We investigate in detail the question of whether a nonvanishing cosmological constant is required by the present-day cosmic microwave background and large scale structure data when general isocurvature initial conditions are taken into account. We also discuss the differences between the usual Bayesian and the frequentist approaches in data analysis. We show that the Cosmic Background Explorer (COBE)-normalized matter power spectrum is dominated by the adiabatic mode and therefore breaks the degeneracy between initial conditions which is present in the cosmic microwave background anisotropies. We find that in a flat universe the Bayesian analysis requires ΩΛ≠0 to more than 3σ, while in the frequentist approach ΩΛ=0 is still within 3σ for a value of h<~0.48. Both conclusions hold regardless of the initial conditions.