In the preceding description, we spoke of processes rather than populations. We
contrast these two ways of thinking about samples or batches of data, as shown in
Figure 1. When we think of a sample as a subset of a population (see the left
graphic), we see the sample as a piece allowing us to guess at the whole: The
average and shape of the sample allow us perhaps to estimate the average and shape
of the population. If we wanted to estimate the percentage of the U.S. population
favoring gun control, we would imagine there being a population percentage of
some unknown value, and our goal would be to estimate that percentage from a
well-chosen sample. Thinking in these terms, we tend to view the population as
static and to push to the background questions about why the population might be
the way it is or how it might be changing.
From the process perspective (as depicted in the right graphic of Figure 1), we
think of a population or a sample as resulting from an ongoing, dynamic process, a
process in which the value of each observation is determined by a large number of
causes, some of which we may know and others of which we may not. This view
moves to the foreground questions about why a process operates as it does and what
factors may affect it. In our gun control example, we might imagine people’s
opinions on the issue as being in a state of flux, subject to numerous and complex
influences. We sample from that process to gauge the net effect of those influences
at a point in time, or perhaps to determine whether that process may have changed
over some time period.
In the preceding description, we spoke of processes rather than populations. We
contrast these two ways of thinking about samples or batches of data, as shown in
Figure 1. When we think of a sample as a subset of a population (see the left
graphic), we see the sample as a piece allowing us to guess at the whole: The
average and shape of the sample allow us perhaps to estimate the average and shape
of the population. If we wanted to estimate the percentage of the U.S. population
favoring gun control, we would imagine there being a population percentage of
some unknown value, and our goal would be to estimate that percentage from a
well-chosen sample. Thinking in these terms, we tend to view the population as
static and to push to the background questions about why the population might be
the way it is or how it might be changing.
From the process perspective (as depicted in the right graphic of Figure 1), we
think of a population or a sample as resulting from an ongoing, dynamic process, a
process in which the value of each observation is determined by a large number of
causes, some of which we may know and others of which we may not. This view
moves to the foreground questions about why a process operates as it does and what
factors may affect it. In our gun control example, we might imagine people’s
opinions on the issue as being in a state of flux, subject to numerous and complex
influences. We sample from that process to gauge the net effect of those influences
at a point in time, or perhaps to determine whether that process may have changed
over some time period.
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