Tests of Skewness
There are several statistical tests and methods to assess the skewness of a dataset. These tests can help you determine whether a dataset is positively skewed, negatively skewed, or approximately symmetric. Here are some common tests and techniques used to assess skewness:
1. Visual Inspection: The simplest way to assess skewness is by creating a histogram or a density plot of the given data. If the plot is skewed to the left, it is negatively skewed, and if the plot is skewed to the right, it is positively skewed. If the plot is roughly symmetric, it has no skewness.
2. Skewness Coefficient (Pearson’s First Coefficient of Skewness): This is a numerical measure of skewness, which determines the skewness when mean and mode are not equal. It is calculated as:
Skewness as per Karl Pearson’s Measure
Skewness = Mean – Mode
Skewness of Karl Pearson’s Measure
- If mean is greater than mode, the skewness will consist positive value.
- In case of mean is smaller than mode, the skewness will be a negative value.
- In case of equality of mean and mode, the skewness will be zero.
3. Quartiles are not equidistant from each other; i.e., [Tex]Q_3-Me\neq Me-Q_1[/Tex]
Skewness – Measures and Interpretation
Skewness is a statistical measure that describes the asymmetry of the distribution of values in a dataset. It indicates whether the data points are skewed to the left (negative skew) or the right (positive skew) relative to the mean. Skewness helps understand the underlying distribution of data, which is crucial for decision-making, risk assessment, and predicting future trends.