Testing for the Normal Distribution

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Study Text: "Essential Mathematics and Statistics for Science", 2nd ed, G Currell and A A Dowman (Wiley-Blackwell)


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:
      Anderson-Darling, Shapiro-Wilk (and Ryan-Joiner), Kolmogorov-Smirnov
> The p-value 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 non-normal.

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 Non-normal 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 p-values for Kolmogorov-Smirnov and Shapiro-Wilk tests - choose the lowest p-value.


 book cover

This on-line 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, Wiley-Blackwell, 2009