Continuous (dependant) variable in each independent groups or categories and Before doing parametric tests, these tests are done.

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

3. Where to do normality tests
Continuous (dependant) variable in each
independent groups or categories
Before doing parametric tests
3

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

9. Box plots
• Look at the box plots. They should be
approximately symmetrical.
9

10. 10

11. 11

12. 12

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

16. 16