Sample Size Calculator
A tool for drafting a study plan. Its output is meant to be reviewed by the person responsible, who remains accountable for the sample size.
Driven by power. Secures the chance of clearing a target lower bound.
Result
Basis · MFDS Korea (power-based)
Positive specimens · sensitivity
Coefficient (1.96 + 0.84)² = 7.8400
Tolerated errors, by the exact (Clopper-Pearson) method
False negatives up to 8
At a collected size of 166, against a 90% target, by the exact method at two-sided 95%
How it was calculated
- Formula
- n= (Z₁₋α/₂ + Z₁₋β)² × P̂(1−P̂) ÷ (P̂ − P_L)²
- Values
- = (1.96 + 0.84)² × 0.95 × 0.05 ÷ (0.95 − 0.90)²
- Working
- = 7.8400 × 0.0475 ÷ 0.0025
- Rounded up
- = 148.96 → round up → 149
- Dropout correction
- n′= 149 ÷ (1 − 0.10) = 165.56 → round up → 166
Negative specimens · specificity
Coefficient (1.96 + 0.84)² = 7.8400
Tolerated errors, by the exact (Clopper-Pearson) method
False positives up to 3
At a collected size of 190, against a 95% target, by the exact method at two-sided 95%
How it was calculated
- Formula
- n= (Z₁₋α/₂ + Z₁₋β)² × P̂(1−P̂) ÷ (P̂ − P_L)²
- Values
- = (1.96 + 0.84)² × 0.98 × 0.02 ÷ (0.98 − 0.95)²
- Working
- = 7.8400 × 0.0196 ÷ 0.0009
- Rounded up
- = 170.74 → round up → 171
- Dropout correction
- n′= 171 ÷ (1 − 0.10) = 190.00 → round up → 190
Z values are taken to two decimal places, per calculation rule 1.
Conditions
The share of collected specimens expected to drop out or be unusable. The minimum is divided by (1 − the rate).
Sample size against the target lower bound
Raising the target lower bound a little raises the sample size a lot. Use this to find the trade-off.
estimate held at 95%, coefficient 7.8400
| Target lower bound | Minimum | Collected (10% dropout) |
|---|---|---|
| 94% | 3,724 | 4,138 |
| 93% | 931 | 1,035 |
| 92% | 414 | 460 |
| 91% | 233 | 259 |
| 90%current setting | 149 | 166 |
| 89% | 104 | 116 |
| 88% | 76 | 85 |
| 87% | 59 | 66 |
| 86% | 46 | 52 |
| 85% | 38 | 43 |
Wording for the study plan
A paragraph to paste straight into a plan. It carries the track, the formula, the inputs and the result.
Basis: MFDS Korea (power-based) Formula: n = (Z₁₋α/₂ + Z₁₋β)² × P̂(1−P̂) ÷ (P̂ − P_L)² Sensitivity — estimate 95%, target lower bound 90%, confidence 95% Two-sided, power 80%, coefficient 7.8400 → minimum 149 With a 10% dropout rate → 166 collected - Sensitivity: at a collected sample size of 166, up to 8 error(s) can be tolerated while still holding the 90% target lower bound (exact method, two-sided 95%). Specificity — estimate 98%, target lower bound 95%, confidence 95% Two-sided, power 80%, coefficient 7.8400 → minimum 171 With a 10% dropout rate → 190 collected - Specificity: at a collected sample size of 190, up to 3 error(s) can be tolerated while still holding the 95% target lower bound (exact method, two-sided 95%). Total specimens: 356 (166 positive + 190 negative) Source: Ministry of Food and Drug Safety, Guideline on Clinical Performance Studies of In Vitro Diagnostic Medical Devices (안내서-0640-03 (2020-11-26)), checked 2026-07-29 This figure supports drafting the plan. The sample size is settled by the responsible reviewer.
Conditions shared by every row
7.84
Sensitivity
Press a row to add that condition to the total below. The ↗ button does not select — it opens the single calculation.
| Estimate % | Target lower bound % | Minimum n | Collected | Errors tolerated | Row actions |
|---|---|---|---|---|---|
Copy two columns out of a spreadsheet and paste into a cell to fill several rows at once.
Specificity
Press a row to add that condition to the total below. The ↗ button does not select — it opens the single calculation.
| Estimate % | Target lower bound % | Minimum n | Collected | Errors tolerated | Row actions |
|---|---|---|---|---|---|
Copy two columns out of a spreadsheet and paste into a cell to fill several rows at once.
Total for the conditions chosen
💡 Choose one row in each table and the two are added together.
Source documents
Ministry of Food and Drug Safety, Guideline on Clinical Performance Studies of In Vitro Diagnostic Medical Devices
안내서-0640-03 (2020-11-26) · Checked 2026-07-29 · Program v1.0
The final judgement rests with the responsible reviewer.
How to use
- Choose the basis first. MFDS if your protocol states a target lower bound and the power to clear it; estimate precision if it fixes how wide the confidence interval may be instead.
- Enter the sensitivity or specificity you expect, with the conditions beside it. The number of specimens appears as you type.
- Add a dropout rate if some collected specimens will not be evaluable, and the count rises to cover it.
- Open the comparison table to see how the count moves as the expected value or the bound changes, and copy it into the protocol.
Worth knowing
- The count is per measure. Sensitivity and specificity are sized separately, so a study reporting both needs enough positive specimens and enough negative ones — the larger of the two is not the answer for both.
- This is a planning figure, not an approval. It reports what the conditions you entered imply; choosing them, and reviewing the result, stay with you.
- Rounding is always upward. Half a specimen cannot be collected, so the count is the next whole number.
- Everything the count depends on is shown beside it. When a number looks wrong, compare those conditions first — the confidence level and the test direction move it more than most people expect.
FAQs
References
Where the sample size equations and the reference values come from.
- Ministry of Food and Drug Safety (MFDS, Korea). 체외진단의료기기 임상적 성능시험 가이드라인(민원인 안내서) [Guideline on clinical performance studies of in vitro diagnostic medical devices], 안내서-0640-03 (2020-11-26), Ch. IV §2 and Ch. V §2.The equation of the power-based (MFDS) track, and the reproduction of its worked example (estimate 0.80, lower bound 0.70, power 90 % → 168)
- Clopper CJ, Pearson ES. (1934) The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26(4):404–413.doi:10.1093/biomet/26.4.404The definition of the exact (Clopper–Pearson) lower bound used for the error allowance, as a beta quantile. The values were checked against 199 reference points computed in arbitrary precision (mpmath, 60 digits)
The precision track cites no particular standard; it applies the general principle of fixing the half-width of a single proportion's confidence interval. CLSI EP12 (3rd ed.) is not cited because the document could not be obtained, and EP24-A2 is out of scope (continuous measurands only).
Often used together
2×2 Test Accuracy
Turns a 2×2 table into sensitivity, specificity and predictive values, each with a confidence interval.
Power Analysis & Sample Size
Works out how many subjects an experimental group needs for a given power.
Bland-Altman plotter
Analyses the agreement and the regression between two measurement methods.