This Sample Size Calculator is presented as a public service of Creative Research Systems survey software. 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.
Enter your choices in a calculator below to find the sample size you need or the confidence interval you have. Leave the Population box blank, if the population is very large or unknown.
The confidence interval (also called margin of error) 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.
There are three factors that determine the size of the confidence interval for a given confidence level:
- Sample size
- Percentage
- Population size
Sample Size
The larger your sample size, 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 prove that 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 or limitation 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. An example of a limitation is using an opt-in online poll, such as one promoted on a website. There is no way to be sure an opt-in poll truly represents the population of interest.
Remember that there is variability associated with your outcomes and statistics.
When you calculate a statistic based on your sample data, how do you know if the statistic truly represents your population? Even if you've selected a random sample, your sample will not completely reflect your population. Each sample you take will give you a different result.
Let's Look at an Example:
Suppose that you want to compare the mean age for those with and without an IV in the prehospital setting. You review the ambulance runs for the past two weeks and calculate a mean age of 10.4 years for those with an IV and 8.5 years for those without an IV. The difference between the two means is 1.9 years. From this, you might conclude that those receiving an IV were older on average.
Suddenly, it's not clear that there's an important difference in age between these two groups. Now suppose you collect the same data over the next six weeks. This time the average age for those with an IV is 9.2 years and the average age for those without an IV is 8.9 years, for a difference of 0.3 years. Suddenly, it's not clear that there's an important difference in age between these two groups. Why did your different samples yield different results? Is one sample more correct than the other?
Remember that there is variability in your outcomes and statistics. The more individual variation you see in your outcome, the less confidence you have in your statistics. In addition, the smaller your sample size, the less comfortable you can be asserting that the statistics you calculate are representative of your population.
Providing a Range of Values
A confidence interval provides a range of values that will capture the true population value a certain percentage of the time. You determine the level of confidence, but it is generally set at 90%, 95%, or 99%. Confidence intervals use the variability of your data to assess the precision or accuracy of your estimated statistics. You can use confidence intervals to describe a single group or to compare two groups. We will not cover the statistical equations for a confidence interval here, but we will discuss several examples.
Example
- Average pulse rate = 101 bpm; Standard Deviation = 50; N = 200
- 95% Confidence Interval = (94, 108)
We are 95% confident that the true pulse rate for our population is between 94 and 108.
Margin of error = (108 – 94) / 2 = ± 7 bpm
The confidence interval in the above example could be described at 94 to 108 bpm (beats per minute) or 101 bpm ± 7 bpm. Here the number 7 is your margin of error. For confidence intervals around the mean, the margin of error is just half of your total confidence interval width.
Sample Size and Variability
The precision of your statistics depends on your sample size and variability. A larger sample size or lower variability will result in a tighter confidence interval with a smaller margin of error. A smaller sample size or a higher variability will result in a wider confidence interval with a larger margin of error. The level of confidence also affects the interval width. If you want a higher level of confidence, that interval will not be as tight. A tight interval at 95% or higher confidence is ideal.
Examples:
- Average Scene Time = 5.5. mins; Standard Deviation = 3 mins; N = 10 runs
- 95% Confidence Interval = (3.6, 7.4)
Margin of Error = ±1.9 minutes- Average Scene Time = 5.5 mins; Standard Deviation = 3 mins; N=1,000 runs
- 95% Confidence Interval = (5.4, 5.6)
Margin of Error = ± 0.1 minutes- Average Scene Time = 5.5 mins; Standard Deviation = 15 mins; N=1,000 runs
- 95% Confidence Interval = (4.6, 6.4)
Margin of Error = ± 0.9 minutes
rev. 05-Aug-2019
Link 1
Link 1
(Description of link)