BOLD Educational Software
Sample Size Calculator

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Sample Size Calculator
Sample Size Calculator

Go straight to sample size calculator

Go straight to confidence interval calculator

Use this sample size calculator to determine how large a sample size you need in order to get statistically accurate results.

How to use the sample size calculator

Enter your information in the sample size calculator at the bottom of the page to find the sample size you need or the confidence interval you need. Leave the Population box blank if the population is very large or unknown.

First, determine your confidence interval.

Determining your confidence interval

The confidence interval is the amount you are willing to be off from the true value. So if your question has a scale of 1 = strongly disagree, 2 = disagree, 3 = neutral, 4 = agree, and 5 = strongly agree, and 77% of the respondents choose agree, you want to know how close that 77% is to the true population. Would only 75% or 70% of the total population agree? Would 80% or 85% of the population agree? Each percentage difference between your sample and the population is another point of error in your results. In order for you to be 100% confident (confidence interval of 100%, or no error), you'd have to sample 100% of your population.

If you are using a RANDOM SAMPLE, you can select a higher confidence interval, say +/-8 or +/-9. If you are doing a NONRANDOM SAMPLE, you're better off with a much lower confidence interval (and therefore a much larger sample size), say +/-5 or +/-6.

Problems introduced with a nonrandom sample Note that when using a nonrandom sample, if you've done nothing else to ensure that your sample is representative of the population, unless you survey a very high percentage of the entire population, you will not be able to generalize your results beyond the sample.
Why would you select a HIGHER confidence interval for a random sample than a nonrandom sample?

Because the sample size calculator doesn't know your sampling method. It can only do the math. By selecting a nonrandom sample, you have chosen to ignore all the possible ways you as a researcher can control getting an accurate sample. So telling the calculator you want a smaller confidence interval, you are really telling it that you need a larger sample size in order to make SOME attempt to get an accurate representation of the population.

The confidence interval is the range where you expect something to be. By saying "expect" you leave open the possibility of being wrong. The degree of confidence measures the probability of that expectation to be true.

Confidence Interval

versus

Confidence Level

Confidence interval and confidence level are linked.

The CONFIDENCE INTERVAL is the range within which the true answer lies. So, in the example above, 77% of the respondents answered 4, agree. In the true population, do you want to be sure the range is somewhere between 75% and 79% [+/- 2] or between 70% and 83% [+/-7]? Those are examples of your confidence intervals.

The CONFIDENCE LEVEL is HOW SURE are you that the population is between 75% and 79% or between 70% and 83% ? Do you want to be 99% sure? Or are you happy with 90% sure?

Let's say you asked, "Do you prefer steak or chicken?" 60% answer steak, and 40% answer chicken. You can estimate that out of the population you sampled, 60% prefer steak. So does 60% of the entire population in prefer steak? There is NO WAY to know that without asking EVERYONE IN THE POPULATION. You CAN be "confident" that the actual proportion of people choosing steak will be somwhere around 60% (between 58% and 62% is a confidence interval of +/-2).

If the survey is based on a sample of 100 persons, you can be 90% confident that the actual proportion of steak will be between 52% and 68% (+/- 8). Also, you can be 99% confident that the actual proportion will be between 48% and 72% (+/- 12)

Notice that, for the same sample size, the higher your confidence, the wider the interval).

If you had sampled 1000 persons instead of 100, you could be 90% confident that the actual proportion is between 57.5% and 62.5% (compare with 52% and 68% for the same confidence with a sample of 100. Larger sample, narrower interval for the same degree of confidence). And you could be 99.99998% (let's say 100%?) confident that the actual proportiion will be between 52% and 68% (compare with a degree of confidence of 90% for the same interval with a sample of 100. Lrger sample, better degree of confidence for the same interval).

Population You should know the size of your population (the group you are trying to generalize to). If it is very large, you can leave that number blank in the calculator and it will calculate an appropriate RANDOM SAMPLE size.
Percentage The accuracy of your results is based on the percentage of your sample who selects a particular answer. If 99% of your sample said "Yes" and 1% said "No," the chances of error are small. 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. What percentage should you use? First, see how many possible answers you have. If your typical question has a scale of 1 = strongly disagrees, 2 = disagrees, 3 = neutral, 4 = agrees, and 5 = strongly agrees, you have 5 answers. Worst case scenario is 20%, so use 20.
Formula

This calculator uses the following formula:

Sample size = Zsq * (p) * (1-p)/Csq

where

Z = Z value (e.g., 1.96 for a 95% confidence interval)
p = percentage of picking a choice, expressed as a decimal (.5 used for sample size needed)
C = confidence interval (e.g., .08 = + 8)

CORRECTION FOR A FINITE POPULATION:

New Sample Size = Sample Size/(1+(1-Sample Size /population))

Copyright BOLD Educational Software 2014
by Diane M. Dusick, Ph.D.
All Rights Reserved

Determine Sample Size

Confidence Level: 95% 99%
Confidence Interval:
Population:
         
Sample size needed:

Find Confidence Interval

Confidence Level: 95% 99%
Sample Size:
Population:
Percentage:
         
Confidence Interval:
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