Use the inverse square root method: to detect a minimum path coefficient of .20 at a 5% significance level with 80% power, PLS-SEM needs at least 155 observations (Kock & Hadaya, 2018). The older 10-times rule (Barclay et al., 1995) usually gives a much smaller number and has been shown to underestimate the sample needed. A G*Power calculation for the most complex regression in your model (Faul et al., 2007) is a defensible alternative and is what many supervisors ask for.
Method 1: the 10-times rule
Barclay, Higgins and Thompson (1995) suggested that the sample should be at least ten times the largest number of structural paths pointing at any one construct, or ten times the largest number of formative indicators of a construct, whichever is larger. It is easy to apply, which explains its popularity. Kock and Hadaya (2018) tested it by simulation and found that it often leads to samples too small to detect realistic effects, and Hair et al. (2022) advise against relying on it alone.
Method 2: the inverse square root method
Kock and Hadaya (2018) derived a simple formula from the fact that a path coefficient's standard error shrinks with the square root of the sample size. For 5% significance and 80% power:
nmin > (2.486 / |pmin|)²
where pmin is the smallest path coefficient you expect to be significant. You can take it from prior studies or choose a conservative value. Some useful values: for .30, n > 68.7, so 69; for .20, n > 154.5, so 155; for .15, n > 274.7, so 275; for .10, n > 618.0, so 619.
Method 3: G*Power for the largest regression
Treat the construct with the most incoming arrows as a multiple regression and use G*Power (Faul et al., 2007): "F tests, Linear multiple regression: Fixed model, R² deviation from zero", effect size f² = .15 (medium; Cohen, 1988), α = .05, power = .80. With 3 predictors this gives 77; with 5 predictors, 92. Hair et al. (2022) present power tables built on the same logic.
Worked example
A model has six constructs. The outcome, Purchase Intention, receives arrows from five predictors. No construct is formative. A previous study in the same field reported a smallest significant path of .18, so the student uses .20 as a round, slightly optimistic figure, then checks a conservative one.
| Method | Calculation | Minimum n |
|---|---|---|
| 10-times rule | 10 × 5 arrows | 50 |
| G*Power | 5 predictors, f² = .15, α = .05, power = .80 | 92 |
| Inverse square root | (2.486 / .20)² = 154.5 | 155 |
| Inverse square root, conservative | (2.486 / .15)² = 274.7 | 275 |
The 10-times rule would suggest 50 respondents, a third of what the inverse square root method requires. The student plans for 155 usable responses as the minimum and aims for about 200 collected, to allow for incomplete and failed-attention-check responses. In the method chapter she writes:
The minimum sample size was estimated with the inverse square root method (Kock & Hadaya, 2018). Assuming a minimum path coefficient of .20, a 5% significance level and 80% power, at least 155 observations were required. The final sample of 214 exceeds this requirement.
Which one to report
Report the inverse square root method as your main justification, because it is designed for PLS-SEM and accounts for the size of the effects you want to detect. Add G*Power if your supervisor expects it. Mention the 10-times rule only to explain why you did not rely on it. And remember that a larger sample also helps with subgroup analyses and with stable bootstrap intervals.
Need real respondents? Genius Data recruits screened respondents for academic surveys (referral link — we may earn a commission).
Run it free
The free sample size calculator computes the inverse square root minimum, G*Power-equivalent regression samples and survey sample sizes, with the source for every formula. When your data are in, run the model with the PLS-SEM tool.
FAQ
Is 100 respondents enough for PLS-SEM?
Only if you expect paths of about .25 or larger: (2.486 / .25)² = 98.9, so 99. For paths of .20 you need 155.
Where do I get the minimum path coefficient?
From prior studies testing the same relationships, or choose a conservative .15 to .20 if you have no estimate.
Does the number of items affect sample size?
Not in these formulas, which concern structural paths. More items per construct do improve estimation stability.
Can I use the 10-times rule if my supervisor accepts it?
You can, but adding the inverse square root calculation protects you from examiners who know its weaknesses.
References
- Barclay, D., Higgins, C., & Thompson, R. (1995). The partial least squares (PLS) approach to causal modeling: Personal computer adoption and use as an illustration. Technology Studies, 2(2), 285–309.
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
- 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
- Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2022). A primer on partial least squares structural equation modeling (PLS-SEM) (3rd ed.). Sage.
- 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. https://doi.org/10.1111/isj.12131