Normal Distribution and Skewness

Normal Distribution

A normal distribution is represented by a bell shaped curve:



This is created when a histogram is plotted from the results and the general trend of the results is shown.

A normal distribution occurs when the mean, median and mode are all the same. It means that the mean value is in the centre of the data set, and therefore representative of the data not affected and skewed by extreme values. It also means that the mean value is the most often occurring. It shows that most values in the data are clustered around the mean with a decreasing number of extreme values either side.

The steeper the curve the more clustered around the mean value the data is, and vice versa. The larger the data set the more likely it is to show a normal distribution, which is why we take a large number of samples when conducting fieldwork.

When the data doesn't conform to normal distribution it is said to be "Skewed", meaning that extreme values are included in the data set and the mean is less reliable.

(Note that extreme values are more likely to be anomalous, so make a data set less accurate!)

http://en.wikipedia.org/wiki/Skewness 

• Negatively skewed data is where the mode and median lie to the right of the mean (it is skewed by extremely small results)
• Positively skewed data is where the mode and median lie to the left of the mean (it is skewed by extremely large results)

Normal Distribution and Skewness are both important as they determine which type of test can be applied to a data set:

• If the data set shows normal distribution then parametric tests should be applied!
• If the data is skewed then non-parametric tests should be applied!