high

Tuesday, May 08, 2007

 

normal Q-Q plot -- normality test



QQ plot is used to check real data against the line plotted with expected values. The expected values are a straight diagonal line, whereas the observed values are plotted as individual points. If the data are normally distributed, then the observed values should fall exactly along the line. Any deviation of the dots from the line represents a deviation from normality.

So if the QQ plot looks like a straight line with a wiggly snake wrapped around it then you have some deviation from normality. When the line sags consistenly above or below the diagonal, this shows that the kurtosis differs from a normal distribution, and when the curve is S-shaped, the problem is skewness.

K-S (Kolmogorov-Smirnov) test is the mostly used method to test normality. When K-S is highly significant, it indicates that distributions are not normal. The test statistic for the K-S is denoted by D, e.g. D(100)=0.10, p<.05 <100: df>

Another test included by SPSS is Shapiro-Wilk: This function is a (semi/non)parametric analysis of variance that detects a broad range of different types of departure from normality in a sample of data.StatsDirect requires a random sample of between 3 and 5000 data for its Shapiro-Wilk test. The null hypothesis of the test is that the sample is taken from a normal distribution, thus P < 0.05 for W rejects this supposition of normality. You should not use any of the parametric methods with samples for which W is significant. (cited from Statsdirect http://www.statsdirect.com/help/statsdirect.htm#parametric_methods/swt.htm)

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