You can use this Sample Size Calculator to determine how many
people you need to get results that reflect the
target population as precisely as needed. You can also find the
level of precision if 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.
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.
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 interval.
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 population size
becomes irrelevant 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
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)