  We present a study of scintillation induced by the mid-latitude ionosphere.
By implementing methods currently used in Interplanetary Scintillation studies
to measure amplitude scintillation at low frequencies, we have proven it is
possible to use the Murchison Widefield Array to study ionospheric
scintillation in the weak regime, which is sensitive to structures on scales
$\sim$300 m at our observing frequency of 154 MHz, where the phase variance on
this scale was 0.06 rad$^{2}$ in the most extreme case observed. Analysing over
1000 individual 2-minute observations, we compared the ionospheric phase
variance with that inferred with previous measurements of refractive shifts,
which are most sensitive to scales almost an order of magnitude larger. The two
measurements were found to be highly correlated (Pearson correlation
coefficient 0.71). We observed that for an active ionosphere, the relationship
between these two metrics is in line with what would be expected if the
ionosphere's structure is described by Kolmogorov turbulence between the
relevant scales of 300m and 2000m. In the most extreme ionospheric conditions,
the refractive shifts were sometimes found to underestimate the small-scale
variance by a factor of four or more, and it is these ionospheric conditions
that could have significant effects on radio astronomy observations.
