Issue # 2: Accuracy of Statistics
Size is
the important issue, but it is not the only consideration in statistical
analysis. Also of interest to analysts is the accuracy of the statistic,
which reflects on its trustworthiness and the extent to which you
can draw certain conclusions.
To understand the issue
of accuracy, let us start by returning to the simple average. In the
previous example we said that the mean spend by our customers was
$1,500. We would call this a point estimate, that is, a statistic
that has a single value.
Is the point estimate
of $1,500 the only issue for you as an analyst or manager? No –
because, from this single point estimate, we cannot gauge how accurately
the average represents all our customers. Let’s examine a pictorial
example of how relative accuracy or inaccuracy operates. Compare Figure 12.3 Customer spending: data close to average of $1,500 and Figure 12.4 Customer data: spending spreads out far from average of $1,500 below, which
describe spending in two samples of equal size (in each sample there
are about 2000 customers).
Figure 12.3 Customer spending: data close to average of $1,500
The data in Figure 12.4 Customer data: spending spreads out far from average of $1,500 spread far
further from the average:
Figure 12.4 Customer data: spending spreads out far from average of $1,500
Note the following:
-
Figure 12.3 Customer spending: data close to average of $1,500 represents the spending of customers in a sample. Here the average is about $1,500, and the spending ranges between a low of about $1,050 and a high of about $2,100. Most of the sample is close to the average, so we would probably say that the point value average of $1,500 represents the spending in the sample well.
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On the other hand, compare this to Figure 12.4 Customer data: spending spreads out far from average of $1,500 . The average Figure 12.4 Customer data: spending spreads out far from average of $1,500 is also about $1,500 (the same as in Figure 12.3 Customer spending: data close to average of $1,500), but here spending spreads out far from the average: some customers spend nothing; some spend double the average ($3,000). Here, the point value estimate of $1,500 does a less satisfactory job of representing the distribution of spending in the sample.
Therefore, in the comparison
of the two sets of spending data, we would assume that the $1,500
average is a more accurate representation of the population in Figure 12.3 Customer spending: data close to average of $1,500 than in the
more spread-out Figure 12.4 Customer data: spending spreads out far from average of $1,500.
In the second case we might even be sufficiently worried about the
sheer spread of data and decide that we have little confidence that
the average represents the data well. If this is the case, accuracy
has become a major issue that overwhelms the size of the statistic
as a consideration.
It is therefore necessary
in statistics not only to generate statistics of interest but also
to assess the accuracy of those statistics. The big question with
accuracy or inaccuracy of a statistic is how we measure it formally.
The next section explains this.
Last updated: April 18, 2017
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