Variance and standard-deviation comparisons

Learning objectives

• Compare spreads between groups.
• Choose robust methods when normality is suspect.
• Interpret variance ratios in operational terms.

Why variance matters

Two methods can share a mean but differ in spread. In garment conformance, tighter spread often matters more than a slightly better mean because tolerances are two-sided.

Chi-square and F methods are sensitive to normality; Levene / Brown-Forsythe methods are more robust.

Garment-factory example

Two sewing methods have equal mean seam allowance but Method B has σ = 0.6 mm versus Method A σ = 1.1 mm — Method B is preferable because both spec limits are within reach.

Method

1. Plot spread by group and by time.
2. Check stability before comparison.
3. Use a robust test in a free tool.
4. Report ratio and CI; investigate mechanism.

Common mistakes

• Comparing σ on unstable, mixed data.
• Claiming lower spread without an uncertainty range.