KIWASCO (2007). Kisumu Water and Sewerage Company Strategic Plan 2007-2012.
[4]	Machiwal D, Jha MK.(2008). Comperative evaluation of statistical tests for time series analysis: Application to hydrological timeseries. Hydrological Sciences, Journal-des Sciences Hydrologiques] 53(3): 353–366
[5]	Maftei C., Barbulescu, A. (2008). Statistical Analysis of Climate Evolution in Dobrudja Region. Proceedings of the World Congress on Engineering 2008 Vol II WCE 2008, July 2-4, London, U.K.
[6]	Onoz, B. and Bayazit, M. (2003). The power of statistical tests for trend detection.
[7]	Sen PK (1968). Estimates of the regression coefficient based on Kendall’s tau. J. Am. Stat. Assoc. 39:1379–1389
[8]	Wagah, G., Onyango, G. and Kibwage, J. (2010). Accessibility of water services in Kisumu Municipality Kenya. Journal of Geography and Regional Planning. Vol. 3(4), pp 114-125.
[9]	World Bank (2003) Water Resources Strategy. World Bank, Washington, D.C.
[10]	World Bank (2005) Water for the Urban Poor: Water Markets, Household Demand, and Service Preferences in Kenya. Water Supply and Sanitation Sector Board p.
[11]	Von Storch, H., (1995). Misuses of statistical analysis in climate research, in Analysis of Climate Variability: Applications of Statistical Techniques, edited by H. V. Storch and A. Navarra, pp. 11-26, Springer-Verlag, NewYork.

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APA Style

Robert Nyamao Nyabwanga, Edgar Ouko Otumba, Fredrick Onyango, Simeyo Otieno. (2015). Statistical Trend Analysis of Residential Water Demand in Kisumu City, Kenya. American Journal of Theoretical and Applied Statistics, 4(3), 112-117. https://doi.org/10.11648/j.ajtas.20150403.16

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ACS Style

Robert Nyamao Nyabwanga; Edgar Ouko Otumba; Fredrick Onyango; Simeyo Otieno. Statistical Trend Analysis of Residential Water Demand in Kisumu City, Kenya. Am. J. Theor. Appl. Stat. 2015, 4(3), 112-117. doi: 10.11648/j.ajtas.20150403.16

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AMA Style

Robert Nyamao Nyabwanga, Edgar Ouko Otumba, Fredrick Onyango, Simeyo Otieno. Statistical Trend Analysis of Residential Water Demand in Kisumu City, Kenya. Am J Theor Appl Stat. 2015;4(3):112-117. doi: 10.11648/j.ajtas.20150403.16

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@article{10.11648/j.ajtas.20150403.16,
  author = {Robert Nyamao Nyabwanga and Edgar Ouko Otumba and Fredrick Onyango and Simeyo Otieno},
  title = {Statistical Trend Analysis of Residential Water Demand in Kisumu City, Kenya},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {3},
  pages = {112-117},
  doi = {10.11648/j.ajtas.20150403.16},
  url = {https://doi.org/10.11648/j.ajtas.20150403.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150403.16},
  abstract = {This study sought to analyse trend in the monthly water demand data series in Kisumu city at both seasonal and non-seasonal levels using the parametric method of Ordinary Least Squares (OLS) and non-parametric methods of Mann-Kendall tau and Sen's T test.  Sen’s test was applied to validate the Mann Kendall trend test and to estimate the magnitude of the trend and its direction. The significance of the slope of the OLS equation was tested using the F-Test based on the Analysis of Variance (ANOVA). Secondary monthly water consumption data obtained from KIWASCO for the period January 2004 to December 2013 were used. Using logarithmically transformed data, the study established by OLS that residential water demand in Kisumu City had a significant increasing trend (FCalc=(105.13) > F(1;119)(α=0:05)=(5.15)). Kendall's tau test corroborated the OLS results of a significant increasing trend. The Sens T test indicated that most of the months registered significant upward trend with Sen’s slope estimates showing positive rates of change in residential water demand for these months.},
 year = {2015}
}

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TY  - JOUR
T1  - Statistical Trend Analysis of Residential Water Demand in Kisumu City, Kenya
AU  - Robert Nyamao Nyabwanga
AU  - Edgar Ouko Otumba
AU  - Fredrick Onyango
AU  - Simeyo Otieno
Y1  - 2015/04/18
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150403.16
DO  - 10.11648/j.ajtas.20150403.16
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 112
EP  - 117
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150403.16
AB  - This study sought to analyse trend in the monthly water demand data series in Kisumu city at both seasonal and non-seasonal levels using the parametric method of Ordinary Least Squares (OLS) and non-parametric methods of Mann-Kendall tau and Sen's T test.  Sen’s test was applied to validate the Mann Kendall trend test and to estimate the magnitude of the trend and its direction. The significance of the slope of the OLS equation was tested using the F-Test based on the Analysis of Variance (ANOVA). Secondary monthly water consumption data obtained from KIWASCO for the period January 2004 to December 2013 were used. Using logarithmically transformed data, the study established by OLS that residential water demand in Kisumu City had a significant increasing trend (FCalc=(105.13) > F(1;119)(α=0:05)=(5.15)). Kendall's tau test corroborated the OLS results of a significant increasing trend. The Sens T test indicated that most of the months registered significant upward trend with Sen’s slope estimates showing positive rates of change in residential water demand for these months.
VL  - 4
IS  - 3
ER  -

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Author Information

Robert Nyamao Nyabwanga

Department of Mathematics, Kisii University, Kisii, Kenya
Edgar Ouko Otumba

Department of Statistics and Actuarial Science, Maseno University, Maseno, Kenya
Fredrick Onyango

Department of Statistics and Actuarial Science, Maseno University, Maseno, Kenya
Simeyo Otieno

School of Business and Economics, Jaramogi Oginga Odinga University, Bondo, Kenya

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APA Style

Robert Nyamao Nyabwanga, Edgar Ouko Otumba, Fredrick Onyango, Simeyo Otieno. (2015). Statistical Trend Analysis of Residential Water Demand in Kisumu City, Kenya. American Journal of Theoretical and Applied Statistics, 4(3), 112-117. https://doi.org/10.11648/j.ajtas.20150403.16

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ACS Style

Robert Nyamao Nyabwanga; Edgar Ouko Otumba; Fredrick Onyango; Simeyo Otieno. Statistical Trend Analysis of Residential Water Demand in Kisumu City, Kenya. Am. J. Theor. Appl. Stat. 2015, 4(3), 112-117. doi: 10.11648/j.ajtas.20150403.16

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AMA Style

Robert Nyamao Nyabwanga, Edgar Ouko Otumba, Fredrick Onyango, Simeyo Otieno. Statistical Trend Analysis of Residential Water Demand in Kisumu City, Kenya. Am J Theor Appl Stat. 2015;4(3):112-117. doi: 10.11648/j.ajtas.20150403.16

Copy | Download

@article{10.11648/j.ajtas.20150403.16,
  author = {Robert Nyamao Nyabwanga and Edgar Ouko Otumba and Fredrick Onyango and Simeyo Otieno},
  title = {Statistical Trend Analysis of Residential Water Demand in Kisumu City, Kenya},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {3},
  pages = {112-117},
  doi = {10.11648/j.ajtas.20150403.16},
  url = {https://doi.org/10.11648/j.ajtas.20150403.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150403.16},
  abstract = {This study sought to analyse trend in the monthly water demand data series in Kisumu city at both seasonal and non-seasonal levels using the parametric method of Ordinary Least Squares (OLS) and non-parametric methods of Mann-Kendall tau and Sen's T test.  Sen’s test was applied to validate the Mann Kendall trend test and to estimate the magnitude of the trend and its direction. The significance of the slope of the OLS equation was tested using the F-Test based on the Analysis of Variance (ANOVA). Secondary monthly water consumption data obtained from KIWASCO for the period January 2004 to December 2013 were used. Using logarithmically transformed data, the study established by OLS that residential water demand in Kisumu City had a significant increasing trend (FCalc=(105.13) > F(1;119)(α=0:05)=(5.15)). Kendall's tau test corroborated the OLS results of a significant increasing trend. The Sens T test indicated that most of the months registered significant upward trend with Sen’s slope estimates showing positive rates of change in residential water demand for these months.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Statistical Trend Analysis of Residential Water Demand in Kisumu City, Kenya
AU  - Robert Nyamao Nyabwanga
AU  - Edgar Ouko Otumba
AU  - Fredrick Onyango
AU  - Simeyo Otieno
Y1  - 2015/04/18
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150403.16
DO  - 10.11648/j.ajtas.20150403.16
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 112
EP  - 117
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150403.16
AB  - This study sought to analyse trend in the monthly water demand data series in Kisumu city at both seasonal and non-seasonal levels using the parametric method of Ordinary Least Squares (OLS) and non-parametric methods of Mann-Kendall tau and Sen's T test.  Sen’s test was applied to validate the Mann Kendall trend test and to estimate the magnitude of the trend and its direction. The significance of the slope of the OLS equation was tested using the F-Test based on the Analysis of Variance (ANOVA). Secondary monthly water consumption data obtained from KIWASCO for the period January 2004 to December 2013 were used. Using logarithmically transformed data, the study established by OLS that residential water demand in Kisumu City had a significant increasing trend (FCalc=(105.13) > F(1;119)(α=0:05)=(5.15)). Kendall's tau test corroborated the OLS results of a significant increasing trend. The Sens T test indicated that most of the months registered significant upward trend with Sen’s slope estimates showing positive rates of change in residential water demand for these months.
VL  - 4
IS  - 3
ER  -

Copy | Download