Normality tests
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The document outlines methods for testing the normality of a dataset, emphasizing the significance of skewness, kurtosis, and various statistical tests including the Shapiro-Wilk test and Kolmogorov-Smirnov test. It explains how to interpret normality through graphical representations such as histograms, Q-Q plots, and box plots. The conclusion stresses that data does not need to be perfectly normal but should be approximately normally distributed for valid parametric tests.
Normality tests
- 1. TESTS OF NORMALITY Dr Lipilekha Patnaik Professor, Community Medicine Institute of Medical Sciences & SUM Hospital Siksha ‘O’ Anusandhan deemed to be University Bhubaneswar, Odisha, India Email: drlipilekha@yahoo.co.in 1
- 2. Session Objectives • How to check normality of a dataset • Skewness and Kurtosis z values • Tests of Normality – Shapiro-Wilk test • Normality plots – Histogram, Q-Q plot, Box plot • Interpretation of normality tests 2
- 4. Skewness and Kurtosis • Start with skewness and kurtosis. • The skewness and kurtosis measures should be as close to zero as possible. • In reality, however, data are often skewed and kurtotic. A small departure from zero is therefore no problem. • As a consequence, you must divide the measure by its standard error, and you need to do this by hand, using a calculator. This will give you the z-value, which should be somewhere within -1.96 to +1.96 4
- 5. Kolmogorov-Smirnov Test & Shapiro-Wilk Test • Kolmogorov-Smirnov Test and the Shapiro-WilkTest are well known tests. • The Shapiro-WilkTest is more appropriate. • The null hypothesis for this test of normality is that the data are normally distributed. • If the Sig. value of the Shapiro-WilkTest is > 0.05, the data is normal. If it is below 0.05, the data significantly deviate from a normal distribution. 5
- 6. Histogram • Look at the graphical figures, for both groups. • Inspect the histograms visually. They should have the approximate shape of a normal curve. • Insert the curve and check. 6
- 7. Q-Q Plot 7
- 8. • In order to determine normality graphically, we can use the output of a normal Q-Q Plot. • In normally distributed data, the dots should be approximately distributed along the line. • If the data points stray from the line in an obvious non-linear fashion, the data are not normally distributed. 8
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- 13. Summary • The skewness & kurtosis z-values, which should be somewhere in the span -1.96 to +1.96. • The Shapiro-Wilk p-value should be above 0.05 • The Histograms, Normal Q-Q plots and Box plots, which should visually indicate that our data are approximately normally distributed. 13
- 14. • Remember that your data do not have to be perfectly normally distributed. • The main thing is that they are approximately normally distributed, and that you check each category of the independent variable. • (In our example, both male and female data) 14
- 15. Interpretation of normality tests Sample characteristics: • A Shapiro-Wilk’s test (P>0.05) and visual inspection of their histograms, normal Q-Q plots and box plots showed that BMI are approximately normally distributed for females with a skewness of 0.385 ( SE=0.263) and a kurtosis of 0.840(SE = 0.520) . • Data are skewed for males with a skewness of 0.499 ( SE=0.225) and a kurtosis of 0.368 (SE = 0.446) for males. 15
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