There is no single number: the sample you need depends on your main analysis. For a medium effect at α = .05 and 80% power, Cohen (1992) gives 85 respondents for a correlation, 64 per group for a t-test, and 91 for a multiple regression with five predictors; PLS-SEM needs about 155 to detect a path of .20 (Kock & Hadaya, 2018). If your aim is to estimate a population percentage within ±5 percentage points, you need about 385 (Cochran, 1977). Work out the number for your analysis, then add a margin for unusable responses.
Why "100" or "200" is not an answer
Students often hear round numbers from friends or forums. Examiners in the UK, Australia, Europe and elsewhere generally do not look for a magic number; they look for a justification. Master's dissertation handbooks at UK and Australian universities typically ask you to explain how your sample size fits your design rather than set a fixed minimum. A power analysis does exactly that: it shows that your sample is large enough to detect the effect you are testing with a stated probability.
Power-based minimums for common analyses
All figures below assume α = .05 (two-tailed), power = .80 and a medium effect, from Cohen (1992):
| Main analysis | Medium effect | Minimum N |
|---|---|---|
| Correlation | r = .30 | 85 |
| Independent t-test | d = 0.50 | 64 per group (128) |
| One-way ANOVA, 3 groups | f = .25 | 52 per group (156) |
| Multiple regression, 3 predictors | f² = .15 | 76 |
| Multiple regression, 5 predictors | f² = .15 | 91 |
| PLS-SEM, minimum path .20 | Inverse square root method | 155 (Kock & Hadaya, 2018) |
If you expect a small effect, numbers grow quickly: a correlation of .10 needs 783 (Cohen, 1992). If your study is descriptive, for instance estimating the share of students who use a service, use Cochran's (1977) formula: n = z² × p(1 − p) / e² = 1.96² × .5 × .5 / .05² = 384.2, so 385. For small populations, apply the finite population correction or the table of Krejcie and Morgan (1970), which gives 384 for very large populations.
Worked example: a UK master's dissertation
A management student plans an online survey testing how workload, autonomy and supervisor support predict job satisfaction. The main analysis is a multiple regression with three predictors. From Cohen (1992), a medium effect needs 76 respondents; G*Power (Faul et al., 2007) gives 77 for the same settings, the difference being rounding. Past studies suggest the effects are medium, so 77 is the minimum usable sample.
She expects about 20% of responses to be incomplete or to fail an attention check, so she aims to collect 77 / .80 = 96.3, about 100 responses. Her method chapter reads:
An a priori power analysis in G*Power 3 (Faul et al., 2007) for multiple regression with three predictors, a medium effect (f² = .15; Cohen, 1988), α = .05 and power = .80 indicated a minimum of 77 participants. Allowing for 20% unusable responses, the target was 100. The final usable sample was 112.
If she later adds a mediator and switches to PLS-SEM, the target rises to 155 usable responses for a minimum path of .20 (Kock & Hadaya, 2018). Deciding the analysis first avoids that surprise in the middle of data collection.
If you cannot reach the target
- Report a sensitivity analysis: the smallest effect your final sample could detect with 80% power.
- Simplify the model: fewer predictors or groups lower the requirement.
- Discuss limited power openly in the limitations section, especially for non-significant results.
- Do not inflate the sample with unscreened responses; low-quality data weaken every analysis.
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The free sample size calculator covers Cochran, Krejcie and Morgan, regression power and the PLS-SEM inverse square root method, and writes the justification paragraph with references. For a ready-made questionnaire workflow, see the survey kit.
FAQ
Is 100 respondents enough for a master's dissertation?
Often, yes, for a correlation or a regression with up to about six predictors and medium effects (Cohen, 1992). Not for PLS-SEM with small paths.
Do I need 385 respondents?
Only if you are estimating a population proportion to ±5 points. Most dissertations test relationships, which uses power analysis instead.
What response rate should I assume?
Base it on your channel and on similar studies; for planning, assume a share of incomplete and inattentive responses and collect extra.
Does a convenience sample need the same size?
Power calculations apply regardless of sampling method, but a convenience sample limits generalisation however large it is.
References
- Cochran, W. G. (1977). Sampling techniques (3rd ed.). Wiley.
- 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
- 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