  We address the effect of particle scattering on the energy spectra of solar
energetic electron events using i) an observational and ii) a modeling
approach. i) We statistically study observations of the STEREO spacecraft
making use of directional electron measurements made with the SEPT instrument
in the range of 45 -- 425 keV. We compare the energy spectra of the
anti-sunward propagating beam with that one of the backward scattered
population and find that, on average, the backward scattered population shows a
harder spectrum with the effect being stronger at higher energies. ii) We use a
numerical SEP transport model to simulate the effect of particle scattering
(both in terms of pitch-angle and perpendicular to the mean field) on the
spectrum. We find that pitch-angle scattering can lead to spectral changes at
higher energies (E $>100$ keV) and further away from the Sun (r $> 1$ au) which
are also often observed. At lower energies, and closer to the Sun the effect of
pitch-angle scattering is much reduced so that the simulated energy spectra
still resemble the injected power-law functions. When examining pitch-angle
dependent spectra, we find, in agreement with the observational results, that
the spectra of the backward propagating electrons are harder than that of the
forward (from the Sun) propagating population. {We conclude that {\it Solar
Orbiter} and {\it Parker Solar Probe} will be able to observe the unmodulated
omni-directional SEP electron spectrum close to the Sun at higher energies,
giving a direct indication of the accelerated spectrum. }
