  Data quality is an important consideration in many engineering applications
and projects. Data collection procedures do not always involve careful
utilization of the most precise instruments and strictest protocols. As a
consequence, data are invariably affected by imprecision and sometimes sharply
varying levels of quality of the data. Different mathematical representations
of imprecision have been suggested, including a classical approach to censored
data which is considered optimal when the proposed error model is correct, and
a weaker approach called interval statistics based on partial identification
that makes fewer assumptions. Maximizing the quality of statistical results is
often crucial to the success of many engineering projects, and a natural
question that arises is whether data of differing qualities should be pooled
together or we should include only precise measurements and disregard imprecise
data. Some worry that combining precise and imprecise measurements can
depreciate the overall quality of the pooled data. Some fear that excluding
data of lesser precision can increase their overall uncertainty about results
because lower sample size implies more sampling uncertainty. This paper
explores these concerns and describes simulation results that show when it is
advisable to combine fairly precise data with rather imprecise data by
comparing analyses using different mathematical representations of imprecision.
Pooling data sets is preferred when the low-quality data set does not exceed a
certain level of uncertainty. However, so long as the data are random, it may
be legitimate to reject the low-quality data if its reduction of sampling
uncertainty does not counterbalance the effect of its imprecision on the
overall uncertainty.
