Follow-up observations at 16 and 33 GHz of extragalactic sources from
  WMAP 3-year data: II - Flux-density variability
  Using the Arcminute Microkelvin Imager (AMI) at 16 GHz and the Very Small
Array (VSA) at 33 GHz to make follow-up observations of sources in the New
Extragalactic WMAP Point Source Catalogue, we have investigated the
flux-density variability in a complete sample of 97 sources over timescales of
a few months to approximately 1.5 years.
  We find that 53 per cent of the 93 sources, for which we have multiple
observations, are variable, at the 99 per cent confidence level, above the flux
density calibration uncertainties of approximately 4 per cent at 16 GHz; the
fraction of sources having varied by more than 20 per cent is 15 per cent at 16
GHz and 20 per cent at 33 GHz. Not only is this common occurrence of
variability at high frequency of interest for source physics, but strategies
for coping with source contamination in CMB work must take this variability
into account.
  There is no strong evidence of a correlation between variability and flux
density for the sample as a whole. Using a maximum-likelihood method, we
calculate the correlation in the variability at the two frequencies in a subset
of sources classified as variable from both the AMI and VSA data and find the
Pearson product-moment correlation coefficient to be very high (0.955 +/-
0.034). We also find the degree of variability at 16 GHz (0.202 +/- 0.028) to
be very similar to that at 33 GHz (0.224 +/- 0.039).
  Finally, we have investigated the relationship between variability and
spectral index, alpha_13.9^33.75 (where S proportional to nu^-alpha), and find
a significant difference in the spectral indices of the variable sources (-0.06
+/- 0.05) and non-variable sources (0.13 +/- 0.04).
