Empirical scaling relations for the electron heat diffusivity χe, the diffusion coefficient D and the inward drift velocity vin in L and H plasmas of ASDEX are presented. They hold for injection powers which are high compared with the Ohmic input. Expressing χe in dimensionless form reveals that particle orbit, collisionality and finite beta effects are involved in the anomalous transport. The empirical χe scaling is incompatible with theoretical expressions derived from present drift wave models and from a non-linear gyrokinetic Vlasov equation. To reconcile empirical and theoretical scalings, it seems to be necessary to include effects due to finite beta and profile parameters.