## Testing for the Normal Distribution

This section of the website is being developed. Please send any comments/suggestions to graham.currell@uwe.ac.uk
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.

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