Skewness Analysis

Measures distribution asymmetry around the mean to detect departures from normality.

Test Overview

What it measures:

Skewness quantifies the degree and direction of asymmetry in a distribution. Normal distributions are perfectly symmetric (skewness = 0), while positive skewness indicates longer right tails and negative skewness indicates longer left tails.

Strengths:

• • Simple to calculate and interpret
• • Directly measures asymmetry
• • Works with any sample size
• • Automated analysis on sixsigmacenter.com

Limitations:

• • Only measures asymmetry aspect
• • Sensitive to outliers
• • May miss other normality departures
• • Requires sufficient sample size

Skewness Statistic & Formula Focus

Third Standardized Moment:

Sample skewness (Fisher-Pearson, bias-corrected)

= sample size

= i-th observation

= sample mean

= sample standard deviation

Values near 0 indicate symmetry; positive values indicate a right (long) tail, negative values a left tail.

Reading the Skewness Shape Plot

Example Result & Signal Interpretation

A cycle-time dataset yields g1=0.85, with a standard error of approximately SE≈0.30 for n = 60.

Approximately Symmetric

• • |skewness| < 0.5: roughly symmetric
• • Consistent with normal-based methods

Notable Skew

• • |skewness| > 0.5-1: moderate to strong asymmetry
• • Positive: long right tail (e.g., occasional long cycle times)
• • Consider transformation before normal-based capability analysis

Implementation Guide

Example Data Layout for Skewness Analysis

Data with Z-scores and cubed values for skewness calculation. Sample Size Recommendation: Minimum 20-30 observations for reliable skewness estimates - adequate sample size ensures stable third moment calculations for meaningful asymmetry 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.