The **confidence interval **is the plus-or-minus figure
usually reported in newspaper or television opinion poll results. For example, if you use
a confidence interval of 4 and 47% percent of your sample picks an answer you can be
"sure" that if you had asked the question of the entire relevant population
between 43% (47-4) and 51% (47+4) would have picked that answer.

The **confidence level** tells you how sure you can be. It is expressed as a
percentage and represents how often the true percentage of the population who would pick
an answer lies within the confidence interval. The 95% confidence level means you can be
95% certain; the 99% confidence level means you can be 99% certain. Most researchers use
the 95% confidence level.

When you put the confidence level and the confidence interval together, you can say that
you are 95% sure that the true percentage of the population is between 43% and 51%.

The wider the confidence interval you are willing to accept, the more certain you can be
that the whole population answers would be within that range. For example, if you asked a
sample of 1000 people in a city which brand of cola they preferred, and 60% said Brand A,
you can be very certain that between 40 and 80% of all the people in the city actually do
prefer that brand, but you cannot be so sure that between 59 and 61% of the people in the
city prefer the brand.

**Factors that Affect Confidence Intervals **

There are three factors that determine the size of the **confidence interval**
for a given **confidence level**. These are: **sample size**, **percentage**
and **population size**.

**Sample Size **

The larger your sample, the more sure you can be that their answers truly reflect the
population. This indicates that for a given **confidence level**, the larger
your sample size, the smaller your **confidence interval**. However, the
relationship is not linear (i.e., doubling the sample size does not halve the confidence
interval).

**Percentage **

Your accuracy also depends on the percentage of your sample that picks a particular
answer. If 99% of your sample said "Yes" and 1% said "No" the chances
of error are remote, irrespective of sample size. However, if the percentages are 51% and
49% the chances of error are much greater. It is easier to be sure of extreme answers than
of middle-of-the-road ones.

When determining the sample size needed for a given level of accuracy you must use the
worst case percentage (50%). You should also use this percentage if you want to determine
a general level of accuracy for a sample you already have. To determine the confidence
interval for a specific answer your sample has given, you can use the percentage picking
that answer and get a smaller interval.

**Population Size **

How many people are there in the group your sample represents? This may be the number of
people in a city you are studying, the number of people who buy new cars, etc. Often you
may not know the exact population size. This is not a problem. The mathematics of
probability proves the size of the population is irrelevant, unless the size of the sample
exceeds a few percent of the total population you are examining. This means that a sample
of 500 people is equally useful in examining the opinions of a state of 15,000,000 as it
would a city of 100,000. For this reason, the
sample calculator ignores the population size when it is "large" or unknown.
Population size is only likely to be a factor when you work with a relatively small and
known group of people .

**Note: **

The confidence interval calculations assume you have a genuine random
sample of the relevant population. If your sample is not truly random, you cannot rely
on the intervals. Non-random samples usually result from some flaw in the sampling
procedure. An example of such a flaw is to only call people during the day, and miss
almost everyone who works. For most purposes, the non-working population cannot be assumed
to accurately represent the entire (working and non-working) population.

Information on this page was obtained from The Survey System

Del Siegle, Ph.D.

Neag School of Education - University of Connecticut

del.siegle@uconn.edu

www.delsiegle.com