skewness statistic | Definition

A skewness statistic is a numerical value that tells how much and in which direction a data distribution is skewed from perfect symmetry.

What Is the Skewness Statistic?

The skewness statistic is a single number that shows whether a dataset is symmetrical or lopsided. It helps researchers see if values in the data tend to bunch up on one side of the average (mean) and stretch out on the other. A symmetrical distribution has a skewness statistic close to zero. If the value is positive or negative, the data is skewed to the right or left.

This statistic is especially useful in social science research. Many statistical methods assume that the data is normally distributed. But real-world data—like survey responses, test scores, income, or attitudes—often show skewness. The skewness statistic helps researchers decide whether their data is appropriate for certain tests or needs transformation.

How Is the Skewness Statistic Calculated?

The skewness statistic is calculated from the values in a dataset. It compares how far each value is from the mean and whether those distances are balanced or uneven on either side.

While the formula can look complex, the basic idea is simple: it looks at how much the values lean to one side of the average. The skewness value is calculated by taking the third moment of the data (which captures asymmetry) and dividing it by the cube of the standard deviation. This standardizes the value so researchers can compare skewness across different datasets.

What the Values Mean

• A skewness statistic of 0 means the data is perfectly symmetrical.
• A positive skewness statistic means the right tail (higher values) is longer.
• A negative skewness statistic means the left tail (lower values) is longer.

Rule of Thumb for Interpreting the Skewness Statistic

• -0.5 to +0.5: The distribution is fairly symmetrical.
• -1 to -0.5 or +0.5 to +1: The distribution is moderately skewed.
• Less than -1 or greater than +1: The distribution is highly skewed.

Why the Skewness Statistic Matters

For Choosing the Right Statistical Tests

Many common statistical tests assume normal distribution. If the skewness statistic shows that data is highly skewed, researchers might need to transform the data or use different tests that don’t require symmetry.

For Understanding Central Tendency

The skewness statistic also helps explain how the mean and median relate to each other:

• In a right-skewed distribution (positive skewness statistic), the mean is higher than the median.
• In a left-skewed distribution (negative skewness statistic), the mean is lower than the median.

For Reporting Results Accurately

Reporting the skewness statistic along with other descriptive statistics gives readers a full picture of the data. This is especially important when data is not normal, because it affects how results are interpreted and whether findings are reliable.

How to Calculate the Skewness Statistic in Practice

Although researchers can calculate the skewness statistic by hand, most use statistical software to do it. Popular tools include:

• SPSS: Reports skewness in the “Descriptive Statistics” output.
• Excel: Offers the SKEW function to return the skewness value.
• R: The skewness() function from the e1071 package is commonly used.
• Python: The scipy.stats.skew() function returns the skewness statistic.

These tools take the raw data and return a value that summarizes its asymmetry.

Different Formulas for Skewness

There are slightly different formulas depending on whether the researcher is using:

• Sample skewness: Used when working with a sample rather than the full population. It adjusts for sample size.
• Population skewness: Used when the data includes the entire population.

Statistical software usually calculates sample skewness by default. This is the more common approach in social science research, where data comes from surveys, experiments, or observations of a subset of people.

Comparing the Skewness Statistic to Other Measures

Skewness Statistic vs. Skewness (Concept)

Skewness refers to the overall idea of asymmetry in a distribution.
The skewness statistic is the specific number that measures that asymmetry.

In short, skewness is the concept; the skewness statistic is the number that describes it.

Skewness Statistic vs. Kurtosis Statistic

While the skewness statistic tells us about the direction and degree of tilt in the data, kurtosis tells us about the height and sharpness of the distribution’s peak. A dataset could have zero skewness (perfect symmetry) but still have high or low kurtosis.

Skewness Statistic vs. Visual Inspection

Graphs like histograms or boxplots can help detect skewness, but they are not precise. The skewness statistic provides an exact value that supports visual findings and adds credibility to the analysis.

Real-World Examples in Social Science Research

Psychology

In a study measuring anxiety levels, most participants may report low to moderate anxiety, but a few may report extremely high levels. The skewness statistic would be positive, indicating right skewness.

Education

When measuring reading test scores for elementary students, a class where most students perform well but a few score very poorly would result in a negative skewness statistic.

Sociology

In household income surveys, the skewness statistic often comes out positive, since most people earn moderate incomes, but a few very high earners stretch the data to the right.

Political Science

In a survey asking how often people vote, the skewness statistic might be negative if most respondents say they vote in every election, but a few say they never do.

Criminal Justice

A study of sentence lengths in criminal courts might show a positive skewness statistic if most sentences are short, but a few extremely long sentences pull the data to the right.

How Skewness Statistic Influences Data Transformation

When the skewness statistic shows high asymmetry, researchers often use data transformations to normalize the distribution. Common methods include:

• Log transformation: Works well for right-skewed data.
• Square root transformation: Good for reducing mild skewness.
• Inverse or reciprocal transformation: Sometimes used when the skewness statistic is very high.

These transformations adjust the data so it more closely follows a normal curve, making it more suitable for analysis with parametric tests.

Limitations of the Skewness Statistic

• It can be sensitive to outliers. A single extreme value can strongly influence the result.
• In small samples, the skewness statistic may not accurately reflect the true distribution.
• It only measures asymmetry, not other important features like spread or peak.

For these reasons, researchers should use the skewness statistic alongside visual inspection and other descriptive tools.

Best Practices for Using the Skewness Statistic

• Always check skewness before running statistical tests that assume normality.
• Report the skewness statistic when summarizing descriptive statistics, especially when data is not clearly normal.
• Use graphs to support the skewness value and help others understand the shape of your data.
• Be aware of sample size, since small datasets may not give reliable skewness results.
• Use transformations or non-parametric tests when skewness is high and normality is important.

Conclusion

The skewness statistic is a powerful tool for identifying asymmetry in a dataset. It provides a clear, numerical value that shows whether a distribution is balanced or tilted to one side. In social science research, where data often comes from messy, real-world sources, the skewness statistic helps researchers make smarter decisions about which tests to use and how to describe their data.

Understanding the skewness statistic can help you analyze your data more accurately and avoid misleading conclusions, whether you’re studying voting behavior, mental health, test scores, or income.

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Last Modified: 03/27/2025