The Three-folded Skewness Test, when a Sample Size is Small
The Pomeranian Academy,
ul. Arciszewskiego 22, 76-200 Słupsk, Poland
e-mail: informpiotr@interia.eu
Received:
Received: 5 February 2009; revised: 16 July 2009; accepted: 16 July 2009; published online: 1 September 2009
DOI: 10.12921/cmst.2009.15.02.195-201
OAI: oai:lib.psnc.pl:675
Abstract:
The aim of this publication is to present a new goodness-of-fit test oriented toward normal distribution. The test uses three different versions of skewness measures: classic, median and Bowley’s skewness. Critical values for these skewness measures at significance level α were determined. The power of the proposed test obtained on the basis of a numerical experiment was compared with the power of the Kolmogorov-Smirnov goodness-of-fit test (K-S test).
Key words:
empirical skewness, power test function, skewness test, Visual Basic for Applications
References:
[1] H. Cramer, Mathematical methods in statistics, Warsaw 1958.
[2] H.A. David, Order statistics, Wiley, New York 1970.
[3] A. Drapella, Statistical inference on the base skewness and kurtosis, Pomeranian Pedagogical Academy, Słupsk 2004.
[4] J.F. Kenney, E.S. Keeping, Mathematics of statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand 101-102 (1962).
[5] P. Sulewski, Testing for normality on the base skewness and kurtosis, Słupskie Prace Matematyczno – Fizyczne nr 3, 45-59 (2005).
[6] P. Sulewski, On differently defined skewness, Computational Methods in Science and Technology 14(1), 39-46 (2008).
[7] J. Walkenbach, Excel 2007 Power Programming with VBA, John Wiley & Sons 2001.
[8] W. Zieliński, Statistical tables, SGGW, Warsaw 2000.
The aim of this publication is to present a new goodness-of-fit test oriented toward normal distribution. The test uses three different versions of skewness measures: classic, median and Bowley’s skewness. Critical values for these skewness measures at significance level α were determined. The power of the proposed test obtained on the basis of a numerical experiment was compared with the power of the Kolmogorov-Smirnov goodness-of-fit test (K-S test).
Key words:
empirical skewness, power test function, skewness test, Visual Basic for Applications
References:
[1] H. Cramer, Mathematical methods in statistics, Warsaw 1958.
[2] H.A. David, Order statistics, Wiley, New York 1970.
[3] A. Drapella, Statistical inference on the base skewness and kurtosis, Pomeranian Pedagogical Academy, Słupsk 2004.
[4] J.F. Kenney, E.S. Keeping, Mathematics of statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand 101-102 (1962).
[5] P. Sulewski, Testing for normality on the base skewness and kurtosis, Słupskie Prace Matematyczno – Fizyczne nr 3, 45-59 (2005).
[6] P. Sulewski, On differently defined skewness, Computational Methods in Science and Technology 14(1), 39-46 (2008).
[7] J. Walkenbach, Excel 2007 Power Programming with VBA, John Wiley & Sons 2001.
[8] W. Zieliński, Statistical tables, SGGW, Warsaw 2000.
