A three-dimensional cloud-resolving simulation of midlatitude continental convection is used to study similarity of several second and third statistical moments and second-moment budgets among five episodes of deep convection. Several convective scales similar to the scales used in the stratocumulus-topped boundary layer and shallow-convection layer studies are utilized. The dimensionless vertical profiles of the vertical velocity variance and its third moment, cumulus kinetic energy (CKE), model prognostic variables' variances and fluxes, their budgets, as well as several triple correlations, cluster together, confirming the dynamical similarity of the simulated convective events. The shallow convection simulation based on the BOMEX data is also presented. The dimensionless budgets of several second-order moments for deep and shallow convection are contrasted. For example, the dissipation rate in the case of deep convection is found to be relatively small compared to the dominant buoyancy production, transport and pressure correlation terms, while it is a dominant player in the case of shallow convection.