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Work Sampling Calculator

Work sampling calculator works out Recommended sample size and Unrounded requirement from Confidence level, Statistical power and Test sidedness. The default figures on this page give recommended sample size of 6,147; change any entry and the result, the working and the sources update together.

Recommended sample size
6,147
Sample Size Calculator
Unrounded requirement
6,146.334113
Total across all groups
6,147
Recruit this many to allow for attrition
6,147
z for the confidence level
1.959964
z for the power
0.841621
Significance level (alpha)
0.05
Formula used
n = z^2 (1 - p) / (p s^2)
Worked out from Cochran, W.G. (1977), Sampling Techniques, 3rd edition, Wiley, chapters 4 and 5 and 8 other sources.
Sample-size calculations for clinical, regulatory or published research should be confirmed by a qualified statistician against the actual analysis plan before a study is registered or a protocol is finalised.

Your figures

Updates as you type
50% is the most conservative choice for a survey because p(1-p) is largest there.
Half-width of the confidence interval, in percentage points.
The smallest difference in means that the study should be able to detect.
Used to turn a required number of events into a number of participants, and as the outcome rate for the events-per-variable rule.
Leave at 0 for a very large or unknown population (no finite-population correction).
Used by the margin-of-error, power, design-effect and finite-population-correction modes.

How this is worked out

3 steps
  1. alpha = 1 - 95/100 = 0.05, two-sided, so z(alpha) = 1.959963985.
  2. z(beta) for 80% power = 0.841621234.
  3. Relative accuracy: n = z^2 (1 - p) / (p s^2) = 3.84145882 x 0.8 / (0.2 x 0.0025) = 6146.3341

Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed

Sources and references

9 sources
Cochran, W.G. (1977), Sampling Techniques, 3rd edition, Wiley, chapters 4 and 5
n = z^2 p(1-p)/e^2 and the finite-population correction n N /(N + n - 1).
Raosoft Inc., Sample Size Calculator - stated formula
x = z^2 r(100-r); n = N x /((N-1)E^2 + x) - algebraically identical to the corrected Cochran form used here.
Fleiss, J.L., Levin, B. & Paik, M.C. (2003), Statistical Methods for Rates and Proportions, 3rd edition, Wiley, chapter 4
Two-proportion sample size in the uncorrected normal-approximation form.
Chow, S.-C., Shao, J. & Wang, H. (2008), Sample Size Calculations in Clinical Research, 2nd edition, Chapman & Hall
Two-mean, paired, noninferiority and equivalence formulas.
Schoenfeld, D.A. (1983), "Sample-size formula for the proportional-hazards regression model", Biometrics 39(2), 499-503
Required number of events d = (z_alpha + z_beta)^2 / (ln HR)^2 p1 p2.
Buderer, N.M.F. (1996), "Statistical methodology: incorporating the prevalence of disease into the sample size calculation for sensitivity and specificity", Academic Emergency Medicine 3(9), 895-900
Kish, L. (1965), Survey Sampling, Wiley
The design effect DEFF = 1 + (m - 1) ICC for equal-sized clusters.
Peduzzi, P. et al. (1996), "A simulation study of the number of events per variable in logistic regression analysis", Journal of Clinical Epidemiology 49(12), 1373-1379
The 10-events-per-variable rule of thumb.
Hinkle, D.E., Wiersma, W. & Jurs, S.G. (2003), Applied Statistics for the Behavioral Sciences, 5th edition
Fisher z sample size for a correlation: n = ((z_alpha + z_beta)/arctanh r)^2 + 3.

What the work sampling calculator calculates

Computes the sample size needed for a survey proportion, a mean, a comparison of two proportions or two means, a paired study, a correlation, a noninferiority or equivalence trial, a log-rank survival study, a diagnostic-accuracy study or a cluster-randomised trial, and works backwards to the margin of error or the power of a sample you already have.

How to use this work sampling calculator

Enter Confidence level, Statistical power, Test sidedness and Expected proportion (group 1). Recommended sample size updates as you type. Change one figure at a time to see what drives the result.

How the result is worked out

Open “How this is worked out” beside the result for the step-by-step calculation behind Recommended sample size, Unrounded requirement and Per group (group 1).

The method follows Cochran, W.G. (1977), Sampling Techniques, 3rd edition, Wiley, chapters 4 and 5, Raosoft Inc., Sample Size Calculator - stated formula, Fleiss, J.L., Levin, B. & Paik, M.C. (2003), Statistical Methods for Rates and Proportions, 3rd edition, Wiley, chapter 4, Chow, S.-C., Shao, J. & Wang, H. (2008), Sample Size Calculations in Clinical Research, 2nd edition, Chapman & Hall and Schoenfeld, D.A. (1983), "Sample-size formula for the proportional-hazards regression model", Biometrics 39(2), 499-503.

What you can compare

Change one input at a time to see how it affects Recommended sample size, Unrounded requirement and Per group (group 1). The inputs you can vary are Confidence level, Statistical power, Test sidedness, Expected proportion (group 1), Expected proportion (group 2) and Margin of error.

Understanding Recommended sample size, Unrounded requirement and Per group (group 1)

Sample-size calculations for clinical, regulatory or published research should be confirmed by a qualified statistician against the actual analysis plan before a study is registered or a protocol is finalised.

Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.

Embed this calculator on your website

Copy this code into any page. The calculator appears with the figures currently entered, sizes itself to fit, and a small credit line links back here. Free, no account, no ads inside it, no tracking of your readers. Set your own figures and fixed fields; Personal removes the credit line, sets your colour and shows you which sites use it.

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Frequently asked questions

What is the 10% rule in sampling?

On the figures this page opens with — confidence level 95%, expected proportion (group 1) 50%, margin of error 5% and population size 0 — the recommended sample size is 6,147. No single number fits everyone: change any figure above and the answer updates as you type, with each step of the arithmetic beside it.

What information do I need for the work sampling calculator?

You need Confidence level, Statistical power, Test sidedness, Expected proportion (group 1), Expected proportion (group 2), Margin of error, Standard deviation and Margin of error (mean scale). The page opens with default figures that give recommended sample size of 6,147, so you can see the scale before entering your own.

What does this work sampling calculator show?

It shows Recommended sample size, Unrounded requirement, Per group (group 1), Per group (group 2), Total across all groups, Recruit this many to allow for attrition, Required number of events and Design effect (DEFF), with the working and any warnings for your entries.

Can I check how the work sampling calculator result was calculated?

Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.

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