Skewness

Definition

Skewness is a measure of the asymmetry or lack of symmetry in the distribution of a dataset. It describes the extent to which a probability distribution or a data set deviates from a normal, symmetric distribution.

5 Must Know Facts For Your Next Test

1. Positive skewness indicates a distribution with an asymmetric tail extending towards more positive values, while negative skewness indicates a tail extending towards more negative values.
2. The mean, median, and mode are affected differently by skewness, with the mean being most sensitive to skewness and the median being the least sensitive.
3. Skewness can be used to identify the presence of outliers in a dataset, as extreme values in one direction will result in a skewed distribution.
4. Skewness is an important consideration when selecting the appropriate statistical analysis techniques, as many parametric tests assume a normal, symmetric distribution.
5. The shape of a distribution, including its skewness, can provide insights into the underlying processes or characteristics of the data being analyzed.

Review Questions

• Explain how skewness affects the relationship between the mean, median, and mode of a dataset.
  • The mean, median, and mode are affected differently by skewness in a dataset. In a positively skewed distribution, the mean is pulled towards the positive tail, resulting in the mean being greater than the median, which is greater than the mode. Conversely, in a negatively skewed distribution, the mean is pulled towards the negative tail, making it less than the median, which is less than the mode. The degree of skewness determines the extent of the differences between these measures of central tendency.
• Describe the role of skewness in the selection of appropriate statistical analysis techniques.
  • The assumption of normality, which underlies many parametric statistical tests, is violated when a dataset exhibits significant skewness. In such cases, the use of parametric tests may not be appropriate, as they can produce biased results. Instead, researchers may need to consider non-parametric tests or transformations of the data to address the skewness before applying parametric analyses. Understanding the skewness of a dataset is, therefore, crucial in selecting the most suitable statistical methods for data analysis.
• Discuss how the shape of a distribution, including its skewness, can provide insights into the underlying processes or characteristics of the data being analyzed.
  • The skewness of a distribution can reveal important information about the data and the processes that generated it. Positive skewness may indicate the presence of a few large values or a long right tail, which could suggest the influence of factors that limit the lower end of the distribution but allow for larger values. Negative skewness, on the other hand, may point to the dominance of factors that limit the upper end of the distribution but allow for smaller values. Understanding the skewness of a dataset can, therefore, help researchers make inferences about the underlying mechanisms or characteristics that shape the observed data.

Related terms

Symmetry:

A characteristic of a distribution where the left and right sides of the distribution are mirror images of each other, resulting in a median that is equal to the mean.

Kurtosis:

A measure of the peakedness or flatness of a probability distribution compared to a normal distribution. It describes the shape of the tails of a distribution.

Outliers:

Data points that lie an abnormal distance from other values in a dataset, which can significantly impact the calculation of measures of central tendency and dispersion.