  Recent experiments have reached detection efficiencies sufficient to close
the detection loophole with photons. Both experiments ran multiple successive
trials in fixed measurement configurations, rather than randomly re-setting the
measurement configurations before each measurement trial. This opens a new
potential loophole for a local hidden variable theory. The loophole invalidates
one proposed method of statistical analysis of the experimental results, as
demonstrated in this note. Therefore a different analysis will be necessary to
definitively assert that these experiments are subject only to the locality
loophole.
