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January 13, 2016
Iowa
Sampling
Error Example
As the Iowa caucuses approach, campaign
tittle-tattle begins to focus on the polls and what appears to be
conflicting polling results.
The following table contains polling results
for Ted
Cruz, Donald Trump, and Marco Rubio in the
Iowa Republican Presidential Caucus compiled by RealClearPolitics.com as of
January 13, 2016. The six polls comprising the RealClearPolitics.com
average for January 13 range from a lead of 4 points for Donald Trump
to a lead of 4 points for Ted Cruz.
| Poll |
Date |
Cruz |
Trump |
Rubio |
Spread |
| RealClearPolitics Average |
1/2-1/10 |
26.7 |
26.2 |
13.0 |
Cruz
+0.5 |
| DM
Register/Bloomberg |
1/7-1/10 |
25 |
22 |
12 |
Cruz
+3 |
| PPP |
1/8-1/10 |
26 |
28 |
13 |
Trump
+2 |
| Quinnipiac |
1/5-1/10 |
29 |
31 |
15 |
Trump
+2 |
| ARG |
1/6-1/10 |
25 |
29 |
10 |
Trump
+4 |
| FOX News |
1/4-1/7 |
27 |
23 |
15 |
Cruz
+4 |
| NBC/WSJ/Marist |
1/2-1/7 |
28 |
24 |
13 |
Cruz
+4 |
After looking at the polling results above,
many would claim that there must be "outlier" polls
because it would be impossible for such a range in the polls between
Cruz and Trump.
They would be wrong.
Sampling error accounts for the differences.
The tables below indicate the results from 50 random samples
based
on the RealClearPolitics.com average for January 13, 2016. The second
column
in the last row shows the average for all 50 samples. The average for
all 50 samples should be the closest to the population (and that's why
averages from polling aggregators like RealClearPolitics.com work).
Your browser randomly assigns a candidate to a population of 125,000
based on the averages above. Your browser then creates 50 random
samples of 500 and tabulates the results. (If the sample tables do not
appear below, update your browser.)
A sample size of 500 was selected to match the sample size of the
DM Register/Bloomberg poll and a population of 125,000 was
selected based on
the approximate Iowa Republican caucus turnout. New samples are created
each time this page
is loaded. Refresh this page to see new sample results.
The results below are from sampling error alone and do not include any
additional error that is caused by the practical difficulties of
conducting a poll (and that additional unknown non-sampling error
is included in the polls in the RealClearPolitics.com table).
Please note:
- The sample results rarely refect the
actual population values. Some sample results may be close, but the
population values are better represented by the 50-sample average.
- The error statement for the DM
Register/Bloomberg poll states:
Questions
based on the subsamples of 503 likely Democratic caucus attendees or
500 likely Republican caucus attendees each have a maximum margin of
error of plus or minus 4.4 percentage points. This means that if this
survey were repeated using the same questions and the same methodology,
19 times out of 20, the findings would not vary from the percentages
shown here by more than plus or minus 4.4 percentage points.
This statement is incorrect. The "This means" portion of the statement
assumes that the survey
results are the actual population values, but there is no way of
knowing that as this example of sampling error
illustrates.
- The sample results for Cruz and Trump
reflect the ranges in the RealClearPolitics.com averages.
- Sampling error cannot be avoided. Each of
the 50 samples is equally as likely to be selected and therefore even
a "high quality" poll with a
sample size of 500 will be subject to the sampling error shown in the
tables and will most likely miss the population values.
- The more polls in the poll averages, the
better as poll
averages should better reflect the population.
- Sampling error can be reduced by
increasing sample sizes, but increasing sample sizes will
not eliminate sampling error.
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