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Study Text: "Essential Mathematics and Statistics for Science", 2nd ed, G Currell and A A Dowman (WileyBlackwell)
Introduction
Study Text: Normal Distribution, Section 8.1 (p212ff)
The standard measures for deviations from normality are skewness and kurtosis.
Skewness and kurtosis
QVA tutorial
Study Text: Skewness and kurtosis (pdf)
Testing for Normality
QVA tutorial
There are several tests for normality which use different calculations:
AndersonDarling, ShapiroWilk (and RyanJoiner), KolmogorovSmirnov
> The pvalue given by these tests is the probability that it would be wrong to decide that the data being tested is NOT derived from a normal distribution.
> You should decide that the sample is NOT normal only if p < 0.05 from one of the above tests or you have reason to believe, from previous information, that the data is likely to be nonnormal.
Testing for Normality using Minitab
Use Minitab to assess whether the following data set may have been drawn from a normal distribution:
3.7

6.4

2.7

3.5

3.9

3.3

3.2

3.2

6.8

6.1

3.7

3.8

8.3

6.4

6.1

3.6

5.3

5.7

2.6

6.7

Video answer: Use of Minitab to perform test for Normality
Transformation of Data from a Nonnormal to a Normal Distribution
Tutorial Notes (pdf)
Testing for Normality using SPSS 19
Use Analyze > Descriptive Statistics > Explore > Select data into Dependent List, In Plots check 'Normality Plots with Tests', (If more than one data sample, In Options check 'Exclude Cases Pairwise'), OK
Produces pvalues for KolmogorovSmirnov and ShapiroWilk tests  choose the lowest pvalue.
This online Study Guide has been developed by Graham Currell in association with:
University of the West of England,
"Essential Mathematics and Statistic for Science", 2nd Edition,
Graham Currell and Antony Dowman, WileyBlackwell, 2009