We evaluated the statistical power of single-indicator latent growth curve models to detect individual differences in change (variances of latent slopes) as a function of sample size, number of longitudinal measurement occasions, and growth curve reliability. We recommend the 2 degree-of-freedom generalized test assessing loss of fit when both slope-related random effects, the slope variance and intercept-slope covariance, are fixed to 0. Statistical power to detect individual differences in change is low to moderate unless the residual error variance is low, sample size is large, and there are more than four measurement occasions. The generalized test has greater power than a specific test isolating the hypothesis of zero slope variance, except when the true slope variance is close to 0, and has uniformly superior power to a Wald test based on the estimated slope variance. (Contains 5 figures, 2 tables and 3 footnotes.)