Sample size calculator for your dissertation

How to use the sample size calculator

1. Choose your main analysis. The minimum sample size depends on the method you will report in your results chapter. If your study uses several methods, compute each and take the largest number.
2. Count the arrows on your model. For PLS-SEM, find the variable that receives the most arrows (usually the final dependent variable). For regression, it is the number of independent variables in your largest equation.
3. Keep the defaults unless you have a reason to change them: f² = 0.15, α = 5%, power = .80. These are the values most theses use and examiners expect.
4. Add an allowance for invalid responses (typically 10–20%) to see how many questionnaires to distribute, not just how many valid responses you need.
5. Paste the paragraph into the sample size section of your methods chapter and adjust the variable names.

Worked examples with real numbers

Regression and PLS-SEM: G*Power

The calculator solves the same problem as G*Power 3.1, “Linear multiple regression: Fixed model, R² deviation from zero” (Faul et al., 2009): the smallest n at which the F test reaches the target power for the chosen effect size f² (Cohen, 1988). With 3 arrows, f² = 0.15, α = 5% and power = .80, n = 77, the same figure G*Power returns; with 5 predictors, n = 92. The verification page compares 36 parameter combinations.

PLS-SEM: the inverse square root method

Kock and Hadaya (2018): n > ((z₁₋α + z₁₋β) / |p_min|)², where p_min is the smallest path coefficient you expect to be significant. With α = 5% (one-tailed) and power .80 the numerator is 1.645 + 0.842 ≈ 2.486, so for p_min = .20, n > (2.486 / 0.2)² ≈ 154.6: you need at least 155 responses. Hair et al. (2022) recommend this method for PLS-SEM, and their table computes each band at its upper bound: .05–.10 needs 619 observations, .11–.20 needs 155, .21–.30 needs 69 and .31–.40 needs 39 (α 5%, power .80). The older 10-times rule is shown only as a cross-check because it often gives samples that are too small.

CB-SEM / CFA (AMOS, lavaan)

Hair et al. (2010) set minimums by model complexity: 100 for five or fewer constructs, each with more than three indicators and communalities of .6 or higher; 150 for seven or fewer constructs with modest communalities (about .5) and no construct under three indicators; 300 when communalities are below .45 or a construct has fewer than three indicators; 500 for models with many constructs. The cross-check is an RMSEA-based power analysis (MacCallum et al., 1996) for the test of close fit (H₀: ε = .05, Hₐ: ε = .08): df = 10 needs 782 observations and df = 100 needs 132, matching Table 4 of the original article.

Moderation, mediation and multigroup analysis

Interaction effects are usually tiny (median f² = 0.002 in Aguinis et al., 2005), so the default is f² = 0.02: X, M and X × M (3 predictors, 1 tested) need 395 observations, against 77 for the whole model at f² = 0.15. For mediation, the calculator looks up the simulation table of Fritz and MacKinnon (2007): with a = b = .26 and a percentile bootstrap you need 162 observations; with a = b = .14, 558. In a multigroup analysis each group must reach the model's minimum (Matthews, 2017): comparing men and women on a model that needs 92 means at least 2 × 92 = 184.

Group tests, correlation and Cochran's formula

Computed as in G*Power 3 (Faul et al., 2007) with Cohen's (1988) conventions: an independent-samples t test with d = 0.5 needs 64 per group; a one-way ANOVA with 3 groups and f = 0.25 needs 159; a 2 × 2 χ² test with w = 0.3 needs 88; a correlation of r = .30 needs 85 by the Fisher z approximation (G*Power's exact method gives 84). For a proportion, Cochran's (1977) n₀ = z²·p(1 − p)/e² gives 384.16 at 95% confidence, a 5% margin and p = 50%, rounded up to 385; with a known population of N = 2,000 the finite population correction gives 323. The Krejcie and Morgan (1970) table is this same formula: N = 1,000 gives 278 and N = 10,000 gives 370.

How to read the result

• The minimum sample size is the number of valid responses after screening, not the number distributed. With a 15% allowance you need n / 0.85 questionnaires (155 valid responses means about 183 collected).
• The cross-checks panel lists other criteria. Tick the box at the bottom of the form and the larger number is used for both the headline figure and the paragraph, with a sentence stating that the sample meets both criteria.
• The paragraph clears when an input is invalid, so you never copy an outdated figure.

How to report sample size in APA 7

State the method, the effect size, α and power, the software and the result. For example: “The minimum sample size was determined by power analysis in G*Power 3.1 (Faul et al., 2009), using the F test for multiple linear regression with 5 predictors, f² = 0.15 (a medium effect; Cohen, 1988), α = .05 and power = .80. The minimum sample size was 92.” The calculator writes this for your chosen method and adds the reference list.

Frequently asked questions

Which f² should I choose?

Cohen (1992) defines 0.02 as small, 0.15 as medium and 0.35 as large. Without prior studies to estimate it, use 0.15. Choosing 0.35 gives a very small sample that is hard to defend in a viva.

For PLS-SEM, should I report G*Power or the inverse square root method?

Report both and use the larger number. The inverse square root method is tied directly to the path coefficients in your model, and reviewers and examiners increasingly ask for it.

My survey uses PLS-SEM: Cochran, Slovin or G*Power?

Use the method tied to the analysis you report: G*Power and the inverse square root method for PLS-SEM, Hair et al. (2010) for CB-SEM. Cochran, Slovin and Krejcie & Morgan answer a different question (how many people are needed to estimate a population proportion with a given margin of error) and hold only under random sampling.

When should I enter the population size N?

Only when you know N exactly and sample at random from that list, for example the 1,200 employees of one company. The finite population correction reduces the sample noticeably only when n₀ is about 5% or more of the population; for a broad population such as “mobile wallet users”, leave it blank.

Should I use Slovin's formula?

Slovin ignores the confidence level and the proportion p, so it suits only rough proportion estimates. Studies that test a model should rely on power analysis or the method-specific rules above.

References

• Aguinis, H., Beaty, J. C., Boik, R. J., & Pierce, C. A. (2005). Effect size and power in assessing moderating effects of categorical variables using multiple regression: A 30-year review. Journal of Applied Psychology, 90(1), 94–107. https://doi.org/10.1037/0021-9010.90.1.94
• Cochran, W. G. (1977). Sampling techniques (3rd ed.). John Wiley & Sons.
• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
• Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155–159. https://doi.org/10.1037/0033-2909.112.1.155
• 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
• Faul, F., Erdfelder, E., Buchner, A., & Lang, A.-G. (2009). Statistical power analyses using G*Power 3.1: Tests for correlation and regression analyses. Behavior Research Methods, 41(4), 1149–1160. https://doi.org/10.3758/BRM.41.4.1149
• Fritz, M. S., & MacKinnon, D. P. (2007). Required sample size to detect the mediated effect. Psychological Science, 18(3), 233–239. https://doi.org/10.1111/j.1467-9280.2007.01882.x
• Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate data analysis (7th ed.). Pearson Prentice Hall.
• 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
• Krejcie, R. V., & Morgan, D. W. (1970). Determining sample size for research activities. Educational and Psychological Measurement, 30(3), 607–610. https://doi.org/10.1177/001316447003000308
• 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
• Matthews, L. (2017). Applying multigroup analysis in PLS-SEM: A step-by-step process. In H. Latan & R. Noonan (Eds.), Partial least squares path modeling (pp. 219–243). Springer. https://doi.org/10.1007/978-3-319-64069-3_10