Sample Size Calculator
This Sample Size Calculator is presented as a public service of Creative
Research Systems. You can use it 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.
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
Sample Size calculator | Confidence
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
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).
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
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.
Sample Size Formulas
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