Short Answer
Sample size calculation is the power analysis that determines the minimum number of patients needed to detect a difference in a statistically reliable way. The calculation rests on four parameters: the expected effect size, the significance level (usually alpha 0.05), the desired power (most often 80 percent or 90 percent), and the type of test. This calculation should be done while the study is being planned, that is, before data collection, and it should be justified in the ethics committee application. The most common mistake is choosing the effect size arbitrarily or optimistically; the correct value is derived from literature in a similar population or from pilot data. The second common mistake is ignoring loss to follow-up; if the calculated number is not adjusted upward according to the expected dropout rate, the study will still remain underpowered.
Serteser Danismanlik is run by a biomedical engineer (BME MSc) with peer-reviewed publications and PROSPERO-registered systematic reviews; it designs and carries out thesis, article, and clinical research statistics, including sample size and power analysis, using SPSS, R, and Python, in a form that is publication-ready and defensible before a jury or reviewers.
"How many patients should I enroll?" is one of the first questions that should be asked in the planning of every clinical study. Enrolling too few patients leaves the study underpowered; enrolling more patients than necessary is an ethical and resource waste.
Why Is Power Analysis Essential?
A study conducted without power analysis faces the following risks:
Type II error: Failing to detect a difference that actually exists. When too few patients are enrolled, the p value does not come out significant, but this does not mean "there is no difference"; it means "we did not have the power to detect the difference."
Ethics committee rejection: Most ethics committees turn down applications in which the sample size is not justified.
Journal rejection: Studies without a sample size calculation are not accepted in high-impact journals.
Four Basic Parameters
Four parameters are needed for power analysis:
1. Effect size
How large is the expected difference? This value comes from the literature. The effect size observed in similar studies is used as a pilot.
Cohen's standard classification:
- d = 0.2: Small effect
- d = 0.5: Medium effect
- d = 0.8: Large effect
2. Significance level (Alpha; α)
The probability of a Type I error. Standard is α = 0.05.
3. Power (1-β)
The probability of detecting a real difference. Usually 80% (β=0.20) or 90% (β=0.10).
4. Type of test
Two independent groups, paired, or survival; each type of test requires a different calculation.
Calculation with G*Power
G*Power is the free and most widely used power analysis tool.
For a two independent groups t-test:
For the chi-square test:
The effect size w is calculated: w = √(χ²/N). Or the expected proportions are entered directly.
For survival analysis:
Log-rank test power analysis; the expected median survival time and accrual period are entered.
Finding the Effect Size from the Literature
If there is no pilot study, the most reliable route is a literature review. Calculate the effect size of studies conducted in a similar population, with a similar intervention:
- For a continuous variable: d = (Mean₁ - Mean₂) / Pooled SD
- For a difference in proportions: h = 2×arcsin(√p₁) - 2×arcsin(√p₂)
If the effect size is not reported in the literature but the mean and SD are available, you can calculate it.
Adjustment for Loss to Follow-up
The expected loss to follow-up rate is added to the calculated sample size:
N_adjusted = N / (1 - dropout_rate)
In clinical studies, a loss to follow-up of 10-20% is generally accepted.
For support with sample size calculation and power analysis, request a free consultation.
Where Do People Get Stuck Most in This Analysis?
- You cannot find the effect size in the literature because there is no similar study or it has not been reported.
- You cannot select the correct test type in G*Power, and different options give different results.
- You do not know how to fill in the power analysis section of the ethics committee form.