How to Choose a Sample Size for a Student Survey

# How to Choose a Sample Size for a Student Survey

Deciding a defensible sample without a statistician, and saying honestly how you decided

A note before we start. No sources were supplied for this article, so nothing here is cited. Where a claim would normally carry a reference, I say so. Treat those claims as unsupported until you trace them to something you have read yourself.

You have a survey to run, a deadline, and no statistician on call. You need a sample size. You need to be able to defend it in a viva or a supervisor's office. And you need to write down how you arrived at it without pretending you did more than you did.

This guide walks through that process. It is written for final-year undergraduate and postgraduate students in Uganda running a first independent study. The method below is standard practice, not a specific finding from a specific paper. Where I state a convention, I say it is a convention.

Start with the question, not the formula

Most students open a textbook, find a sample size formula, and start plugging in numbers. That is backwards.

The sample size follows from four decisions you make first:

1. What are you measuring? A proportion (what share of students use mobile money) needs a different calculation from a mean (average monthly transport spending).
2. How precise does the answer need to be? A margin of error of ±5% is common in student work. ±10% is looser but sometimes acceptable. ±2% is usually beyond what an undergraduate survey can afford.
3. How confident do you need to be? 95% confidence is the near-universal convention. 90% appears in some exploratory work.
4. How big is the population, and can you list it? A survey of 200 students in one hall of residence is a different problem from a survey of 15,000 students across a university.

Answer these four in plain sentences before you touch a calculator. Those sentences become your methodology paragraph.

The formula most students use, and what it actually says

For a single proportion, the standard formula is:

n = Z² × p × (1 − p) / e²

Where:

• Z is the Z-score for your confidence level. At 95% confidence, Z = 1.96. This is a fixed value from the normal distribution, not a judgement call.
• p is your expected proportion. If you have no idea, use 0.5. This gives the largest sample size and is the safe default.
• e is your margin of error, expressed as a decimal. ±5% means e = 0.05.

Plug in the defaults — Z = 1.96, p = 0.5, e = 0.05 — and you get:

n = (1.96)² × 0.5 × 0.5 / (0.05)² = 384.16

Round up to 385.

That number, 385, appears in countless student proposals. It is not magic. It is the sample size you need to estimate a proportion within ±5 percentage points at 95% confidence, assuming maximum uncertainty about the answer and a population large enough that the population size barely matters.

If your margin of error is ±10%, the same formula gives 96. If it is ±7%, you get 196. The formula is sensitive to e because e is squared in the denominator.

When the population is small

The 385 figure assumes your population is large — tens of thousands or more. If you are surveying 300 students in one faculty, 385 is larger than your entire population. That is obviously wrong.

For finite populations, apply the correction:

n_adjusted = n / (1 + (n − 1) / N)

Where N is the population size.

If N = 300 and n = 385:

n_adjusted = 385 / (1 + 384/300) = 385 / 2.28 = 169

So you would need about 169 respondents from a population of 300. That is a meaningful reduction, and it is defensible.

If N is large — say 10,000 — the correction barely changes anything. 385 becomes 371. Many textbooks tell you to skip the correction when N is above 10,000. That is a reasonable convention.

What if you cannot list the population?

Many student surveys cannot. You do not have a register of all students who use a particular campus canteen, or all boda boda riders in a district, or all small business owners in a market.

When you cannot list the population, you cannot take a true probability sample. You are doing non-probability sampling — convenience, purposive, snowball, or quota. The formula above does not strictly apply, because it assumes random selection.

This is where honesty matters more than technique.

If you use convenience sampling, say so. Say that the sample size was chosen for practical reasons — time, access, cost — and that the results cannot be generalised to the whole population with a known margin of error. That is a limitation, not a failure. Supervisors respect it. What they do not respect is a student who applies a probability formula to a convenience sample and then writes as if the margin of error means something.

A defensible sentence: "Because no sampling frame was available, a convenience sample of 120 respondents was used. The sample size was determined by the number of students accessible during the two-week data collection period, not by a power calculation. Results should be read as indicative of this group only."

That sentence will survive a viva. A fake 385 will not.

Sample size for comparing groups

If your study compares two groups — male and female students, or two faculties — the calculation changes. You now need enough respondents in each group to detect a difference if one exists.

The formula for comparing two proportions is more involved and depends on:

• The difference you expect to find
• The power you want (80% is the usual convention)
• The significance level (usually 0.05)

A common rule of thumb is that you need roughly equal numbers in each group, and that detecting small differences requires much larger samples than detecting large ones. Rule-of-thumb figures circulate widely in this area. If you use one, present it as a convention you are following, not as a finding.

If your study is primarily descriptive — most student surveys are — you probably do not need a power calculation. Say that. "This study is descriptive and does not test a hypothesis about differences between groups, so a power calculation was not performed."

The response rate problem

Your calculated sample size is the number of completed, usable responses you need. It is not the number of people you contact.

If you expect a 60% response rate and you need 200 responses, you must contact about 333 people. If you expect 40%, you must contact 500.

Response rates vary enormously. They depend on how you distribute the survey, how long it is, whether there is an incentive, and whether you have any prior relationship with respondents. I cannot give you a reliable figure for your context. Ask your supervisor what response rates their previous students achieved. Ask classmates who have run surveys in the same population. Treat any number you have not verified as a guess, and write it as a guess.

A defensible sentence: "Assuming a response rate of 70%, based on the supervisor's estimate for similar surveys in this faculty, 280 questionnaires were distributed to obtain the target of 196 completed responses."

Writing the decision down

Your methodology section needs four things:

1. The target sample size, with the formula or reasoning that produced it.
2. The population and sampling frame, or an honest statement that no frame was available.
3. The sampling method, and whether it supports generalisation.
4. The expected response rate, and where that expectation came from.

Here is a template you can adapt. Replace the bracketed parts with your own details.

The target population was [group] in [place] during [time period]. A sample of [number] was calculated using the formula for a single proportion, assuming 95% confidence, a margin of error of [figure], and an expected proportion of 0.5. This gave a required sample of [number] completed responses. Because the population was estimated at [number], a finite population correction was applied, reducing the target to [number]. Assuming a response rate of [figure] based on [basis], [number] questionnaires were distributed. Sampling was [method]. [If non-probability: Because no sampling frame was available, results cannot be generalised beyond the sample.]

Every bracket is a place where you must know your own answer. Do not leave them for your supervisor to fill in.

What to do when you cannot defend the number

Sometimes you cannot. You have two weeks, one contact person, and a population you cannot count. You will collect whatever you can get.

In that case, do not dress it up. Write:

"The sample size was determined by practical constraints rather than a statistical calculation. [Number] responses were collected over [period]. This is a limitation of the study. Findings should be treated as exploratory and not generalised to the wider population."

That is a complete, honest, defensible methodology paragraph. It tells the reader exactly what they are looking at. It does not pretend to a precision you do not have.

Common mistakes

Using 385 without checking the population. If your population is 200, 385 is impossible. Apply the correction.

Confusing distributed with completed. If you distributed 400 and got 150 back, your sample size is 150, not 400.

Applying probability formulas to convenience samples. The formula assumes random selection. If you did not select randomly, the margin of error does not mean what the formula says it means.

Leaving the response rate unstated. If you do not say how many you distributed versus how many you got back, the reader cannot judge your sample.

Rounding down. Always round up. A sample of 384 when you need 384.16 is slightly under. Use 385.

A note on local requirements

Some departments and faculties in Uganda have their own minimum sample size expectations for student dissertations. Some supervisors will insist on 100 responses regardless of the calculation. Some will accept 50 for a qualitative-leaning study.

I do not know what your department requires. You should. Ask your supervisor before you finalise your methodology. If there is a departmental minimum, cite it as a departmental requirement, not as a statistical finding.

Similarly, whether you can obtain a student register or a list of members of a particular group depends on the institution and the gatekeeper. That access should be treated as unknown until someone confirms it. Do not assume a large public university will release a registration list to an undergraduate. Ask first.

The short version

1. Decide what you are measuring, your margin of error, and your confidence level.
2. Use n = Z² × p × (1 − p) / e² for a proportion. Defaults give 385.
3. Apply the finite population correction if your population is small.
4. If you cannot list the population, say so, and do not claim a margin of error.
5. Adjust for response rate when deciding how many to distribute.
6. Write down every assumption and where it came from.
7. If the number is not statistically defensible, say that plainly and call the study exploratory.

The goal is not a big number. The goal is a number you can explain, and an explanation that survives scrutiny.

Related reading on PassResearch:

• How to Write a Research Proposal: A Practical Guide for University Students in Uganda
• How to Write a Research Proposal Methodology Section: Justify Every Choice
• Clearer Academic Writing Without Losing Rigour
• How to Structure a University Dissertation, Chapter by Chapter
• Using AI in Academic Research Responsibly: Accuracy, Citations, Originality, and Academic Integrity

Reminder: No sources were supplied for this article. Nothing here is cited. Claims about statistical convention are marked as convention. Claims about local conditions are marked as unknown. If you use any figure from this article in your own work, trace it to a source you have read and cite that source, not this page.

Related reading

• How to Write a Research Proposal: A Practical Guide for University Students in Uganda
• How to Structure a University Dissertation, Chapter by Chapter
• Clearer Academic Writing Without Losing Rigour