How to Identify and Handle Skewed Distributions in EDA

Skewed distributions are a common occurrence in real-world datasets and play a critical role in exploratory data analysis (EDA). Identifying and handling these distributions effectively can significantly improve the performance and interpretability of data models. A skewed distribution occurs when the data points are not symmetrically distributed around the mean. This skewness can impact statistical analyses and modeling techniques that assume normality. Here’s a comprehensive guide on how to identify and handle skewed distributions during EDA.

Understanding Skewed Distributions

A skewed distribution is one where the tail on one side of the distribution is longer or fatter than the other. Skewness can be:

• Positive Skew (Right Skew): The tail on the right side is longer or fatter. Most values cluster on the left with fewer large values on the right.

• Negative Skew (Left Skew): The tail on the left side is longer or fatter. Most values cluster on the right with fewer small values on the left.

Skewness affects statistical measures like mean, median, and standard deviation, and it can lead to misleading interpretations if not addressed.

Identifying Skewed Distributions

1. Visual Inspection

• Histograms: Plot histograms to see the shape of the distribution. A visible tail suggests skewness.

• Boxplots: Help identify the direction of skew through the asymmetry of the box and whiskers.

• Density Plots (KDE): Provide a smooth curve that highlights skew direction.

2. Statistical Measures

• Skewness Coefficient: A numerical measure of the asymmetry.

  • 0 indicates symmetric distribution.

  • 0 indicates positive skew.

  • <0 indicates negative skew.

  • Values above +1 or below -1 indicate high skewness.

• Mean vs Median:

  • If mean > median, the distribution is right-skewed.

  • If mean < median, the distribution is left-skewed.

3. Q-Q Plots (Quantile-Quantile)

Compare the quantiles of the data with those of a normal distribution. Deviations from the straight line indicate skewness.

4. Shapiro-Wilk and D’Agostino’s K-squared Tests

These are normality tests that indirectly detect skewness by testing for deviation from normal distribution.

Implications of Skewness

• Impact on Descriptive Statistics: Skewed data can distort summary statistics, especially mean and standard deviation.

• Violation of Model Assumptions: Many statistical models (e.g., linear regression) assume normally distributed errors. Skewness can lead to poor model performance.

• Influence on Machine Learning Algorithms: Algorithms like linear regression, logistic regression, and k-means clustering assume or perform better on normally distributed data.

Handling Skewed Distributions

1. Data Transformation Techniques

Transformations can help reduce skewness and bring distributions closer to normal.

• Log Transformation: Effective for right-skewed data. Replace x with log(x).

• Square Root Transformation: Less aggressive than log; useful for moderate right skew.

• Box-Cox Transformation: Identifies the optimal power transformation to stabilize variance and reduce skewness.

• Yeo-Johnson Transformation: An extension of Box-Cox that handles zero and negative values.

python
CopyEdit
from scipy.stats import boxcox
from sklearn.preprocessing import PowerTransformer

# Box-Cox (only for positive values)
transformed_data, lambda_val = boxcox(data)

# Yeo-Johnson (handles zero/negative values)
pt = PowerTransformer(method='yeo-johnson')
transformed_data = pt.fit_transform(data)

2. Outlier Treatment

Outliers can exaggerate skewness. Consider:

• Capping (Winsorizing): Limit extreme values to a certain percentile.

• Removing Outliers: Based on z-scores or IQR methods, cautiously applied to preserve data integrity.

3. Binning

Group continuous skewed variables into categories using binning techniques. While this simplifies the data, it can lead to loss of information.

• Equal-width binning

• Equal-frequency binning

• Custom binning based on domain knowledge

4. Use of Non-Parametric Models

If transformation doesn’t help or distorts the data meaningfully, consider models that do not assume normality:

• Decision Trees

• Random Forests

• Gradient Boosting Machines

These models are less sensitive to skewness in feature distributions.

5. Feature Engineering

Sometimes it’s more effective to create new features that better represent the underlying distribution or relationship with the target variable. Examples include:

• Creating ratios

• Interaction terms

• Applying domain-specific transformations

Skewness in Target Variables

When the target variable in supervised learning is skewed, it requires careful handling:

• For Regression Tasks:

  • Apply log or other transformations to normalize the target.

  • Evaluate model performance in both transformed and original space.

• For Classification Tasks:

  • Use stratified sampling during train-test splits.

  • Consider balanced metrics (e.g., AUC, F1-score) if class imbalance results from skew.

Practical Tips for EDA

• Always visualize distributions before choosing a handling method.

• Combine multiple techniques: transformation + outlier treatment often works best.

• Document all transformations to ensure reproducibility and interpretability.

• Recheck skewness post-transformation to evaluate effectiveness.

Conclusion

Skewed distributions are pervasive in real-world datasets and require deliberate identification and handling during EDA. From visual inspections to statistical tests, recognizing skewness is the first step. Corrective actions like data transformation, outlier treatment, or choosing robust models ensure that downstream analyses are accurate and meaningful. By systematically addressing skewed data, analysts can significantly improve the quality of their insights and the performance of predictive models.