How Many Participants Do I Need? Sample Size Planning
Andrzej Szymkowiak · Last reviewed September 2026
Your supervisor looks up from your proposal and asks, "How did you decide on this number of participants?" The number of participants you need depends on your analysis method, expected effect size, alpha level, and target power. An a-priori power analysis calculates the minimum N before data collection — typically targeting power ≥ .80 at α = .05 for your smallest expected effect — and it is the approach reviewers and funding bodies expect to see.
One of the most common planning mistakes in survey research is deciding on sample size after the data are collected. By then it is too late to change. Reviewers will ask whether you had enough power to detect your effects. Funding bodies will ask how you justified the recruitment budget. This guide explains how to think about sample size before you launch your study — and how to plan for the participants you will lose along the way.
Why plan sample size before collecting data
Three reasons push for early planning.
Statistical power. Power is the probability of detecting an effect that truly exists. A study with low power will often miss real effects, leading to a false null result. The conventional minimum for power is .80, meaning you accept a 20% chance of missing a real effect. To reach that power, you need a minimum sample size — which depends on how large the effect is and how strict your significance threshold is.
Budget. Recruiting participants costs money and time. Knowing the minimum needed sample in advance lets you estimate cost before committing. Discovering after the fact that you needed twice as many participants is expensive.
Reviewer expectations. Journals increasingly ask authors to report a power analysis. If your paper does not include one, reviewers may reject it or ask for a revision. A prospective power analysis, done before data collection, is stronger evidence than one done after the results are known. For a complete walk-through of the design decisions that precede data collection, see from research question to questionnaire →.
The logic of a-priori power analysis
A-priori power analysis sets the sample size you need before you collect data. Four inputs determine the required N:
- Effect size: the smallest effect you expect, or the smallest one that would be practically meaningful (your SESOI — smallest effect size of interest). Base this on prior work wherever possible — a meta-analysis, the closest published study, or a pilot — rather than on a generic label. Cohen's (1988) benchmarks (for ANOVA, small f = .10, medium f = .25, large f = .40; for regression, small f² = .02, medium f² = .15, large f² = .35) are only a last-resort fallback, and they tend to overstate the effects seen in many fields, so planning around them can leave you underpowered.
- Alpha (α): the significance threshold, usually .05.
- Power (1 − β): the acceptable chance of detecting the effect, usually .80.
- Number of predictors or groups: affects the degrees of freedom in the model.
Given these four inputs, a power formula or calculator returns the minimum N. For t-tests, correlations, regression and ANOVA, the free G*Power program (Faul et al., 2007) does this. For CFA and SEM, Explonia's free calculator at /tools/sample-size-sem/ gives a rule-of-thumb N (cases per free parameter, with a 200-case minimum) and an RMSEA-based power analysis (MacCallum, Browne, & Sugawara, 1996) for the degrees of freedom of your model.
How many participants do you need by analysis method?
These are starting points, not substitutes for a proper power calculation. Use them to cross-check your calculation or for quick estimates at the proposal stage.
| Method | Rough rule | Notes |
|---|---|---|
| Independent t-test (medium effect) | ~64 per group | Cohen (1988), d = .50, α = .05 (two-tailed), power = .80 |
| Pearson correlation (medium effect) | ~85 total | Detecting r ≈ .30 |
| Multiple regression | ~10–15 per predictor (rough); Green (1991): N ≥ 50 + 8 × predictors | More predictors and smaller effects need larger N |
| CFA / CB-SEM | 5–10 per estimated parameter | Often cited (e.g., Hair et al., 2019); a common practical minimum is about 200, which is also the typical sample size in SEM studies (Kline, 2016), but verify with power analysis |
| PLS-SEM | Inverse-square-root method or power analysis — not the old "10× paths" rule | The 10-times rule is criticized as unreliable, even by PLS proponents (Hair et al., 2019; Kock & Hadaya, 2018) |
| Between-groups ANOVA (medium effect) | ~53 per group for three groups (total N ≈ 159) | f = .25, α = .05, power = .80; the per-group N depends on the number of groups |
For structural equation models, the parameter count matters. A simple two-factor CFA with 12 items and one factor correlation might estimate around 25 parameters. At 5 per parameter, that is a minimum of 125 participants. Many reviewers expect at least 200 for a multi-factor CFA, and more for complex SEM models. Treat all of these as starting points, not guarantees of adequate power.
For PLS-SEM, ignore the once-common "ten times the number of paths" rule: it routinely under-estimates the sample needed and has been criticized even by its own proponents (Hair et al., 2019). Use the inverse-square-root method (Kock & Hadaya, 2018), which ties N to the smallest path coefficient you expect to detect, or a formal power analysis. For any latent-variable model, the most defensible approach is a Monte Carlo simulation (Muthén & Muthén, 2002): you specify the model and expected parameter values, then simulate the sample size that yields adequate power and stable, unbiased estimates. Read more at /methods/sample-size/. If you are still choosing between the two SEM families, see PLS-SEM vs CB-SEM: how to choose.
Planning for dropout and screen-outs
Your target sample is the number of usable, complete responses. That is not the same as the number of people who start your survey. Two forces reduce your final count.
Dropout (partial completion). Even well-designed surveys lose respondents mid-way. In online panels, dropout rates of 10–25% are common for surveys of 10–20 minutes. A longer or more demanding survey can lose 30–40% or more.
Screen-outs. If your study requires a specific population — product users, parents, professionals in a given field — you will screen out participants who do not qualify. If only one in three panel members meets your criteria (an incidence rate of 33%), you need three times as many starts to fill your target.
Practical rule: divide your target usable N by the expected completion rate and the incidence rate. For a step-by-step guide to recruiting your sample from an online panel, see how to recruit participants on Prolific →.
Target starts = (target usable N) ÷ (completion rate) ÷ (incidence rate)
Example: you need 200 usable responses, expect 80% completion, and your incidence rate is 50%. You need 200 ÷ .80 ÷ .50 = 500 starts. Set your panel order for 500 or slightly above.
On top of that formula, always add a 10–15% safety margin, because you may also remove responses for straight-lining, fast completion times, or failed attention checks.
Cost when recruiting on a paid panel
If you recruit through a paid panel such as Prolific (available in-panel on Explonia's Academic PRO tier), you pay participants mainly for completed responses, usually a smaller amount for anyone screened out inside the survey, plus the platform's service fee on top. Rates and fees change over time and differ between platforms, so check the provider's current pricing before you budget rather than relying on a fixed figure. As an illustration only: if the participant rate were around £9 per hour and the survey took 10 minutes, each completed response would cost roughly £1.50 in participant pay, before the service fee. Longer surveys, lower incidence (more screen-outs), and stricter quality criteria all raise the total.
Budget the participant pay as:
Participant pay ≈ (completed responses) × (survey duration in hours) × (hourly rate), then add in-survey screen-out payments and the platform service fee
This makes it clear why efficient measurement matters: fewer unnecessary items means a shorter survey, which reduces cost and dropout simultaneously.
Common mistakes to avoid
- Picking a round number (100, 200) with no power analysis behind it.
- Using the PLS "10 times the paths" rule — it is outdated and under-powers studies.
- Running a post-hoc "observed power" analysis to justify a non-significant result (Hoenig & Heisey, 2001).
- Forgetting to inflate the target for expected dropout and failed attention checks.
- Guessing the effect size instead of grounding it in prior studies, a pilot, or a smallest effect of interest.
- Treating "PLS works with small samples" as a licence to skip sample planning.
Frequently asked questions
How many participants do I need for SEM?
A common rule of thumb for CB-SEM is 5–10 participants per estimated parameter, with a practical minimum of around 200, but treat that as a heuristic and confirm it with a power analysis or a Monte Carlo simulation (Muthén & Muthén, 2002). For PLS-SEM, do not rely on the old "10 times the largest number of paths" rule — it is now considered unreliable, even by its main proponents (Hair et al., 2019). Use the inverse-square-root method (Kock & Hadaya, 2018) or a power analysis tied to the smallest path you want to detect; PLS can sometimes run on smaller samples, but the "small-sample friendly" reputation is overstated, and weak effects still need a substantial N. The right answer depends on model complexity, expected effect sizes, and the number of items per factor. Use Explonia's calculator at /tools/sample-size-sem/ for a model-specific estimate.
What is the difference between a-priori and post-hoc power analysis?
A-priori power analysis is done before data collection. You set effect size, alpha, and power, and the analysis returns the required N. It is the standard approach for planning a study. Post-hoc (observed) power analysis is done after data collection, using the sample size you already have. It is largely circular — a non-significant result with low observed power just restates what you already know — and is discouraged for justifying null results (Hoenig & Heisey, 2001). Use a-priori analysis for planning; avoid post-hoc analysis as evidence.
How much should I over-recruit to account for dropout?
The precise answer comes from the formula above: target starts = (target usable N) ÷ (completion rate) ÷ (incidence rate), then add a 10–15% safety margin for responses you later discard for straight-lining, fast completion, or failed attention checks. If you do not yet have completion or incidence estimates, a rough shortcut is to recruit 20–30% more starts than your target usable N for a typical 10–15 minute online survey with moderate quality screening and a high incidence rate — but that figure only stands in for the formula. For longer surveys, lower-incidence populations, or strict attention-check criteria, the formula will call for substantially more (often 40–50% or more). Track your completion and discard rates from any pilot study to calibrate for your specific instrument.
What effect size should I assume if I have no prior data?
Prefer a value taken from prior work — a meta-analysis, the closest published study, or your own pilot — rather than a guess. If you genuinely have nothing to anchor on, a better choice than a generic label is the smallest effect size that would be practically meaningful to you (your SESOI), and you size the study to detect that. A "medium" effect (Cohen's d = .50; r = .30; f² = .15) is sometimes used as a placeholder (Cohen, 1988), but it is not a safe default: real effects are frequently smaller, so planning around "medium" often leaves a study underpowered. A smaller expected effect requires a larger sample. Reviewers will ask how you chose your effect size, so justify it from the literature, a pilot, or a stated practical threshold — never present it as a guess.
Can Explonia calculate my sample size?
Yes, for CFA and SEM. Explonia's free calculator at /tools/sample-size-sem/ takes the number of factors, items and structural paths, and returns a rule-of-thumb N and an RMSEA-based power analysis for your alpha and target power, with the formula and R code used. For t-tests, correlations, regression or ANOVA, use G*Power. You then run the analysis on the data you collect, inside the same platform.
References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39(2), 175-191. https://doi.org/10.3758/BF03193146
Green, S. B. (1991). How many subjects does it take to do a regression analysis? Multivariate Behavioral Research, 26(3), 499–510.
Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate data analysis (8th ed.). Cengage.
Hoenig, J. M., & Heisey, D. M. (2001). The abuse of power: The pervasive fallacy of power calculations for data analysis. The American Statistician, 55(1), 19–24.
Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press.
Kock, N., & Hadaya, P. (2018). Minimum sample size estimation in PLS-SEM: The inverse square root and gamma-exponential methods. Information Systems Journal, 28(1), 227–261.
MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1(2), 130-149. https://doi.org/10.1037/1082-989X.1.2.130
Muthén, L. K., & Muthén, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 9(4), 599–620.
How Explonia does this for you
Explonia provides a free sample-size calculator for CFA and SEM at /tools/sample-size-sem/. Enter the number of factors, items and structural paths: it estimates the free parameters, gives a rule-of-thumb N with a 200-case minimum, and runs an RMSEA-based power analysis for your alpha and target power, with R code you can check. It does not cover t-tests or ANOVA, and it does not adjust for dropout or incidence, so apply the starts formula above yourself. No sign-up is required to use the calculator.
For study-level planning within your survey project, see worked examples → for a walkthrough of how a realistic survey is designed, sized, and launched. After you have collected data and run your model, see how to report SEM fit indices → for the next step.
Ready to size your study with confidence? Plan your sample in Explonia and run the analysis on the data you collect. Start free →
How to cite this article
If this article helped your research, you can cite it (APA 7):
Szymkowiak, A. (2026). How Many Participants Do I Need? Sample Size Planning. Explonia. https://explonia.com/blog/sample-size-before-data-collection/
Last updated: September 2026
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