“Do we need three samples, or thirty?” There is no magic answer determined by experiment type alone. You must know which effect you cannot afford to miss, how variable values are, and which errors you will accept.
This unit asks one question.
How do we plan the amount of information needed for a conclusion before an experiment begins?
Four quantities form one relationship
Simple planning for a mean comparison needs:
- effect
Δ: the smallest practically meaningful difference to detect - variability
σ: expected SD among independent experimental units - significance level
α: Type I error accepted when H0 is true - power
1−β: probability of detecting a specified true Δ
Choose three of these and the analysis structure, and you can calculate n. A smaller effect or larger variability lowers Δ/σ, the signal-to-noise ratio, and requires more n. A stricter α or a higher power target also raises n.
For equal allocation to two independent groups with known σ, a normal approximation makes per-group n roughly proportional to (σ/Δ)². Halving Δ needs about four times as many observations. This is why asking to find even slightly smaller differences can be expensive.
The minimum detectable difference is not a difference seen in a past sample
Planning Δ is the smallest effect the study cannot reasonably miss. Putting a chance-large pilot difference directly into the calculation can under-plan n. Justify Δ with prior evidence, process tolerances, clinical importance, measurement units, and decision costs.
σ is uncertain as well. A small-pilot SD varies greatly and can be reduced by selected conditions. Use a conservative upper value, external data, a blinded internal pilot, or a sensitivity table, and present n at several plausible σ values.
Post hoc power calculated from the observed effect in the same data largely restates the p-value. To explain a non-significant result, report the pre-specified plan, CI width, detectable effects, and the information actually collected.
Power is a curve for each effect
A sample size does not have just one power. When the effect is zero, a properly calibrated α-level test rejects near α; power rises as the effect grows. A power curve shows which effects this n can find, and how well.
A one-sided test may have more power in its pre-specified direction, but it does not test the opposite direction. Switching to one-sided after seeing data to reduce n or lower a p-value is not acceptable.
In-Silico Lab: inspect sensitivity of planned n
The Lab uses a normal approximation for two independent groups, two-sided α=.05, equal n, and a known common SD.
- Reduce Δ from 2 to .5 and inspect the increase in per-group n.
- Raise SD from 2 to 4 and confirm the squared relationship.
- Compare the cost of 80%, 90%, and 95% power.
- Before fixing the calculation as the study n, list the missing design elements.
효과·산포·검정력으로 독립 n을 계획하세요
두 독립 집단, 양측 α=.05, 동일 배분의 정규 근사를 투명하게 계산합니다. 이것은 시작값이지 모든 설계를 대신하는 답이 아닙니다.
처음이라면: 무엇을 눌러야 하나요?
- 1. 질문을 먼저 읽기Lab 제목에서 이번에 비교할 한 가지를 확인합니다.
- 2. 조건 하나만 바꾸기처음에는 n, 효과, 산포 같은 입력 중 하나만 바꾸십시오.
- 3. 새 합성 표본 누르기새 합성 데이터가 만들어집니다. 같은 조건도 표본에 따라 달라질 수 있습니다.
- 4. 그림과 계산 결과 비교하기바꾸기 전후 무엇이 움직이고 무엇이 그대로인지 한 문장으로 적어보십시오.
막히면 초기화로 돌아가 기본 결과를 본 뒤 조건 하나만 바꾸십시오. 이 Lab은 정답 판정기가 아니라 패턴 관찰 도구입니다.
같은 설정의 합성 관측
계산 결과
탈락률을 더하는 것과 군집·반복측정의 설계효과를 반영하는 것은 별도 단계입니다. 사후 관측효과로 power를 재계산해 p값을 반복 설명하지 마십시오.
교육용 synthetic model · bjs-comparison-sequence-v1. 실제 연구 판단에는 실험단위, 결측, 분포, 다중성, 사전계획과 도메인 기준을 별도로 반영해야 합니다.
Real sample sizes are larger than a simple formula
These may need separate adjustment, simulation, or a specialist model:
- expected attrition, analysis exclusions, and measurement failure
- unequal allocation and cost differences
- cluster design effects, such as wells within donors or patients within sites
- repeated-measure correlation and paired SD
- multiple endpoints, interim analyses, and multiple comparisons
- different estimands: non-inferiority, equivalence, survival, or proportions
- integer block sizes and a minimum number of batches
For 10% attrition, increase from the n that must remain analysable—such as n/(1−0.10)—rather than simply n×1.10. In clustered data, both the number of individuals and clusters matter; more wells cannot replace donor-level information.
In JMP output, input assumptions are part of the result
효과·SD·α·검정력 중 알고 있는 값을 바탕으로 나머지를 계산합니다.
효과가 달라질 때 검출확률이 연속적으로 바뀌는 모습을 봅니다.
독립 n, 검정방향, 배분비와 분석법이 계획과 일치해야 합니다.
Keep more than a result screenshot. Record analysis method, two- versus one-sided choice, Δ, SD, α, power, allocation ratio, unit of calculated n, and software version. Usually round up, then adjust for the required block or pair structure.
Example planning statement
The primary endpoint was the difference in donor mean day-7 viability. We planned 55 donors per group for a minimum detectable difference of 5 percentage points, between-donor SD of 8, two-sided α=.05, 90% power, and 1:1 allocation. Allowing 10% to be non-analysable, we will recruit 62 donors per group. Technical well replicates will improve measurement precision but will not count toward independent n.
Takeaways
- Adequate n is a function of effect, variability, α, power, and analysis structure.
- Δ is a pre-specified effect that matters scientifically.
- Reflect uncertainty in σ through sensitivity analysis.
- Power is a curve over effects.
- Do not reinterpret results with observed-effect post hoc power.
- Add attrition, clustering, repetition, and multiplicity to practical planning.
The next units move from group differences to relationships between two continuous variables. Read the scatterplot before the correlation coefficient.
Official supplementary resources
The n in this Lab is an educational normal approximation. Review a real study plan against its design and applicable requirements.