Teaching · For Teachers · Research and data

A survey number
with its honest
margin attached.

Type the sample size and either the mean and standard deviation or how many said yes. The calculator gives the confidence interval and margin of error, shows each step, and tells you how much a bigger sample would buy.

Find the intervalWhat you get
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Included with Caveat Classroom and Whole-school licenses. Or get it in the For Teachers toolkit, $79 for 72 items.

The confidence interval calculator

The worked example is made up: 48 families reporting minutes read at home per night. Nothing you type leaves this browser.

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What you get

Teaching · For Teachers$12 · included with Classroom and Whole-school licenses

What you finish with
The confidence interval, margin of error, standard error and critical value for a mean or a proportion, the steps, and the margin at four times the sample. It prints as a summary and downloads as a spreadsheet.
Who it is for
Teachers doing action research, survey and data teams, program evaluators and graduate students in education.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
$12 one-time, yours on every device you sign in on; the tool opens once you are signed in with it. Included with Caveat Classroom and Whole-school licenses. Also in the For Teachers toolkit ($79) and the Teaching Suite pass ($199), and 1 more bundle. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The For Teachers space in Caveat Teaching.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Say what you are estimating and choose a mean or a proportion.
  2. Choose a confidence level.
  3. Type the sample size and the mean and SD, or the count with the trait.
  4. Read the interval and margin of error, then the steps.
  5. Print the summary or download the spreadsheet.

Find the interval

How the interval is built

An estimate, plus and minus its noise.

The worked example, from spread to intervalStandard error1.61711.2 ÷ √48Critical t2.01295%, 47 degrees of freedomMargin of error± 3.25t × standard error95% interval20.25 to 26.7523.5 ± marginThe worked example, from spread to intervalStandard error1.61711.2 ÷ √48Critical t2.01295%, 47 degrees of freedomMargin of error± 3.25t × standard error95% interval20.25 to 26.7523.5 ± margin
The 48 families’ answers spread with an SD of 11.2 minutes; averaged, that spread shrinks to a standard error of 1.62, and about two of those either side of 23.5 makes the 95% interval.

Means and proportions

For a mean, the standard error is the SD divided by the square root of n, and the interval is the mean plus and minus a critical t value times that error. For a proportion this page uses the Wilson score interval, which stays inside 0 to 100 percent and keeps close to its stated coverage even for small samples and percents near the ends, where the textbook Wald interval falls short.

What 95 percent means

If you drew many samples the same way, about 95 percent of intervals built like this would contain the true value. It covers only the luck of the draw. A survey answered mostly by the most engaged families can be precise and still wrong; low response rates and who chose to answer matter more than the margin of error.

Sources

  1. Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22(158), 209–212.
  2. Brown, L. D., Cai, T. T., and DasGupta, A. (2001). Interval estimation for a binomial proportion. Statistical Science, 16(2), 101–133.
  3. NIST/SEMATECH e-Handbook of Statistical Methods, section 7.2.2 and 7.2.4: confidence limits for a mean and a proportion (itl.nist.gov).
  4. National Center for Education Statistics. NCES Statistical Standards (nces.ed.gov): standard errors and nonresponse in survey estimates.

The worked example is made up. The interval covers sampling error only. Your figures stay in this browser. Support: team@caveatacademic.com.