|
You can use this sample size calculator to determine how many people you
need to interview in order to get results that reflect the target
population as precisely as needed. You can also find the level
of precision you have in an existing sample.
Before using the sample size calculator, there are two terms that you need
to know. These are: confidence interval and confidence level.
If you are not familiar with these terms, click here. To learn more about the factors
that affect the size of confidence intervals, click here.
This calculator requires Internet Explorer 3.0 or later or Netscape 3.0
or later or a compatible browser. Leave the Population box blank,
if the population is very large or unknown. Do not enter a comma as
a thousands separator.
Sample
Size Terminology
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 Survey System 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 (e.g.,
the members of an association).
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.
|
