EXAMPLE 12.6

The common standard deviation estimate. In the Facebook friends study, there are I = 5 groups and the sample sizes are n₁ = 24, n₂ = 33, n₃ = 26, n₄ = 30, and n₅ = 21. The sample standard deviations are s₁ = 1.00, s₂ = 0.85, s₃ = 1.07, s₄ = 1.43, and s₅ = 1.02.

The pooled variance estimate is

The pooled standard deviation is

This is our estimate of the common standard deviation σ of the social attractiveness scores for the five profiles.