# What is "normality"?

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*#A normal distribution is a symmetric bell-shaped curve defined by two things: the mean (average) and variance (variability). There are an infinite number of normal distributions because there are an infinite number of permutations of the mean and variance. | *#A normal distribution is a symmetric bell-shaped curve defined by two things: the mean (average) and variance (variability). There are an infinite number of normal distributions because there are an infinite number of permutations of the mean and variance. | ||

*#Most statistical tests rest upon the assumption of normality. Deviations from normality, called non-normality , render those statistical tests inaccurate, so it is important to know if your data are normal or non-normal. | *#Most statistical tests rest upon the assumption of normality. Deviations from normality, called non-normality , render those statistical tests inaccurate, so it is important to know if your data are normal or non-normal. | ||

- | *#To provide a rough example of normality and non-normality, see the following histograms. The black line superimposed on the histograms represents the bell-shaped "normal" curve. Notice how the data for variable1 are normal, and the data for variable2 are non-normal. In this case, the non-normality is driven by the presence of an outlier. For more information about outliers, see | + | *#To provide a rough example of normality and non-normality, see the following histograms. The black line superimposed on the histograms represents the bell-shaped "normal" curve. Notice how the data for variable1 are normal, and the data for variable2 are non-normal. In this case, the non-normality is driven by the presence of an outlier. For more information about outliers, see [[What are outliers?]], [[Detecting Outliers - Univariate | How do I detect outliers?]], and [[Dealing with Outliers | How do I deal with outliers?]]. |

- | <center><table><td>[[Image:V1hn0.png|350px]]</td><td>[[Image: | + | <center><table><td>[[Image:V1hn0.png|350px]]</td><td>[[Image:V2hnn0.png|350px]]</td><table> |

## Revision as of 03:31, 17 February 2008

**What is "normality"?**- A normal distribution is a symmetric bell-shaped curve defined by two things: the mean (average) and variance (variability). There are an infinite number of normal distributions because there are an infinite number of permutations of the mean and variance.
- Most statistical tests rest upon the assumption of normality. Deviations from normality, called non-normality , render those statistical tests inaccurate, so it is important to know if your data are normal or non-normal.
- To provide a rough example of normality and non-normality, see the following histograms. The black line superimposed on the histograms represents the bell-shaped "normal" curve. Notice how the data for variable1 are normal, and the data for variable2 are non-normal. In this case, the non-normality is driven by the presence of an outlier. For more information about outliers, see What are outliers?, How do I detect outliers?, and How do I deal with outliers?.

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