How to Calculate Sample Size for a Survey Study
There is no single "correct" sample size. There is, however, a defensible sample size for every research design — and getting it right before you launch saves you from underpowered findings or wasted budget.
The three drivers of sample size
Every sample-size calculation balances three quantities:
- Effect size — how large the relationship you expect to find is. Small effects need large samples to detect.
- Power — your tolerance for missing a real effect (Type II error). Convention is 80% (1 − β = 0.80).
- Alpha (α) — your tolerance for false positives. Convention is 5% (two-tailed).
Fix two and the third falls out. Most researchers fix power at 0.80 and α at 0.05, then ask: what sample do I need to detect the effect I expect?
What effect size should you assume?
If your literature review found similar studies, use the effect sizes they reported. If not, default to a conservative medium effect:
| Statistic | Small | Medium | Large |
|---|---|---|---|
| Pearson r | .10 | .30 | .50 |
| Cohen's d | .20 | .50 | .80 |
| Cohen's f² (regression) | .02 | .15 | .35 |
| Cohen's f (ANOVA) | .10 | .25 | .40 |
If you have any doubt, plan for a small effect. Sample sizes that detect small effects will also detect medium and large ones.
By design — concrete sample sizes
Pearson correlation
To detect a medium correlation (r = .30) with 80% power at α = .05: n = 84. For a small correlation (r = .10): n = 783. The jump is huge — which is why you should pin down an expected effect size before settling on "around 100 respondents".
Independent-samples t-test
To detect a medium difference (d = .50) at 80% power, α = .05, two-tailed: n = 64 per group (128 total). For a small difference (d = .20): n = 393 per group (786 total).
One-way ANOVA
For four groups, medium effect (f = .25), 80% power, α = .05: n = 45 per group (180 total).
Multiple regression
The rule of thumb is N ≥ 50 + 8k for testing the overall model and N ≥ 104 + k for individual predictors (where k = number of predictors). For a medium effect (f² = .15), 80% power, α = .05, with 5 predictors: n = 92. With 10 predictors: n = 118.
Mediation
Mediation analyses (a × b paths) need more power than simple regressions because they test an indirect effect. Practical rule of thumb based on Monte Carlo simulations:
- To detect a small-to-medium indirect effect: n ≈ 150–250
- For moderated mediation: n ≈ 250–400
Use bootstrapping (1,000–5,000 resamples) regardless of sample size — it's now the standard.
Structural equation modelling (SEM / CFA)
The classic Bentler & Chou rule is N ≥ 5 cases per parameter, with N ≥ 200 as a floor. For a typical mediation SEM with around 30 parameters: n ≈ 200. Models with complex paths or many indicators benefit from n ≈ 300–500.
Adjust for the real world
The numbers above are the minimum required for the analysis. Always inflate them for:
- Incomplete responses — assume 70–80% completion of started surveys. Inflate by 25%.
- Attention-check failures — assume 5–15% of completers will fail an attention check. Inflate by 10%.
- Attrition in longitudinal designs — assume 30–50% attrition between waves. Inflate by 50%.
- Subgroup analyses — if you need to compare gender × industry × experience-level combinations, you need enough in each cell.
A typical cross-sectional study aiming for n = 200 complete cases should send the survey to roughly 250–300 invitees.
Common mistakes
- Calculating sample size after data collection. Always calculate before — it's a planning tool, not an audit tool.
- Assuming a large effect size to justify a small sample. Reviewers see through this.
- Ignoring power. A non-significant result with 80 respondents could just mean you didn't have the power to detect a real effect.
- Confusing the response rate with the completion rate. A 20% response rate from 5,000 invitees is a different distribution than a 100% response from 1,000 carefully recruited respondents.
Calculate it in SmartForm
SmartForm includes a free sample-size calculator that handles correlation, t-test, ANOVA, and regression designs — with built-in inflation for non-response and attrition. Open the Settings panel inside any draft questionnaire.
Final thought
Sample size isn't a number to back-calculate after collection — it's a contract you make with yourself before you launch. Pick an effect size you're willing to defend, fix power at 0.80, fix α at 0.05, and use a published calculator. Then add 25–50% for the messy realities of survey research.