Statistical Methods in Medical Research 4ed

46 Describing data
against their effect may be sought. We shall discuss in §4.2 the idea of estimating
the mean of a large population from a sample of observations drawn from it. In
most situations we should be content to do this by calculating the mean of the
sample values, but we might sometimes seek an estimator that is less influenced
than the sample mean by occasional outliers. This approach is called robust
estimation, and a wide range of such estimators has been suggested. In §2.4 we
commended the sample median as a measure of location on the grounds that it is
less influenced by outliers than is the mean. For positive-valued observations, the
logarithmic transformation described in §2.5, and the use of the geometric mean,
would have a similar effect in damping down the effect of outlying high values,
but unfortunately it would have the opposite effect of exaggerating the effect of
outlying low values. One of the most widely used robust measures of location is
the trimmed mean, obtained by omitting some of the most extreme observations
(for example, a fixed proportion in each tail) and taking the mean of the rest.
These estimators are remarkably efficient for samples from normal distributions
(§3.8), and better than the sample mean for distributions `contaminated' with a
moderate proportion of outliers. The choice of method (e.g. the proportion to be
trimmed from the tails) is not entirely straightforward, and the precision of the
resulting estimator may be difficult to determine.
Similar methods are available for more complex problems, although the
choice of method is, as in the simpler case of the mean, often arbitrary, and
the details of the analysis may be complicated. See Draper and Smith (1998,
Chapter 25) for further discussion in the case of multiple regression (§11.6).