  The number density of extragalactic 21-cm radio sources as a function of
their spectral line-widths -- the HI width function (HIWF) -- is a sensitive
tracer of the dark matter halo mass function (HMF). The $\Lambda$ cold dark
matter model predicts that the HMF should be identical everywhere provided it
is sampled in sufficiently large volumes, implying that the same should be true
of the HIWF. The ALFALFA 21-cm survey measured the HIWF in northern and
southern Galactic fields and found a systematically higher number density in
the north. At face value, this is in tension with theoretical predictions. We
use the Sibelius-DARK N-body simulation and the semi-analytical galaxy
formation model GALFORM to create a mock ALFALFA survey. We find that the
offset in number density has two origins: the sensitivity of the survey is
different in the two fields, which has not been correctly accounted for in
previous measurements; and the $1/V_{\mathrm{eff}}$ algorithm used for
completeness corrections does not fully account for biases arising from spatial
clustering in the galaxy distribution. The latter is primarily driven by a
foreground overdensity in the northern field within $30\,\mathrm{Mpc}$, but
more distant structure also plays a role. We provide updated measurements of
the ALFALFA HIWF (and HIMF) correcting for the variations in survey
sensitivity. Only when systematic effects such as these are understood and
corrected for can cosmological models be tested against the HIWF.
