At what sample size do latent variable correlations stabilize?

We conducted a Monte-Carlo simulation within a latent variable framework by varying the following characteristics: population correlation (ρ = 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, and 1.00) and composite score reliability (coefficient omega: ω = 0.40, 0.50, 0.60, 0.70, 0.80, and 0.90). The sample sizes required to estimate stable measurement-error-free correlations were found to approach N = 490 for typical research scenarios (population correlation ρ = 0.20; composite score reliability ω = 0.70) and as high as N = 1000+ for data associated with lower, but still sometimes observed, reliabilities (ω = 0.40–0.50). We encourage researchers to take into consideration reliability, when evaluating the sample sizes required to produce stable measurement-error-free correlations.