NIGERIAN JOURNAL OF SCIENCE AND ENVIRONMENT
Journal of the Faculties of Science and Agriculture, Delta State University, Abraka, Nigeria
A survey was conducted to obtain data set on scratched mobile smart and ordinary (conventional) phones screen, and to further investigate if the data set obtained are normally distributed or not. The Mahalanobis distance, the correlation coefficient, Chi squared and the quantile quantile plots are applied to determine if the data set obtained based on the categorization is normally distributed or otherwise. The techniques revealed that the data set are not normally distributed. The mean and the standard deviation approach based on the concept of data contamination validated the previous conclusions. At level of significance, the hypothesis was rejected, implying non-normality of the data set. In general, the conclusions based on all techniques indicated that the data set are not normally distributed. This implies that though users of mobile phones are both diligent and non-diligent alike
Alqallaf, F.A., Konis, K.P., Martin, R.D., and Zamar, R.H. (2002). Scalablerobust covariance and correlation estimates for data mining, Proceedings of the Seventh ACM SIGKDD Internationa Conference on Knowledge Discovering and Data Mining, Edmonton, Alberta. pp.14-23.
Cox, D.R., and Small, N.J.H. (1978). Testing multivariate normality, Biometrika 65:263-272.
D' Agostino, R.B., and Stephens, M.A. (1986). Goodness of fit techniques (Marcel Dekker, New York).
Epps, T.W., and Pulley, I.B. (1983). A test for normality based on the emperical characteristic function. Biometrika 70:723-726.
Farrell, P. J., and Rogers-Stewart, K. (2006). Comprehensive study of tests for normality and symmetry: extending the Spiegelhalter test. J. Stat. Comput. Simul. 76:803-816.
Filliben, J. J. (1975). The probability plot correlation coefficient test for normality. Technometrics 17:111-117.
Fisher, R.A. (1915). Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika 10:507-521.
Gnanadesikan, R. (1977). Methods for statistical analysis of multivariate data (John Wiley, New York).
Hair, J.F., Anderson, R.E., Tatham, R.L., and Black, W.C. (1998). Multivariate data analysis (Prentice Hall, New Jersey).
Johnson, R.A., and Wichern, D.W. (2008). Applied multivariate statistical analysis (Prentice -Hall International, Inc.
Kim, N., and Bickel, P. (2003). The limit distribution of a test statistic for bivariate normality. Statistica Sinica. pp. 13:327-349.
Kinnison, R. (1989). Correlation coefficient goodness of fit test for the extreme value distribution. Am. Stat. 43:98-100.
Leslie, J.R., Stephens, M.A., and Fotopoulos, S. (1986). Asymptotic distribution of the Shapiro-Wilk W for testing for normality. Ann. Stat. 14:1497-1506.
Liesenfeld, R., and Jung, R.C. (2000) Stochastic volatility models: conditional normality versus heavy tailed distributions. J. Appl. Econ. 15:137-160.
Machado, S.G. (1983). Two statistics for testing multivariate normality, Biometrika 70:713-718.
Maronna, R. A., and Yohai, V. (1998). Robust estimation of multivariate location and scatter, In "Encyclopedia of statistical sciences", Updated Volume 2 ((S. C. R Kotz and Banks , Eds), Wiley, New York).
Maronna, R. A., and Zamar, R. (2002). Robust estimation of location and dispersion for high dimensional datasets. Technometrics 44:307-317.
Mathur, S., and Dolo, S. (2008). A new efficient statistical test for detecting variability in the gene expression data, Statistical Methods Medical Research 17.
Min, I. (2007). A nonparamentric test of the conditional normality of housing demand. Appl. Econ. Lett. 14:105-109.
Muttlak, H.A., and Al-Sabah, W.S. (2003). Statistical quality control based on ranked set sampling. J. Appl. Stat. 30:1055-1078.
Oakland, J.S. (2008). Statistical process control (Butterworth Heinemann, UK).
Ramzan, S., Zahid, F.M., and Ramzan, S. (2013). Evaluating multivariate normality: A graphical approach. Middle-East J. Sci. Res. 13:254-263.
Romao, X., Delgado, R., and Costa, A. (2013). An empirical power comparison of univeriate goodness of fit test for normality. J. Stat. Comput. Simul. 80(5):545-591.
Rousseeuw, P.J., and Leory, A.M. (1987). Robust regression and outlier detection (Wiley-Interscience, New York).
Rousseeuw, P.J., and Van Zomeren, B.C. (1991). Robust distances: Simulation and cutoff values, In: "Directions in robust statistics and diagnostics" Part II (W. Stahel and Weisberge S., Eds) (Springer Verlag, New York).
Ryan, T.A., and Joiner, B.L. (1976). Normal probability plots and tests for normality, Statistics Department, The Pennsylvania State University.
Schoder, A.H., and Wilhelm, K.P. (2006). Preliminary testing for normality: Some statistical aspects of a common concept. Clin. Exp. Dermatol. 31:757-761.
Shapiro, S. S., and Wilk, M.B. (1968). A comparative study of various tests for normality. J. Am. Stat. Assoc. 63:1343-1372.
Surucu, B., and Koc, E. (2007). Assessing the validity of a statistical distribution:Some illustrative examples from dermatological research. Clin. Exp. Dermatol. 33:239-242.
Vamman, V., and Albing, M. (2007). Process capability indices for one sided specification intervals and skewed distributions. Q. Reliab. Eng. Intelligent 23:755-765.
Vogel, R. (1986). The probability plot correlation coefficient. Water Resour. Res. 22:587-590.
Zimmerman, D.W., Zumbo, B.D., and Williams, R.H. (2003). Bias in estimation and hypothesis testing of correlation. Psicologica 24:133-158.