We investigate in detail the question whether a non-vanishing cosmological constant is required by present-day cosmic microwave background and large scale structure data when general isocurvature initial conditions are allowed for. We also discuss differences between the usual Bayesian and the frequentist approaches in data analysis. We show that the 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 \Omega \Lambda \neq 0 to more than 3 \sigma, while in the frequentist approach \Omega \Lambda = 0 is still within 3 \sigma for a value of h < 0.48. Both conclusions hold regardless of initial conditions.