Abstract
Biometrical Techniques are often used in Genetic Statistics involving plants and animal studies for assessing their genetic potential in selection trails for genetic material improvement. For such purposes, genetic parameters namely means, variances, variance components, heritability parameters, genotypic correlations etc., have been often estimated by using genetic statistical methods. In the Biometrical research analysis, the applications of most of the advanced experimental statistical tools based on certain crucial assumptions such as the assumptions of independence, homoscedasticity of observations on study variable and assumption of normality of observations in the data. Departures from these assumptions may lead to biased and inconsistent estimators; and incorrect conclusions. Thus, the Biostatistician has to test these assumptions on observations rather than to presume that they are correct. In the present article, an attempt has been made by developing test procedures for testing hypotheses about population’s symmetry and population’s kurtosis by using some modified Beta measures. Further, a test for normality of errors in linear regression model has been developed by using modified Fisher’s g-statistics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
E.S. Pearson, R.B. D’Agostino, K.O. Bowman, Tests for departure from normality: comparison of powers. Biometrika 64, 231–246 (1977)
D.S. Moore, Tests of chi-squared type, in Goodness-of-Fit Techniques, eds. by R.B. D’Agostino, M.A. Stephens (Marcel Dekkar, New York, 1986), pp. 63–95
H.C. Thode Jr, Testing for Normality (Marcel Dekkar, New York, 2002), pp. 479
R.A. Fisher, Statistical Methods for Research Workers, 1st edn. (Oliver and Boyd, Edinbergh, Scotland, 1925)
K.D. Bowman, L.R. Shenton, Omnibus contours for departures from normality based on \(\sqrt {b_{1} }\) and b2. Biometrika 62, 243–250 (1975)
R.B. D’Agostino, A. Belanger, R.B. D’Agostino Jr, A suggestion for using powerful and informative tests of normality. J. Am. Stat. Assoc. 44, 316–321 (1990)
R.B. D’Agostino, E.S. Pearson, tests for departure from normality; empirical results for the distributions of b2 and \(\sqrt {b_{1} }\). Biometrika, 60, 613–622 (1973)
R. Groeneveld, G. Meeden, Measuring skewness and kurtosis. Statistician 33, 391–399 (1984)
J.J.A. Moors, A quantile alternative for kurtosis. Statistician 37, 25–32 (1988)
M. Naresh, Advanced statistical techniques for agricultural research. Unpublished Ph.D. thesis in Statistics, S.V. University, Tirupati, Andhra Pradesh, 2017
K. Pearson, Contributions to the mathematical theory of evolution. Philos. Trans. Roy. Soc. Lond. 91, 343–358 (1895)
M.M. Rahman, Z. Govindarajulu, A modification of the test of shapiro and wilk for normality. J. Appl. Statist. 24, 219–236 (1997)
K. Vijaya Kumar, P. Balasiddamuni et al., Testing Normality in Linear Statistical Models (Lap Lambert Academic, Germany, 2013). ISBN: 978-3-659-50283-5
H.J. Zar, Biostatistical Analysis, 5th edn. (Prentice Hall, Upper Saddle River, NJ, 2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Naresh, M., Sarojamma, B., Srivyshnavi, P., Madhusudan, G., Vishnupriya, P., Balasiddamuni, P. (2020). Inferential Procedures for Testing Assumptions on Observations for Applications of Biometric Techniques. In: Jyothi, S., Mamatha, D., Satapathy, S., Raju, K., Favorskaya, M. (eds) Advances in Computational and Bio-Engineering. CBE 2019. Learning and Analytics in Intelligent Systems, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-030-46939-9_33
Download citation
DOI: https://doi.org/10.1007/978-3-030-46939-9_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-46938-2
Online ISBN: 978-3-030-46939-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)