  Parton distribution functions (PDFs) play a central role in calculations for
the Large Hadron Collider (LHC). To gain a deeper understanding of the
emergence and interplay of constraints on the PDFs in the global QCD analyses,
it is important to examine the relative significance and mutual compatibility
of the experimental data sets included in the PDF fits. Toward this goal, we
discuss the L2 sensitivity, a convenient statistical indicator for exploring
the statistical pulls of individual data sets on the best-fit PDFs and
identifying tensions between competing data sets. Unlike the Lagrange
Multiplier method, the L2 sensitivity can be quickly computed for a range of
PDFs and momentum fractions using the published Hessian error sets. We employ
the L2 sensitivity as a common metric to study the relative importance of data
sets in the recent ATLAS, CTEQ-TEA, MSHT, and reduced PDF4LHC21 PDF analyses at
NNLO and approximate N3LO. We illustrate how this method can aid the users of
PDFs to identify data sets that are important for a PDF at a given kinematic
point, to study quark flavor composition and other detailed features of the
PDFs, and to compare the data pulls on the PDFs for various perturbative orders
and functional forms. We also address the feasibility of computing the
sensitivities using Monte Carlo error PDFs. Together with the article, we
present a companion interactive website with a large collection of plotted L2
sensitivities for eight recent PDF releases.
