Sample size for a thesis: formula and examples
Calculate and justify the sample size of your thesis: Cochran's formula, finite population correction, minimum for regression and PLS-SEM, sampling methods.
Data Académique
10/13/20264 min read
"How many people do I need to survey?" This question comes up sooner or later in every thesis, and juries often ask it at the defense. The answer depends on your population, the precision you want and the type of analysis. Here is how to calculate and justify your sample size, with the most widely used formula and worked examples.
In short: for a large population, Cochran's formula gives 384 respondents with a 5% margin of error and a 95% confidence level. If the population is known and limited, a correction reduces this number. In practice, the size also depends on the planned analysis and the resources available, and any limitation must be justified in the methodology.
Population and sample: definitions
The population is the set of people concerned by your study (for example, the 1,000 bachelor's students enrolled in your faculty).
The sample is the part of this population you actually survey.
The larger and better chosen the sample, the more precise your results and the more they can be generalized to the population.
Cochran's formula
To estimate a proportion (the most common case with a questionnaire), use:
n = Z² × p × (1 − p) / e²
Z = 1.96 for a 95% confidence level;
p = the expected proportion. If you do not know it, use 0.5: it is the most cautious case and gives the largest sample;
e = the accepted margin of error (often 5%, i.e. 0.05).
With these values: n = 1.96² × 0.5 × 0.5 / 0.05² = 384.16, i.e. 385 people (always round up). This is the famous "384" seen in many theses, valid for a large population.
Correcting for a known, limited population
If your population is small and known (the nurses of a hospital, the employees of a company), apply the finite population correction: adjusted n = n / (1 + (n − 1) / N), where N is the population size.
With a 5% margin of error and 95% confidence, here is the required sample by population size:
N = 100: 80 respondents
N = 200: 132 respondents
N = 300: 169 respondents
N = 500: 218 respondents
N = 1,000: 278 respondents
N = 2,000: 323 respondents
N = 5,000: 357 respondents
N = 10,000: 370 respondents
Very large population: 385 respondents
These values are very close to the Krejcie and Morgan (1970) table, which you can also cite.
What if I cannot reach this number?
This is common, especially in a bachelor's thesis with little time. You have three honest options:
Accept a larger margin of error: 196 respondents for 7%, 97 for 10% (large population). State it clearly.
Reduce the population: one faculty instead of the whole university, one department instead of the whole hospital.
Present the limitation in the discussion: a smaller sample reduces generalization without making the study useless.
Also plan 10 to 20% extra responses to compensate for incomplete questionnaires.
Advanced analyses
Cochran's formula is for estimating a proportion. Other analyses have other benchmarks:
Multiple regression: a frequently cited rule is 50 + 8 × (number of explanatory variables) (Tabachnick & Fidell).
Factor analysis: at least 100 to 200 respondents, or 5 to 10 respondents per item.
SmartPLS (PLS-SEM): see our guide SmartPLS for beginners.
Group comparisons (t-test, ANOVA, chi-square): a power analysis with the free G-Power software is the most rigorous method.
Sampling: how to choose respondents
Simple random: everyone has the same chance of being selected (ideal, but requires a complete list).
Stratified: you respect the distribution of the population (by program, by department…).
Convenience: you survey people who are accessible. Very common in theses, but less representative: say so in the limitations.
Snowball: respondents share the questionnaire with others. Useful for hard-to-reach populations.
How to write it in the methodology
"The study population includes 1,000 students. The sample size was calculated with Cochran's formula, with a 95% confidence level, a 5% margin of error and a proportion of 0.5, then corrected for a finite population, giving a minimum of 278 respondents. Stratified sampling by program was used."
The complete data analysis path
For a questionnaire-based thesis, the steps follow this order:
cross categorical variables with the chi-square test;
test the effect of several variables with linear regression;
for models with latent variables: SmartPLS and PLS-SEM.
Does your model include several latent variables? Our SmartPLS (PLS-SEM) course shows you how to test it, even with a small sample.
You can also run this calculation in a spreadsheet: see our Excel course for data analysis.
Frequently asked questions
What is the minimum number of respondents for a thesis?
There is no universal minimum. What matters is justifying your choice. Also ask your supervisor whether they expect a minimum.
Should I calculate a sample size for a qualitative study?
No. In qualitative research we talk about data saturation: you stop interviewing when interviews no longer bring new information (often 10 to 20 interviews in a thesis).
Do I need more respondents for a regression?
Yes, the size also depends on the number of variables. A frequently cited rule for multiple regression recommends at least 50 + 8 × k respondents, k being the number of explanatory variables. See linear regression in SPSS.
Need help with your methodology?
Data Académique calculates and justifies your sample size with you, builds the data collection strategy and carries out the statistical analysis. Discover our thesis support or message us on WhatsApp.
