Kurtosis Analysis

A measure of the "tailedness" of a distribution, indicating whether data has heavy or light tails compared to a normal distribution. Kurtosis helps detect outliers and distribution shape.

Statistical Overview

Excess Kurtosis & Formula

Sample excess kurtosis (bias-corrected)

= sample size

= i-th observation

= sample mean

= sample standard deviation

Excess kurtosis is centered so a normal distribution has kurtosis = 0.

Key Assumptions

• • Sample size > 20 is recommended before interpreting kurtosis (see sample size guidance below)
• • Data are continuous and measured on an interval or ratio scale
• • Extreme outliers heavily influence the fourth-moment estimate, so screen for data errors first

Reading the Kurtosis Tail-Weight Plot

Interpretation Guidelines

Kurtosis Values:

• • -2 to 2: Approximately normal distribution
• • > 2: Heavy tails (more outliers likely)
• • < -2: Light tails (fewer outliers expected)
• • Normal Distribution: Exactly 0 (by definition)

Statistical Significance:

• • SE(Kurtosis): √(24/n)
• • z-score: Kurtosis / SE(Kurtosis)
• • |z| > 1.96: Significantly different (α = 0.05)
• • Critical values: ±1.96 (95% confidence)

Practical Guidelines:

• • High kurtosis suggests potential outlier issues requiring investigation
• • Use with skewness for complete distribution shape assessment
• • Requires sample size > 20 for meaningful interpretation
• • Values closer to 0 indicate better normality assumption
• • Consider robust alternatives when kurtosis is extreme

Sample Size Requirements:

Small (n < 30)

Unreliable - avoid interpretation

Medium (30-100)

Acceptable - interpret with caution

Large (> 100)

Reliable - confident interpretation

Implementation Guide

Example Data Layout for Kurtosis Analysis

Data with calculated Z-scores and fourth powers for kurtosis analysis. Sample Size Recommendation: Minimum 20-30 observations for reliable kurtosis estimates - adequate sample size ensures stable estimates of the fourth moment and meaningful tail heaviness assessment.

This is how your spreadsheet or CSV file should be structured before you upload it. Match the column names, keep one row per observation, and leave the analysis to the platform.