Analysis of Yam Yield Data: A Comparison of One –Way Anova and Kruskal -Wallis Test
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Abstract
This paper applied the Analysis of Variance Test Statistic on yam data set, to examine the hypothesis that the five plots of yam have identical distributions. It also, examined if any of the basic assumptions of the Analysis of Variance are violated. Secondary data were collected from Otobi Benue State substation of the National Root Crop Research Institute Umudike in Abia State, Nigeria. SPSS software showed that both non-normality and equal variances assumptions were present when Analysis of Variance test statistic was applied. The result from one way analysis of variance (ANOVA) shows that The Fcal = 2.489 < Ftab= 2.76 and the significance of 0.069 is greater than 0.05. The mean= 47.33, standard deviation =19.824 and N = 30, showing that the assumption for normality had been violated in the five plots of yam. This led to the use of Kruskal-Wallis test statistic on the data sets. The Kruskal Wallis result showed that , = ; since .Both test statistics results showed that the five plots of yam have identical distributions. Therefore, the paper concludes that the application of either ANOVA or Kruskal Wallis test when a sample has assumption of ANOVA with homogenous variance but normality is violated leads to the same result.
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References
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Laerd Statistics (2013). Kruskal-Wallis H Test using SPSS Statistics, available at: https://statistics.laerd.com/spss-tutorials/kruskal-wallis-h-test-using-spss-statistics.php
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Montgomery, D. C. (2001). Design and Analysis of Experiments (5th ed.). New York: Wiley. ISBN 978-0-471-31649-7.
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Nguyen C. T., Hiroyuki S., Etsushi K. and Michio K.(2017) “Effects of elevated CO2 concentration on growth and photosynthesis of Chinese yam under different temperature regimes” Journal of Plant Production Science vol. 20 Issue 2 page 227-236. http://dx.doi.org/10.1080/1343943X.2017.1283963.
Omekara, C.O. and Acha, C.K. (2017), Nonparametric Statistics (first edition) PRISAT Nigeria Limited-ISBN: 978-978-54309-6-7.
Scheffé, H. (1959). The Analysis of Variance. New York. Wiley. ISBN 9780471345053. https://doi.org/10.1080/00401706.1960.10489917.
Siegel; C. (1988). Nonparametric Statistics for the Behavioral Sciences (Second edition). New York: McGraw–Hill. ISBN 0070573573.
Spurrier, J. D. (2003). "On the null distribution of the Kruskal–Wallis statistic". Journal of Nonparametric Statistics. 15 (6): 685–691. doi:10.1080/10485250310001634719.
Acha, C. K. (2011b) Comparative Analysis of Quadratic and Cubic Models on Egg Production. Animal Production Research Advances, 7(2), 110 – 115.
Adepoju O.T. (2012) Effects of processing methods on nutrient retention and contribution of white yam (Dioscorea rotundata) products to nutrient intake of Nigerians. Africa Journal Food Science, 6(6), 163–167.
Ajayi, S.S., Akinrinde, E. A. and Asiedu, R.(2006) Fertilizer Treatment Effects on Yam (Dioscorea species) Tuber Yield in Two Soil Types of Nigeria. Journal of Agronomy, 5, 492-496. DOI: 10.3923/ja.2006.492.496. URL: http://scialert.net/abstract/?doi=ja.2006.492.496
Bailey, R. A. (2008). Design of Comparative Experiments. Cambridge University Press. ISBN 978-0-521-68357-9. Pre-publication chapters are available on-line.
Cochran, W. G.; Cox, Gertrude M. (1992). Experimental designs (2nd ed.). New York: Wiley. ISBN 978-0-471-54567-5.
Cohen, J. (1992). "Statistics a power primer". Psychological Bulletin. 112 (1): 155–159. doi:10.1037/0033-2909.112.1.155. PMID 19565683.
Conover, W. J. and Iman, R. L. (1979) "On multiple-comparisons procedures" Report from Los Alamos Scientific Laboratory. Retrieved 2016-10-28.
Conover, W.J (1980) Practical Nonparametric Statistics, (2nd edition) New York John Wiley.
Corder, G. W. and Foreman, D. I. (2009) Nonparametric Statistics for Non-Statisticians. Hoboken: John Wiley & Sons. pp. 99–105. ISBN 9780470454619.
Cox, D. R. (2006). Principles of statistical inference. Cambridge New York: Cambridge University Press. ISBN 978-0-521-68567-2.
Cox, D. R. (1958). Planning of experiments. Reprinted as ISBN 978-0-471-57429-3
Daniel, W. W. (1990). "Kruskal–Wallis one-way analysis of variance by ranks". Applied Nonparametric Statistics (2nd ed.). Boston: PWS-Kent. pp. 226–234. ISBN 0-534-91976-6.
Dunn, O. J. (1964). "Multiple comparisons using rank sums". Technometrics. 6 (3): 241–252. doi:10.2307/1266041.
Freedman, D. A.(2005). Statistical Models: Theory and Practice, Cambridge University Press. ISBN 978-0-521-67105-7.
Gelman, A. (2005). "Analysis of variance? Why it is more important than ever". The Annals of Statistics. 33: 1–53. doi:10.1214/009053604000001048.
Gelman, A. (2008). "Variance, analysis of". The new Palgrave dictionary of economics (2nd ed.). Basingstoke, Hampshire New York: Palgrave Macmillan. ISBN 978-0-333-78676-5.
Hinkelmann, K.& Kempthorne, O. (2008). Design and Analysis of Experiments. I and II (Second ed.). Wiley. ISBN 978-0-470-38551-7.
Ike P. C. and Inoni O. E. (2006) Determinants of Yam Production and Economic Efficiency among Small-Holder Farmers in Southeastern Nigeria, 27 June 2006. pp. 337–341. Retrieved 16 June 2011. Available at: https://en.wikipedia.org/wiki/Yam_production_in_Nigeria.
Kruskal; W. (1952). "Use of ranks in one-criterion variance analysis". Journal of the American Statistical Association. 47 (260): 583–621. doi:10.1080/01621459.1952.10483441.
Kruskal; W. (1952). "Use of ranks in one-criterion variance analysis". Journal of the American Statistical Association. 47 (260): 583–621. doi:10.1080/01621459.1952.10483441.
Laerd Statistics (2013). Kruskal-Wallis H Test using SPSS Statistics, available at: https://statistics.laerd.com/spss-tutorials/kruskal-wallis-h-test-using-spss-statistics.php
Meyer; S. (2006). "Expanded tables of critical values for the Kruskal-Wallis H statistic". Paper presented at the annual meeting of the American Educational Research Association, San Francisco. Critical value tables and exact probabilities from Meyer and Seaman are available for download at http://faculty.virginia.edu/kruskal-wallis/. A paper describing their work may also be found there.
Montgomery, D. C. (2001). Design and Analysis of Experiments (5th ed.). New York: Wiley. ISBN 978-0-471-31649-7.
Moore, D. S. & McCabe, G. P. (2003). Introduction to the Practice of Statistics (4e). W H Freeman & Co. ISBN 0-7167-9657-0
Nguyen C. T., Hiroyuki S., Etsushi K. and Michio K.(2017) “Effects of elevated CO2 concentration on growth and photosynthesis of Chinese yam under different temperature regimes” Journal of Plant Production Science vol. 20 Issue 2 page 227-236. http://dx.doi.org/10.1080/1343943X.2017.1283963.
Omekara, C.O. and Acha, C.K. (2017), Nonparametric Statistics (first edition) PRISAT Nigeria Limited-ISBN: 978-978-54309-6-7.
Scheffé, H. (1959). The Analysis of Variance. New York. Wiley. ISBN 9780471345053. https://doi.org/10.1080/00401706.1960.10489917.
Siegel; C. (1988). Nonparametric Statistics for the Behavioral Sciences (Second edition). New York: McGraw–Hill. ISBN 0070573573.
Spurrier, J. D. (2003). "On the null distribution of the Kruskal–Wallis statistic". Journal of Nonparametric Statistics. 15 (6): 685–691. doi:10.1080/10485250310001634719.