Data from longitudinal studies may be analyzed both cross-sectionally and longitudinally. Discrepancies between estimates obtained from these analyses pose questions about the validity of cross-sectional estimates of change. The report, shows that when the true relation between a dependent variable and age is non-linear (e.g. quadratic), but is modeled as linear, the estimated age effect will be a function of the age distribution. In a continuous-time idealization, if the age distribution is Gaussian, the estimated age effects agree. If the age distribution is symmetric and the non-linearity is quadratic, cross-sectional and longitudinal results agree. Otherwise they do not. The paper illustrates these points by analysis of the relation between aging and pulmonary function in middle and old age using data from a large, prospective, longitudinal study.