We measure the effects of interstellar scattering on average pulse profiles from 13 radio pulsars with simple pulse shapes . We use data from the LOFAR High Band Antennas , at frequencies between 110 and 190 MHz . We apply a forward fitting technique , and simultaneously determine the intrinsic pulse shape , assuming single Gaussian component profiles . We find that the constant \tau , associated with scattering by a single thin screen , has a power-law dependence on frequency \tau \propto \nu ^ { - \alpha } , with indices ranging from \alpha = 1.50 to 4.0 , despite simplest theoretical models predicting \alpha = 4.0 or 4.4 . Modelling the screen as an isotropic or extremely anisotropic scatterer , we find anisotropic scattering fits lead to larger power-law indices , often in better agreement with theoretically expected values . We compare the scattering models based on the inferred , frequency dependent parameters of the intrinsic pulse , and the resulting correction to the dispersion measure ( DM ) . We highlight the cases in which fits of extreme anisotropic scattering are appealing , while stressing that the data do not strictly favour either model for any of the 13 pulsars . The pulsars show anomalous scattering properties that are consistent with finite scattering screens and/or anisotropy , but these data alone do not provide the means for an unambiguous characterization of the screens . We revisit the empirical \tau versus DM relation and consider how our results support a frequency dependence of \alpha . Very long baseline interferometry , and observations of the scattering and scintillation properties of these sources at higher frequencies , will provide further evidence .