Hello hotmark!
Basically, the answer is that at point B, candidate R is doing better
than candidate Q, while at point A we couldn't conclude this. Let's
see why.
First of all, we need to understand what's the "confidence" and
"error" (or "error margin") in a poll. The objective of the poll is to
estimate the proportion of the *population* that will vote for R or Q.
However, the poll is conducted on only a sample of the whole
population. Therefore, it's expected that the proportion you get from
the poll will not be exactly the same as the population proportion
(for example, even if half the population supported each candidate,
you might be "unlucky" and ask who they prefer only to people
supporting R). Thus, the confidence and error are measures of how
accurate is the poll.
Let's take the first poll, for example, in which candidate R gets 53%
of the votes. We have that both polls have 90% confidence with an
error of +/-4. This means the following: "although candidate R got 53%
in this particular poll, in 90 out of 100 polls conducted, the result
will be that candidate R gets anywhere between 49% and 57% of the
votes". (the 49 comes from 53-4, and 57 comes from 53+4). This is due
to the sampling errors I've talked about in the previous paragraph. So
let's see what this implies for the proportion of the votes obtained
in the poll.
Point A
With 90% probability:
- Candidate R has between 49% and 57% of the population votes.
- Candidate Q has between 43% and 51% of the population votes.
Conclusion: we can't tell which of them is actually winning, as it's
perfectly possible that Q has 51% of the population votes while
candidate R has 49%.
Point B
With 90% probability:
- Candidate R has between 52% and 60% of the votes.
- Candidate Q has between 40% and 48% of the votes.
Conclusion: there is a probability of at least 90% that more than half
the population supports candidate R. Note that, with 90% probability,
candidate R has at least 52% of the population votes.
Therefore, it's possible to conclude that candidate R is doing better
at point B than he was doing at point A.
I highly recommed you read this page in order to learn more about
confidence and error margins and how to interpret them:
Margin of Error
http://www.westgroupresearch.com/research/margin.html
Google search terms used:
marketing confidence error poll statistics
://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&q=marketing+confidence+error+poll+statistics
I hope this helps. If there's anything unclear about my answer, please
request a clarification before rating it. Otherwise, I await your
rating and final comments.
Best wishes!
elmarto |
