To calculate sample size for a survey-based final year project, first define who belongs to your population, how you will select participants, and how much error you can tolerate. Agree a design-appropriate justification; the proportion-estimation calculations below are examples, not an exhaustive choice of methods. Writing "Taro Yamane was used" in Chapter 3 without showing the population, the inputs and the arithmetic does not justify your sample, and it leaves the sample choice unexplained.
Your calculation needs a clear explanation of the population, assumptions and actual response count. UniDraft helps organise those confirmed decisions and results into an editable project document. Start your project write-up using the final-year project workflow. You still choose and verify the calculation with the appropriate methods adviser; UniDraft does not execute statistics.
The short answer
- Finite-population proportion-estimation example, subject to design assumptions: Taro Yamane,
n = N / (1 + N × e²). With N = 500 and e = 0.05, you need 223 completed responses. - Large-population proportion example under suitable sampling assumptions: Cochran's
n₀ = z² × p × (1 − p) / e². At 95% confidence, 5% error and p = 0.5, that is 385. - Finite-population proportion estimate, with suitable sampling assumptions: Cochran with the finite population correction, or the Krejcie-Morgan table. For N = 500 these give 218 and 217.
- Always: round up, name the source of N, and report the number of responses you actually got in Chapter 4.
Step 1: Define the population and its source
"Students in Nigeria" is not a usable population for a one-department survey. "All 500 registered final-year students in the Faculty of Education during the 2025/2026 session, according to the faculty office register" is defined well enough to verify and sample. State where the count came from and its date. If you do not have a reliable count, do not invent one to make a formula work; treat the population as unknown and say so.
These are survey proportion-estimation examples under suitable probability-sampling assumptions. They do not automatically cover clustered or weighted designs, group comparisons, response bias or measurement error.
The population also has to match your research questions. If your questions concern students who used a particular service, "all registered students" may be the wrong denominator; settle the inclusion and exclusion criteria first. If you have not yet pinned down your research questions and objectives, do that before any calculation, because they decide who you must ask.
Step 2: Understand the three inputs
The proportion-estimation formulas discussed here use these inputs; other study aims need different calculations:
- N, the population size (if known).
- Confidence level, chosen for the study. For a normal-approximation calculation, 95% corresponds to z = 1.96 (about 2).
- Margin of error, e, written as a decimal: 0.05 means ±5 percentage points; 0.10 means ±10.
- p, the expected proportion giving a particular answer. When you do not know it, use 0.5, which gives the largest sample under this binary-proportion calculation.
Smaller e means a larger sample. Halving the margin of error roughly quadruples the sample needed, but the choice should follow the needed precision and design, not simply the workload.
Step 3: Taro Yamane, worked step by step
Yamane's simplified formula (from his 1967 textbook Statistics: An Introductory Analysis) is widely taught for finite populations. Agricultural extension guidance from the University of Florida gives it as n = N / (1 + N(e)²) and notes that it assumes 95% confidence and P = 0.5 (see Sources).
For this fictional calculation, suppose a verified register lists N = 500 eligible students and your approved plan uses e = 0.05:
e² = 0.05 × 0.05 = 0.0025
N × e² = 500 × 0.0025 = 1.25
1 + N e² = 1 + 1.25 = 2.25
n = 500 / 2.25 = 222.22...
Round up to 223 completed responses. Rounding down to 222 would put you below the target.
Two more checks show how e changes the answer. With e = 0.10: 500 / (1 + 500 × 0.01) = 500 / 6 = 83.33, so 84. With N = 300 and e = 0.05: 300 / (1 + 300 × 0.0025) = 300 / 1.75 = 171.43, so 172.
Yamane is popular because it needs only N and e. Its weakness is that it hides its assumptions (95% confidence, p = 0.5), so state them in your text.
Step 4: Cochran's formula, with and without correction
Cochran's formula for a proportion is n₀ = z² × p × (1 − p) / e². For a large or unknown population at 95% confidence, e = 0.05 and p = 0.5:
z² = 1.96 × 1.96 = 3.8416
p(1 − p) = 0.5 × 0.5 = 0.25
n₀ = 3.8416 × 0.25 / 0.0025
= 0.9604 / 0.0025 = 384.16
Round up to 385. This is the well-known "385" in questionnaire studies of large populations.
If your population is known and small relative to 385, apply the finite population correction: n = n₀ / (1 + (n₀ − 1) / N). For N = 500:
(n₀ − 1) / N = 383.16 / 500 = 0.76632
1 + 0.76632 = 1.76632
n = 384.16 / 1.76632 = 217.49...
Round up to 218. Notice that this is close to Yamane's 223, but a little lower.
If you have evidence that the proportion is not 50%, for example from a pilot, you can use it: with p = 0.3, n₀ = 3.8416 × 0.21 / 0.0025 = 322.69, so 323. Without evidence, keep p = 0.5 rather than picking a convenient value.
Step 5: The Krejcie-Morgan table
Krejcie and Morgan (1970) published a table of sample sizes for given populations, computed from a chi-square-based formula at 95% confidence and a 0.05 margin of error: s = X²NP(1 − P) / (d²(N − 1) + X²P(1 − P)), with X² = 3.841 and P = 0.5. For N = 500:
numerator = 3.841 × 500 × 0.25 = 480.125
denominator = 0.0025 × 499 + 3.841 × 0.25
= 1.2475 + 0.96025 = 2.20775
s = 480.125 / 2.20775 = 217.47
The published table lists 217 for N = 500 (they tabulated to the nearest whole number). If your supervisor expects "round up", write 218 and explain, or cite the table value; do not switch silently between them. Because the table is ready-made, many students cite it directly and show only the lookup. That is acceptable when your supervisor agrees, but you still must state N and the confidence level.
Which method should you use?
| Situation | Sensible choice |
|---|---|
| Department names a formula | Confirm it fits the design, clarify conflicts with your adviser and show the working |
| Finite-population binary proportion with appropriate probability sampling | Evaluate Yamane or a finite-population calculation under the stated assumptions |
| Large-population binary proportion with appropriate sampling | Cochran under chosen confidence, precision and p inputs; 385 only for the worked inputs |
| Wanting a proportion other than 0.5 justified | Cochran, with p from a pilot or published study |
| Comparing groups or testing an effect | Power analysis (see below) |
| Interviews or focus groups | Justify for your qualitative approach, information needs and analysis plan, not a survey formula |
Your department may require a particular method; your supervisor and methodology guidance take priority over this article. If the method is unfamiliar, consult your supervisor or a statistician before collecting data rather than retrofitting a formula afterwards.
Completed responses are not invitations
If you need 223 completed questionnaires and reasonably expect an 80% return rate, a planning estimate is 223 / 0.80 = 278.75, so 279 questionnaires distributed. For the Cochran figure, 218 / 0.80 = 272.5, so 273. This is an estimate, not a guarantee: ineligible respondents and half-filled forms can still shrink the usable count. Keep four numbers distinct in your report: the calculated target, the number distributed, the number returned, and the number analysed.
Never write that 223 students responded because your formula produced 223. Chapter 4 must report what you obtained. If you fall short, report it and assess the implications with the actual design, selection and non-response in mind. Shortfalls are common and honest disclosure is easier to defend than a claim the panel can check against your data. See how to write Chapter 4 for reporting response rates.
Sampling is more than a number
A sample size tells you how many; your sampling method tells you whether the numbers mean anything.
- Simple random sampling: every eligible student on the list has an equal chance; use a random number generator on the register.
- Stratified sampling: split the population by department, level or gender, then sample within each group. Proportional allocation for N = 500 and n = 223 across four departments of 200, 150, 100 and 50 students gives 89.2, 66.9, 44.6 and 22.3, rounded to 89, 67, 45 and 22 (total 223).
- Convenience sampling: whoever is available. The formula does not repair this. State it as a limitation and avoid claiming the results represent all students.
If your questionnaire is still a draft, the questionnaire design guide covers the instrument this sample will answer, and validity and reliability covers pilot testing, which can also supply your p.
When a survey formula is the wrong tool
- Very small, accessible population. If only 40 students qualify, try to study all of them (a census). No formula is needed; the formulas give near-N answers anyway (Yamane for N = 40 gives 36).
- Comparing groups or testing a treatment. These need a power analysis based on the expected effect size, not a survey shortcut. The choice of test also affects it, so read which statistical test fits your project early.
- Qualitative interviews. Agree a qualitative sampling rationale appropriate to your approach, scope and analysis. Saturation is relevant in some approaches, but is not a universal stopping rule for every qualitative study.
- Very large populations. Above roughly 100,000 the answer barely changes: Cochran stays near 385.
A model Chapter 3 paragraph (illustrative)
The wording below is an example of structure, not text to copy; every number must be replaced with your own verified figures.
The target population comprised 500 final-year students registered in the Faculty of Education for the 2025/2026 session, as recorded in the faculty office register dated 12 January 2026. The sample size was determined using Yamane's formula, n = N / (1 + N e²), at a 95% confidence level and a 5% margin of error. Substituting N = 500 and e = 0.05 gave n = 222.22, rounded up to 223. Allowing for an expected 80% return rate, 279 questionnaires were distributed, allocated proportionally across four departments using stratified random sampling from the register.
Notice what it does: it names the source and date of N, states the assumptions, shows the substitution, and separates the target from the distribution plan. The return rate and the number analysed then belong in Chapter 4, where you report them as facts.
Planning the fieldwork around your number
A sample of 223 is a workload as well as a statistic. Before you commit to a margin of error, work out whether you can realistically reach that many people in the time you have. A few practical points:
- Check access early. If the faculty office cannot release a register, ask your supervisor to confirm an alternative source of N before you design the rest of the study.
- Budget the follow-up. Printing, transport and repeated visits to lecture halls or hostels cost time and Naira. Online forms reduce cost but can skew who responds, which you must note as a limitation.
- Pilot first. Agree a pilot purpose and size with your methods adviser. A small pilot can reveal instrument problems but may give an unstable estimate of p; do not reduce the main sample on that basis without justification.
- Tell your supervisor about a trade-off. Moving from e = 0.05 to e = 0.10 cuts the Yamane sample for N = 500 from 223 to 84, but it widens your uncertainty. Get that agreed in writing, ideally in your project proposal, so nobody is surprised at the defence.
If you are still choosing what to study, the free topic generator can help you find a topic where a reachable, well-defined population exists. A topic that needs an unlistable population, such as "all Nigerian graduates", will make every step in this article harder.
Common mistakes supervisors flag
- No source for N. "The population is 500" with no register or date.
- Formula pasted, no working. Show every input and step.
- Using Yamane for an experiment. It is a survey shortcut.
- Rounding down. 222.22 becomes 223.
- Reporting target as achieved. Chapter 4 numbers must match the returned forms.
- Changing e without saying why. If you use 10% to reduce workload, say so and accept the wider margin.
- Ignoring the sampling method. A number without a selection procedure.
These are also the questions that come up at a defence; the common defence questions post shows how panels probe methodology.
A Chapter 3 checklist
- Target population, its source, and the date of the count.
- Sampling frame and inclusion and exclusion criteria.
- Selection method (random, stratified, and so on) and how it was carried out.
- The chosen method, every input (N, confidence level, e, p) and the arithmetic.
- Allowance for non-response, and the planned number of questionnaires.
- Citation of the source for the formula.
The rest of the chapter sits within the wider methodology chapter. The formula's source belongs in your references; the citation finder helps you find real, checkable sources, and the references guide covers the format.
Where UniDraft fits in
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Pair the number with a selection plan
The calculation answers “how many?”, not “who gets selected?”. Use the sampling-techniques guide to document the frame, selection procedure and non-response plan. A public questionnaire link does not become a probability sample because you reached the calculated number. Keep the planned invitations, actual responses and final analysis count separate, and explain any shortfall honestly.
Sources
- Determining Sample Size for Research Activities, Krejcie and Morgan (1970), Educational and Psychological Measurement 30(3), 607-610 (Crossref bibliographic record; the DOI is 10.1177/001316447003000308, and the publisher page may block automated access)
- Determining Sample Size, University of Florida IFAS Extension (PD006): gives Yamane's formula, Cochran's formula and the finite population correction.