Skewness and Types

Skewness, in statistics, is the degree of distortion from the symmetrical bell curve, or normal distribution, in a set of data. Skewness can be negative, positive, zero or undefined. A normal distribution has a skew of zero, while a lognormal distribution, for example, would exhibit some degree of right-skew.

The three probability distributions depicted below depict increasing levels of right (or positive) skewness. Distributions can also be left (negative) skewed. Skewness is used along with kurtosis to better judge the likelihood of events falling in the tails of a probability distribution.

Right skewness

Key Takeaways

• Skewness, in statistics, is the degree of distortion from the symmetrical bell curve in a probability distribution.

• Distributions can exhibit right (positive) skewness or left (negative) skewness to varying degree.

• Investors note skewness when judging a return distribution because it, like kurtosis, considers the extremes of the data set rather than focusing solely on the average.

Broadly speaking, there are two types of skewness: They are

(1) Positive skewness

(2) Negative skewness

Positive skewness

A series is said to have positive skewness when the following characteristics are noticed:

• Mean > Median > Mode.

• The right tail of the curve is longer than its left tail, when the data are plotted through a histogram, or a frequency polygon.

• The formula of Skewness and its coefficient give positive figures.

Negative skewness

A series is said to have negative skewness when the following characteristics are noticed:

• Mode> Median > Mode.

• The left tail of the curve is longer than the right tail, when the data are plotted through a histogram, or a frequency polygon.

• The formula of skewness and its coefficient give negative figures.

Thus, a statistical distribution may be three types viz.

• Symmetric

• Positively skewed

• Negatively skewed

Test of Skewness Its Importance:

• Distribution Shape:

Skewness helps in understanding the shape of the data distribution. A skewness of zero indicates a symmetric distribution, while positive skewness means that the tail on the right side is longer or fatter than the left side, and negative skewness means the opposite.

• Data Analysis and Interpretation:

Recognizing skewness helps in interpreting data more accurately. For instance, if a dataset is positively skewed, it may indicate that there are a few unusually high values compared to the rest. This can affect statistical measures like the mean, median, and mode.

• Model Assumptions:

Many statistical models, such as linear regression, assume normally distributed errors (which implies zero skewness). Detecting skewness can help in choosing the appropriate transformations or alternative models to better fit the data.

• Robust Statistics:

Skewness can inform the choice of statistical methods. For example, if data are skewed, robust statistical methods or non-parametric tests may be preferred over traditional parametric tests which assume normality.

• Financial and Risk Analysis:

In finance, skewness is used to understand the risk and return profiles of investments. Positive skewness in investment returns may indicate the potential for high gains, though possibly with high risk, while negative skewness might indicate the risk of significant losses.

• Quality Control:

In quality control and process management, skewness can help in identifying issues with process distributions. For example, if the distribution of a product measurement is skewed, it might indicate problems with the production process or quality control mechanisms.