Sample size and power for small DNP projects
You have access to one clinic, one cohort, or one unit. The eligible population is small, and extending recruitment may not be possible. The question is not whether a particular number automatically makes your project acceptable. It is what you can learn with the information available.
Power is the probability that a planned test detects a specified effect when that effect is present, under the assumptions used in planning. It depends on the effect, variability, number of independent units, significance threshold, and analysis design. [1] It is not the probability that your intervention will work.
Smaller changes need more information
Consider a paired before and after comparison. The relevant information comes from participants with linked measurements at both times, and the relevant variability is the variability of their changes.
| Assumed standardized mean change | Approximate complete pairs needed |
|---|---|
| 0.30 | 90 |
| 0.50 | 34 |
| 0.80 | 15 |
Illustrative calculation, not a recruitment recommendation. These values use a two-sided paired t test, alpha of .05, 80% power, normally distributed independent differences, and no allowance for missing data or clustering. Standardized change is the mean change divided by the standard deviation of change. Values were calculated for this draft using the noncentral t distribution. [1]
The lesson is the direction of the relationship: a smaller effect is harder to distinguish from variation. Do not assume a large effect simply to make a small available population appear sufficient.
Smaller effects require more information
Show the data
| Assumed standardized mean change | Complete pairs required |
|---|---|
| 0.3 | 90 |
| 0.5 | 34 |
| 0.8 | 15 |
When the available number is fixed
Hypothetical example. An education project has 22 eligible staff members. You can invite all 22, but the paired analysis may include fewer because not everyone provides both assessments. Twenty-two invitations are not 22 complete pairs.
State that the accessible population limits recruitment. Ask which outcomes can still inform a useful decision. Implementation reach, delivery, and an estimated change with a confidence interval may be informative even when the project cannot reliably detect a modest effect. This does not turn an underpowered effectiveness study into a feasibility study after the results are known. Define the purpose before data collection and obtain approval for any later change.
Precision is a separate planning question
Power asks about detecting an assumed effect. Precision asks how narrowly you can estimate an outcome or change. A wide confidence interval can leave both little benefit and worthwhile benefit compatible with the data. Reporting only “not significant” hides that uncertainty.
Repeated observations can be valuable, but they do not automatically create more independent participants. Ten ratings from each of 20 people do not equal 200 independent people. Clustered and repeated measurements need planning that recognizes their dependence.
Your next decision
Bring your advisor the eligible population, expected complete observations, primary outcome, and planned comparison. Discuss a defensible effect or precision target and the practical recruitment limit. Keep the final claims proportional to the design and uncertainty. See Planning for dropout and missing data for missing data and Statistical vs clinical significance for interpretation.