Difference between Dispersion and Skewness

What is Skewness?

Skewness can be defined as a statistical measure that describes the lack of symmetry or asymmetry in the probability distribution of a dataset. It quantifies the degree to which the data deviates from a perfectly symmetrical distribution, such as a normal (bell-shaped) distribution. Skewness is a valuable statistical term because it provides insight into the shape and nature of a dataset’s distribution. For example, understanding whether a dataset is positively or negatively skewed can be important in various fields, including finance, economics, and data analysis, as it can impact the interpretation of data and the choice of statistical techniques....

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:...

Positive and Negative Skewness

Positive skewness and negative skewness are two different ways that a dataset’s distribution can deviate from perfect symmetry (a normal distribution). They describe the direction of the skew or asymmetry in the data....

Measurement of Skewness

I. Karl Pearson’s Measure...

I. Karl Pearson’s Measure

Karl Pearson’s Measure of Skewness uses the mean, median, and standard deviation of the given data set to quantify the asymmetry or lack of symmetry in the distribution. It is a dimensionless number that provides valuable insights into the shape of a dataset’s distribution. This measure is valuable in various fields of statistics and data analysis, helping researchers and analysts understand the direction and degree of skewness in their datasets, which can inform subsequent modeling and analytical decisions....

II. Bowley’s Measure

Bowley’s Skewness Coefficient, named after the British economist Arthur Lyon Bowley, is a statistical measure used to assess the skewness or asymmetry in a probability distribution. Unlike some other skewness measures that rely on moments or deviations from the mean, Bowley’s Skewness Coefficient is based on quartiles. This coefficient provides a simple and intuitive way to understand the direction and magnitude of skewness in a dataset. Bowley’s Skewness Coefficient is especially useful when dealing with data that may not follow a normal distribution or when a robust measure of skewness is required....

III. Kelly’s Measure

Kelly’s measure of skewness is a way to quantify the degree of skewness in a distribution by comparing the values of certain percentiles (typically the 10th, 50th, and 90th percentiles) or deciles (10th, 20th, …, 90th percentiles) of the dataset. Specifically, it involves comparing the difference between the median (50th percentile) and the average of the 10th and 90th percentiles (or deciles) to assess the skewness of the data....

Interpretation of Skewness

Interpreting skewness involves understanding the nature of the skewness (left or right) and its magnitude. Here is how to interpret skewness:...

Difference between Dispersion and Skewness

Basis DispersionSkewnessFocus Focuses on the variability or spread of data points around the central tendency (mean, median).Focuses on the shape of the distribution and the direction of the skewness (left or right).Measurement Common measures of dispersion include variance, standard deviation, range, and interquartile range (IQR).Common measures of skewness include Pearson’s first coefficient of skewness, moment skewness, and graphical methods like Q-Q plots.Relationship to Mean Dispersion measures are not directly related to the mean, although they can affect the mean’s interpretation when it is used as a measure of central tendency.Skewness provides information about the relationship between the mean and the median. Positive skewness implies that the mean is greater than the median, and negative skewness implies the opposite.Interpretation High dispersion indicates that data points are scattered or dispersed widely from the center, suggesting a wide range of values.Positive skewness indicates a right-skewed distribution with a longer right tail, while negative skewness indicates a left-skewed distribution with a longer left tail. Zero skewness suggests a symmetric distribution.Application Dispersion measures are useful for understanding the variability of data and assessing how tightly or loosely data points are clustered around the central value.Skewness is useful for understanding the shape of a distribution and identifying whether it is skewed to the left or right. It helps assess the asymmetry of the data.Examples Examples of dispersion include the spread of test scores in a classroom, the variability of stock prices over time, or the range of ages in a population.Examples of skewness include income distributions (often right-skewed), response times for a website (potentially right-skewed with outliers), and exam score distributions (which can be either left-skewed or right-skewed)....