Research planning guide
How to Report Sample Size Calculation in a Proposal
A defensible sample-size rationale names the target estimate or test, effect or precision, alpha, power where relevant, allocation, design, attrition, software, and every assumption.
Answer first
Calculate sample size from the analysis goal, then report every input
For estimation, choose sample size to achieve a target margin of error or interval precision. For hypothesis testing, a priori power analysis links the planned test, meaningful effect, alpha, desired power, and sample size.
Increase the result for attrition, nonresponse, clustering, unequal allocation, multiple outcomes, or complex designs as justified. Do not invent a sample size after seeing the results.
A method you can reuse
Separate precision planning from power planning
Precision asks how narrow an interval should be. Power asks how often a planned test would reject the null for a specified alternative under assumptions. They are related but not interchangeable.
A clinically or practically meaningful effect should come from prior evidence, a decision threshold, or subject-matter reasoning, not from the effect that gives a convenient sample.
Define the primary objective and analysis
Name the estimand, test or model, primary outcome, groups, and design.
Choose justified input values
Specify effect or margin of error, variability or event rate, alpha, power, allocation, and correlation or design effect where relevant.
Calculate the analyzable sample
Use software or a validated formula and record the version, procedure, and options.
Adjust for loss and design
Divide by expected retention, apply design effect, and round up at each required unit such as participant or cluster.
Run sensitivity scenarios
Show how sample size changes across plausible effect, variance, event-rate, attrition, or intracluster-correlation values.
Worked from start to finish
Sample size for estimating one proportion
A survey wants a 95 percent interval with margin of error 0.05. With no prior proportion, p = 0.50 gives the largest simple variance.
z = 1.96, p = 0.50, E = 0.05
n = 1.96² × 0.50 × 0.50 / 0.05²
n = 3.8416 × 0.25 / 0.0025
n = 384.16, round up to 385 analyzable responses
If 90 percent response is expected:
Invitations needed = 385 / 0.90 = 427.78
Round up to 428
The nonresponse adjustment increases invitations, but it does not correct nonresponse bias. If responders differ systematically from nonresponders, a large sample can still be biased.
For a finite population, stratified survey, or clustered design, the standard error and sample-size method change. State those design features explicitly.
Inputs that belong in a sample-size report
A reproducible paragraph lets another analyst rebuild the calculation.
| Input | What to report | Why it matters |
|---|---|---|
| Primary analysis | Test, model, parameter, and outcome | Determines the calculation family |
| Effect or precision | Meaningful effect, margin of error, or interval width | Defines the target information |
| Error rates | Alpha, sidedness, desired power | Controls decision properties |
| Variability or event rate | SD, proportion, baseline risk, correlation | Drives standard error |
| Design | Groups, allocation, pairing, clusters, repeated measures | Changes information per observation |
| Inflation | Attrition, nonresponse, unusable data | Determines recruitment target |
For cluster-randomized designs, the design effect is often related to average cluster size and intracluster correlation. Increasing participants within the same cluster may add much less information than adding clusters.
In regression, a simple subjects-per-predictor rule is rarely enough. Event frequency, model complexity, shrinkage, overfitting, planned validation, and the target performance measure can all matter.
What students report
Real student experiences, with context
These public comments are personal experiences, not universal outcomes. They are included because they show where students commonly get stuck and how the method above helps.
“Power analysis is important, conducted before the study.”
Student discussion in r/statistics
An a priori analysis connects the planned test, meaningful effect, alpha, desired power, and sample size. Post hoc power usually adds little after the p-value is known.
“Power analyses aren’t the only way to determine sample size”
Student discussion in r/statistics
Precision targets, resource limits, minimum event counts, and design-based requirements can also determine sample size. The rationale should match the study purpose.
“I am having a lot of trouble understanding power calculations.”
Student discussion in r/biostatistics
Power becomes clearer when every input is named in plain language and sensitivity scenarios show which assumptions drive the result.
Failure-mode review
Common problems and how to repair them
Using the observed study effect for post hoc power
Report the estimate and confidence interval. Post hoc power largely restates information already in the p-value.
Selecting an effect only to reduce n
Justify a meaningful or plausible value from evidence and show sensitivity scenarios.
Forgetting attrition and unusable records
Distinguish analyzable sample from recruitment or invitation target.
Reporting only “G*Power said 128”
Name the test, effect, alpha, power, sidedness, allocation, software version, and options.
Before you submit or move on
A practical final check
- The primary objective and estimand are explicit.
- The analysis method matches the design.
- Effect or precision is justified.
- Alpha, sidedness, and power are stated where relevant.
- Variance, event rate, and correlation inputs are sourced.
- Clustering, pairing, and allocation are represented.
- Attrition or nonresponse inflation is transparent.
- Sensitivity scenarios are included.
Questions students ask
Frequently asked questions
How do I report a sample size calculation?
State the primary analysis, effect or precision target, variability or event rate, alpha, sidedness, power, allocation, design, software and version, and attrition adjustment.
What is the difference between power and sample size?
Power is the probability of rejecting the null for a specified alternative under assumptions. Sample size is one input that affects it.
Should I do power analysis after the study?
Observed post hoc power is generally not useful. Report effect estimates and confidence intervals, and discuss design sensitivity if needed.
How do I adjust sample size for 10 percent attrition?
Divide the required analyzable sample by 0.90, then round up. Do not simply add 10 percent to the original if precise retention adjustment matters.
Why use p = 0.50 for a proportion?
When the true proportion is unknown, 0.50 maximizes p(1-p) and gives a conservative simple sample size for fixed margin of error.
Sources and further reading
- NIST Engineering Statistics Handbook: Confidence Intervals. Primary government reference for confidence interval construction and interpretation.
- American Statistical Association Statement on P-Values. Official principles for responsible p-value interpretation.
Forum quotations are short excerpts from public discussions. They describe individual experiences and have not been independently verified. Factual guidance in this article is grounded in the primary and institutional sources listed above.