An Introduction to Critical Thinking and Creativity - always yours

148 STATISTICS AND PROBABILITY
• Leading questions: These are questions that are formulated in such a way
that answers are likely to be skewed in a certain direction. For example, "Do
you want to give vitamin pills to your children to improve their health?" is
likely to solicit more positive answers than the more neutral "Do you intend
to give vitamin pills to your children?" (See also the discussion about anchoring
in Section 20.2.1.)
• Observer effect: It is often difficult to conduct a statistical study without
affecting the results in some way. People might change their answers depending
on who is asking them. Animals change their behavior when they
realize they are being observed. Even measuring instruments can introduce
errors. We just have to be careful when we interpret statistical results.
17.1.5 What about the margin of error?
Many statistical surveys include a number known as the margin of error. This
number is very important for interpreting the results. The concept is a bit difficult
to grasp, but it is worth the effort, especially if you are a journalist or someone who
has to report statistics or make decisions based upon them.
The margin of error arises in any sampling study because the sample is smaller
than the whole population, and so the results might not reflect the reality. Suppose
you want to find the average weight of a Korean by weighing a random sample
of Koreans. The average weight of your sample would be the statistical result,
which might or might not be the true result—the average that is calculated from
the whole Korean population. If you do manage to weigh the whole population,
then your statistical result will be the same as the true result, and your margin or
error will be zero indeed (assuming there are no other sources of error like faulty
weighing machines.)
When the sample is smaller than the population, the margin of error will be
larger than zero. The number reflects the extent to which the true result might
deviate from the estimate. The margin of error is defined with respect to a confidence
interval. In statistics, we usually speak of either the 99% confidence interval,
the 95% confidence interval, or the 90% confidence interval. If the confidence
interval is not specified, it is usually (but not always!) 95%.
Suppose an opinion poll about an upcoming election says that 64% of the people
support Anson, with a margin of error of 3%. Since the confidence interval is
not mentioned, we can assume that the margin of error is associated with the 95%
confidence interval. In that case, what the poll tells us is that the 95% confidence
interval is 64 + 3%. What this means is that if you repeat the poll 100 times, you
can expect that in 95 times the true result will be within the range specified. In
other words, in 95% of the polls that are done in exactly the same way, the true
level of support for Anson should be between 61% and 67%.
There are at least two reasons why it is important to consider the margin of error.
First, if the margin of error is unknown, we do not know how much trust we
should place in the result. With a small sample size and a large margin of error, the