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Home  >  Volume 22 (2012)

Assessing the Validity of Normality Assumption Using Probability Plots and Letter Value Diagnostics by Osemeke Reuben F. and Ehiwario J. C Volume 22 (November, 2012), pp 241 – 248
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Abstract

The P-P plots, Q-Q plots as well as letter value diagnostics offer an effective and qualitative tool in examining a situation where the normality distributional assumption is assessed and validated. The normal probability plot is a graphical tool for comparing a sample data(x1, x2,…,xn) set with the normal distribution, based on a subjective visual examination of the data. The observed data(xi i= 1,2,…,n) are first ordered x(1)≤x(2)≤ x(3)≤,…,≤x(n) .Two types of probability plots have been suggested for normality validation. The plot of observed data against the cumulative probability (Pi =i/(n+1)), i= 1… n) for the P-P plots and the plot of observed data against the inverse cumulative probability (mi = Ф¬¬-(Pi)) for the Q-Q plots and this is accompanied with relative tail thickness, symmetrically distributed and 450 (y=x) linearity curve of 95% confidence limits. In addition, equality of data for the mid-summary values was used to show a normal validation. Non-normality of the data was corrected through trial by error transformation. Square-root transformations were closer to normality 

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