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In many statistical tests the assumption of normal distribution is made for variables measured at an interval or ratio scale. If more than 30 cases are part of the analysis, then, based on the central limit theorem, the variable might be assumed to be normally distributed.

A better way to check the assumptions of normality is to calculate the skewness and the kurtosis. Both values should lie between the limits of -0.05 and +0.05 or, when you are less strict, between -1.00 and +1.00.

Furthermore, two tests on normality can be applied: the Kolmogorov-Smirnov test and the Shapiro-Wilks test. Both test should be not-sigificant to conclude that the variable is normally distributed.

The most common reason for a variable not to be normally distributed is because there are some outliers. It is hard to give reasons why an outlier should be excluded. Do we have to change the data from the real world, because than it fits with the assumptions of statistics?

Related topics to tests for normality

• Variable 
  • Nominal level
  • Ordinal level
  • Interval level 
  • Ratio level 
• Kolmogorov-Smirnov test 
• Shapiro-Wilks test 
• Skewness 
• Kurtosis 
• Outlier