AbstractIn order to investigate currently used model fitting strategies for twin data, analysis of variance (ANOVA) and path‐maximum‐likelihood (PATH‐ML) methods of analyzing twin data were compared using simulation studies of 50 monozygotic (MZ) and 50 dizygotic (DZ) twin pairs. Phenotypic covariance was partitioned into additive genetic effects (A), environmental effects common to cotwins (C), and environmental variance unique to individuals (E). ANOVA and PATH‐ML had identical power to detect total covariance. The PATH‐ML AE model was much more powerful than ANOVA comparisons ofrMZ andrDZ to detect A. However, to be unbiased, the AE model requires the assumption that C = 0.0. To allow use of the AE model to estimate A, the null hypothesis C = 0.0 is tested by comparing the goodness of fit of the ACE and AE models. Simulation of 50 MZ and 50 DZ pairs revealed that C must be greater than 55% of total variance before the null hypothesis would be rejected (P<0.05) 80% of the time. Several recent publications were reviewed in which the null hypothesis C = 0.0 was accepted and apparently upwardly biased estimates of A, containing C, were presented with unrealisticPvalues. It was concluded that use of the AE model to estimate A gives an inflated view of the power of relatively small twin studies. It was recommended that ANOVA or comparison of the ACE and CE PATH‐ML models be used to estimate and test the significance of A as neither requires that C = 0.0. © Wil