  We present two different halo-independent methods to assess the compatibility
of several direct dark matter detection data sets for a given dark matter model
using a global likelihood consisting of at least one extended likelihood and an
arbitrary number of Gaussian or Poisson likelihoods. In the first method we
find the global best fit halo function (we prove that it is a unique piecewise
constant function with a number of down steps smaller than or equal to a
maximum number that we compute) and construct a two-sided pointwise confidence
band at any desired confidence level, which can then be compared with those
derived from the extended likelihood alone to assess the joint compatibility of
the data. In the second method we define a "constrained parameter
goodness-of-fit" test statistic, whose $p$-value we then use to define a
"plausibility region" (e.g. where $p \geq 10\%$). For any halo function not
entirely contained within the plausibility region, the level of compatibility
of the data is very low (e.g. $p < 10 \%$). We illustrate these methods by
applying them to CDMS-II-Si and SuperCDMS data, assuming dark matter particles
with elastic spin-independent isospin-conserving interactions or exothermic
spin-independent isospin-violating interactions.
