
The
Statistics Calculator
Statistical
Analysis Tests At Your Fingertips

Sampling Menu
The formula to determine sample size
depends upon whether the intended
comparisons involve means or percents.
The Sampling menu has two
selections:
Sample size for percents
This menu selection is used to
determine the required size of a sample
for research questions involving
percents.
Four questions must be answered to
determine the sample size:
1. Best estimate of the population
size: You do not need to know the exact
size of the population. Simply make your
best estimate. An inaccurate population
size will not seriously affect the
formula computations. If the population
is very large, this item may be left
blank.
2. Best estimate of the rate in the
population (%): Make your best estimate
of what the actual percent of the survey
characteristic is. This is based on the
null hypothesis. For example, if the null
hypothesis is "blondes don't have
more fun", then what is your best
estimate of the percent of blondes that
do have more fun? If you simply do not
know, then enter 50 (for fifty percent).
3. Maximum acceptable difference (%):
This is the maximum percent difference
that you are willing to accept between
the true population rate and the sample
rate. Typically, in social science
research, you would be willing to accept
a difference of 5 percent. That is, if
your survey finds that 25 percent of the
sample has a certain characteristic, the
actual rate in the population may be
between 20 and 30 percent.
4. Desired confidence level (%): How
confident must you be that the true
population rate falls within the
acceptable difference (specified in the
previous question)? This is the same as
the confidence that you want to have in
your findings. If you want 95 percent
confidence (typical for social science
research), you should enter 95. This
means that if you took a hundred samples
from the population, five of those
samples would have a rate that exceeded
the difference you specified in the
previous question.
Example
A publishing
wants to know what percent of the
population might be interested in a new
magazine on making the most of your
retirement. Secondary data (that is
several years old) indicates that 22% of
the population is retired. They are
willing to accept an error rate of 5% and
they want to be 95% certain that their
finding does not differ from the true
rate by more than 5%. What is the
required sample size?
Best estimate of
the population size: (left blank)
Best estimate of the rate in the
population (%): 22
Maximum acceptable difference (%): 5
Desired confidence level (%): 95

Required sample
size = 263
Sample size for means
This menu selection is used to
determine the required size of a sample
for research questions involving means.
Three questions must be answered to
determine the sample size:
1. Standard deviation of the
population: It is rare that a researcher
knows the exact standard deviation of the
population. Typically, the standard
deviation of the population is estimated
a) from the results of a previous survey,
b) from a pilot study, c) from secondary
data, or d) or the judgment of the
researcher.
2. Maximum acceptable difference: This
is the maximum amount of error that you
are willing to accept. That is, it is the
maximum difference that the sample mean
can deviate from the true population mean
before you call the difference
significant.
3. Desired confidence level (%): The
confidence level is your level of
certainty that the sample mean does not
differ from the true population mean by
more than the maximum acceptable
difference. Typically, social science
research uses a 95% confidence level.
Example
A fast food
company wants to determine the average
number of times that fast food users
visit fast food restaurants per week.
They have decided that their estimate
needs to be accurate within plus or minus
onetenth of a visit, and they want to be
95% sure that their estimate does differ
from true number of visits by more than
onetenth of a visit. Previous research
has shown that the standard deviation is
.7 visits. What is the required sample
size?
Population
standard deviation: .7
Maximum acceptable difference: .1
Desired confidence interval (%): 95

Required sample
size = 188
How to Order Statistics Calculator
