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Sunday, December 19, 2010

Determining normality of data

I learned new thing in my quest to know what normality test base on Kolmogorov-Smirnov and Shapiro-Wilk is. Despite the fact that the normality test can be determined using the table, I can also refer to graphical representations of the few other measures. This is because Kolmogorov-Smirnov is sensitive and stringent. Han & Yoon (2008) in their book; Introduction to Statistical Analysis in Social Sciences write that normality test from the table (Normality test table of Kolmogorov-Smirnov and Shapiro-Wilkis) sensitive and stringent. For that matter, a researcher may use boxplot, Normal q-q plot and Detrended Q-q plot. All these have their own interpretations of how we can determine that our data is normally distributed. Once we are clear with these, we can now concentrate on outliers. In determining outliers, Pallant (2006) in her book SPSS Survival Manual; A step by Step Guide to Data Analysis Using SPSS, affirms that extreme value needs to be eliminated from the data. However, value with symbol 'O' may be eliminated or may not be. In deciding to retain the 'O' value, we need to refer to 5% Trimmed Mean. If the 5% Trimmed Mean does not differ that much from the mean values (need to refer to Descriptive table in the SPSS output) we can decide to retain the value. For instance 26.73 and 26.64 does not differ much, so we may consider to keep the value for analysis. Apart from that one must also look at skewness and kurtosis. If the former is lesser than 2 while the latter is from -1 to +1, distribution of data may be assumed to be normal (Hair, Anderson, Tatham & Black, 1998 in Fah & Yoon, 2008) as well.

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