How to justify sample size in a quantitative research proposal
Build a sample-size justification around your research goal, assumptions, and access limits. Includes a worked power example and a proposal checklist.
About 8 min read · Allow extra time for the practical checks
“The study will include 100 participants” gives the reader a number. It does not explain why that number is appropriate. Nor does adding a citation to a familiar rule settle the question if the rule assumes a different design or purpose.
A sample-size justification explains what information the planned sample should provide, under which assumptions, and with what limitations. It also distinguishes the number you need for the intended analysis from the number you can realistically recruit.
There is no universal minimum that makes a quantitative study adequate. The same number of participants can support one question reasonably well and leave another highly uncertain.
Begin with the conclusion you want the study to support
Before opening a calculator, specify the main outcome and the decision the study is meant to inform. Are you estimating a proportion, estimating a difference, testing a hypothesis, developing a prediction model, or doing something else?
In Sample Size Justification, Daniël Lakens connects sample planning to the information a study is intended to provide. The paper discusses several approaches, including power, precision, and explicit resource constraints. A calculation is useful when its assumptions fit that purpose.
For example, a researcher might want an estimate of the proportion of staff who can access a training resource. Another might compare average task scores between two independently assigned training groups. A third might examine several relationships in a questionnaire model. These are not interchangeable sample-planning problems.
Write the main question in a form that identifies the outcome and the planned comparison or estimate. If those are still unsettled, revisit your research question before treating any calculated sample size as final.
Distinguish power from precision
Power planning asks how likely a specified test would be to reject its null hypothesis if a particular alternative were true, under the assumed design. That alternative needs to be stated. A power calculation without an effect assumption is incomplete.
Precision planning asks how narrowly you want to estimate a quantity. The uncertainty around an estimate matters even when testing a hypothesis is not the main goal.
Neither approach supplies the substantive judgement for you. You must explain why the chosen effect would matter or why a particular degree of uncertainty would be useful. An effect chosen solely because it produces an affordable sample is not a strong scientific justification.
Keep the primary purpose visible. If you need precise subgroup estimates as well as an overall comparison, the overall sample calculation may not address that additional requirement. Discuss the design with someone who can evaluate those needs together rather than adding unrelated calculator outputs.
Make an assumption sheet before calculating
The relevant inputs depend on the method. For a straightforward comparison of two independent means, a planning record would normally identify the anticipated difference, outcome variability, allocation between groups, significance level, target power, and direction of the test. The R documentation for power calculations for t tests shows these inputs and makes clear that its sample count is per group.
For your own study, record where each input came from:
On a narrow screen, scroll the table sideways to read every column.
| Decision | What to document |
|---|---|
| Primary outcome and comparison | The outcome that drives the calculation and why it is primary |
| Effect or precision target | Its practical or theoretical relevance, not only a conventional label |
| Variability or event assumptions | The source, its similarity to your setting, and uncertainty around it |
| Design structure | Independent groups, repeated observations, clustering, or other dependencies |
| Planned analysis | The method the calculation actually represents |
| Access and missingness | Recruitment capacity and reasons some observations may not enter the analysis |
A published estimate can inform an assumption, but check what produced it. A different outcome definition, population, or comparison may make it a poor match. Examine a plausible range when the input is uncertain. Small pilot estimates can also be unstable; an available estimate is not automatically a dependable planning value.
Worked example: one changed assumption, a different sample
This example is synthetic. Its assumptions are chosen to demonstrate a calculation, not to recommend an effect size, significance level, or power target for your study. No participant data or client results are involved.
Suppose a researcher plans a two-sided, equal-allocation comparison of means between two independent groups. For this illustration, assume normally distributed outcomes with equal population variances, an ordinary pooled-variance t test, a significance level of 0.05, and target power of 0.80. There is one primary comparison, no clustering, and no allowance yet for missing data.
The standardised difference, d, is the mean difference divided by the common population standard deviation. Compare two hypothetical planning values:
On a narrow screen, scroll the table sideways to read every column.
| Assumed standardised difference | Calculated observations per group, rounded up | Total analysable observations |
|---|---|---|
| 0.50 | 64 | 128 |
| 0.30 | 176 | 352 |
These values use the noncentral t distribution for the specified two-sided test. The method corresponds to the design documented for R’s power.t.test; the calculations were checked using the two rejection tails of the noncentral t distribution.
The lesson is about the assumptions. Under this particular design, targeting the smaller difference requires substantially more observations. Neither row provides a minimum for surveys, regression, PLS-SEM, or studies with repeated or clustered observations.
The most important part of the real justification would come before this table: why should the study be planned around that difference? The synthetic example supplies no answer for your field. A conventional label such as “medium effect” would not explain what a difference means for the outcome or why it deserves attention.
Common counting mistake
Also keep the distinction between per-group and total counts explicit. Recruiting 64 people in total would not meet the first row’s specification. And if the design or analysis changes, the calculation must be revisited.
Separate recruitment from usable information
A calculated analysis target is not the same as the number of invitations you need to send. Some people may decline, become ineligible, withdraw, or provide incomplete information. Account for those possibilities using evidence relevant to your recruitment process and analysis plan.
Be precise about the numbers being discussed: people approached, enrolled, measured, and included in a particular analysis may differ. Do not apply a convenient percentage simply because it appeared in another proposal.
More observations also do not automatically correct a biased recruitment process. If an online invitation mostly reaches one part of the population, increasing the number of similar respondents may leave the same coverage problem. AAPOR’s survey-research guidance explains the importance of the sampling frame, recruitment method, and transparent reporting alongside the eventual sample.
The structure of the observations matters too. Multiple responses from the same person are not multiple independent participants. Employees within the same team may share conditions. Use a planning method that represents those dependencies; the simple example above does not.
If the accessible sample is fixed, say so
Sometimes access determines the maximum available sample. You may have a complete list of eligible staff, a finite set of records, or a firm recruitment window. Hiding that constraint behind a numerical rule does not improve the design.
Explain the constraint and assess what the available sample can support. Depending on the question, that could involve examining achievable precision or conducting a sensitivity analysis for specified effects. If the resulting information is insufficient for the original objective, consider a narrower question or a different design.
Do not describe an invitation to the entire accessible group as proof of complete population coverage. Nonresponse and the definition of the target population still matter. Studying everyone in one organisation does not make the organisation representative of a wider sector.
For an exploratory study, state its purpose and limits clearly. “Exploratory” should not be used to imply that every planned model is supportable with the data available.
Write a justification another researcher can inspect
A proposal paragraph should connect the goal, assumptions, method, result, and feasibility. Avoid a sentence that merely names software and reports its output.
For the first synthetic scenario, a transparent account would explain that 64 analysable observations are needed per group under the stated model and assumed standardised difference of 0.50. It would then give the substantive basis for that difference and explain how the study expects to achieve the required observations. Because the illustration has no real empirical basis for its effect assumption, it is not a ready-made justification to copy into a proposal.
Keep the full calculation settings or code in your research record. State the software and version actually used, and distinguish prespecified plans from later changes. If recruitment falls short, report that honestly and reassess the strength of the conclusions. A calculation written after seeing results cannot recreate a planning decision that was never made.
Before submitting, ask:
- Does the justification address the primary research goal?
- Is the method appropriate for the planned design and analysis?
- Can I explain the origin and importance of each consequential assumption?
- Have I examined uncertainty in inputs where it matters?
- Are counts clearly identified as per group, total, recruited, or analysable?
- Have I separated sample size from representativeness and measurement quality?
- Are practical constraints and the resulting limits visible?
Our research support can help you understand the assumptions behind an analysis plan and the information your study can reasonably provide. A defensible explanation begins with the research problem, not a universal participant count.
