How Many People Do You Need to Survey? Sample Size, Worked Through

In short

For a national survey, roughly 1,000 completed interviews gives a margin of error near plus or minus 3 percentage points at 95% confidence. About 1,500 takes you to roughly 2.5 points, and 2,400 to roughly 2 points. The returns flatten fast, which is why doubling a sample rarely doubles what you learn.

Population size barely matters once you are past a few thousand people. A national sample for Nigeria is not meaningfully larger than a national sample for Ghana, and both are smaller than most people expect.

What actually drives sample size is the breakdowns you intend to report separately. Every subgroup you plan to quote, each state, each age band, each segment, needs its own usable sample underneath it. Most studies that look expensive are expensive because of the reporting cuts, not the headline number.

The formula, and what each part is doing

For a large population, the sample size needed for a proportion is:

n = z² × p(1−p) / e²

Where z is the score for your confidence level, 1.96 for 95%. p is the proportion you expect, and e is the margin of error you want, as a decimal.

The one choice people get wrong is p. If you have no idea what the answer will be, use 0.5, because p(1−p) is at its maximum there. That gives you the most conservative, largest sample, and it is the right default. If you genuinely know a proportion will be small, say 10% of households own a particular appliance, using 0.1 reduces the sample needed considerably, but only use that where you have grounds.

Worked at 95% confidence, p = 0.5, e = 0.03:

n = 1.96² × 0.25 / 0.0009 = 1,067

That is where the familiar "about a thousand" comes from.

Why population size hardly matters

This is the single most counter-intuitive thing in survey sampling, and the hardest to explain to a client.

A properly drawn sample of 1,000 gives you about the same precision whether the population is 200,000 or 200 million. There is a finite population correction, but it only bites when your sample is a large fraction of the whole population, which almost never happens outside small institutional surveys.

So the question "Nigeria has over 200 million people, surely we need tens of thousands?" has a genuine answer: no, and the reason is that precision depends on how many people you asked, not on how many you did not ask.

Sample size at a glance

At 95% confidence, p = 0.5, large population:

Note the shape. Going from 400 to 1,000 buys you nearly two points of precision. Going from 2,400 to 10,000 buys you one. The fourth thousand costs the same as the first and delivers a fraction of the value.

The thing that actually drives cost: subgroups

Here is where briefs go wrong.

A national sample of 1,000 gives a national figure at ±3 points. It does not give you a usable figure for each of the six geopolitical zones, because once you divide 1,000 by six you have roughly 167 per zone, and 167 carries a margin of error around ±7.6 points. Two zones could differ by seven points and you would not be able to say they differ at all.

If you need each zone readable at ±5 points, you need roughly 400 per zone, so 2,400 nationally. If you need all 36 states and the FCT readable at even ±7 points, you are looking at roughly 200 per state, which is about 7,400 interviews, and the study is a different size of project entirely.

So the useful question is never "how big should the sample be". It is "what will you want to say separately, and about whom". Answer that and the sample size calculates itself.

The reporting cut nobody budgets for

The classic overrun is a brief that asks for a national read, and then in the analysis meeting someone wants the figure for women aged 18 to 34 in the North West. If that cut was not designed in, the base will be forty people and the honest answer is that the data cannot support the claim.

Decide these before fieldwork. Afterwards is too late, and the pressure to quote an unreliable base is exactly how research gets into trouble.

Margin of error, read properly

A margin of error of ±3 points at 95% confidence means: if you repeated this survey many times with the same method, 95 times in 100 the result would fall within 3 points of what you got.

Three things it does not mean.

It is not a measure of how right you are. It describes sampling variability only. It says nothing about a badly worded question, a sample frame that misses people, or respondents who were not candid.

It applies to the whole sample, not to every number in the report. Each subgroup has its own, wider, margin.

Comparisons need more care than single figures. If two groups each carry ±3 points, a four-point gap between them is not automatically significant. Testing the difference is a different calculation from reporting each figure.

Design effect

Most real surveys do not draw a simple random sample. They cluster, by community or enumeration area, because sending interviewers to geographically scattered individuals is prohibitively expensive, and they weight afterwards to correct imbalances.

Both reduce effective precision. The design effect quantifies it, and an effective sample size is the achieved sample divided by that factor. A design effect of 1.5 means 1,500 interviews behave statistically like 1,000.

Any serious quote should tell you whether a margin of error is calculated on the raw sample or the effective one. Where we cluster, we report the design effect rather than quoting a margin of error that assumes we did not.

Non-response, and the number that actually matters

You do not get a completed interview from everyone you approach. Plan on the completion rate from the outset, because the number that matters is completed interviews, not contacts attempted.

Completion rates vary enormously by mode. A short SMS survey may convert in low single digits. A telephone interview with a warm panel converts far better. In-person fieldwork converts best of all and costs the most.

Two consequences. Your fieldwork plan needs a contact target well above the sample target. And the people who do not respond are rarely a random slice of those who do, which is a bias no sample size fixes. That is why mode matters: a study run only on digital channels misses rural, older and lower-income respondents systematically, and adding more interviews on the same channel makes the result more precise without making it more accurate.

Precision is not accuracy. A larger sample drawn the wrong way gives you a tighter confidence interval around the wrong number.

How to size a study, in practice

1. List what you will report separately. Zones, states, age bands, customer segments, anything that will appear as its own row.
2. Set the precision each cut needs. A headline might need ±3. A regional breakdown might be fine at ±6.
3. Work the base for each cut, then the total.
4. Apply the design effect if the sample will be clustered.
5. Divide by the expected completion rate to get the contact target.
6. Check it against the budget, and if it does not fit, cut the number of separate cuts rather than the precision of the headline. Fewer well-powered findings beat many unreliable ones.

A worked example

A consumer brand wants to understand purchase intent in Nigeria, with results readable nationally and for each of the six geopolitical zones, and separately for under-35s.

• Zones readable at ±5 points: about 400 per zone, so 2,400 national.
• Under-35s as a cut: they are a large share of the Nigerian population, so a 2,400 sample will already contain well over 1,000 of them. No uplift needed.
• Clustered in-person fieldwork in part of the sample, design effect around 1.4: effective sample is roughly 1,700, so the national figure lands near ±2.4 points. Still comfortable.
• Expected completion across modes around 25%: contact target roughly 9,600.

The brief said "about a thousand should be enough". The zone requirement, which nobody mentioned at first, is what made it 2,400.

Related reading

• Writing survey questions that work
• Likert scales explained
• What we can field, and how
• Talk to us about a study

Frequently asked questions

How do you calculate sample size for a survey?

For a proportion in a large population, n = z² × p(1−p) / e², where z is 1.96 for 95% confidence, p is the expected proportion and e is the margin of error as a decimal. Use p = 0.5 when you do not know what to expect, because it produces the most conservative sample size. At 95% confidence with a ±3 point margin that gives about 1,067 completed interviews.

How many people do I need to survey for a national study?

Around 1,000 completed interviews gives a national figure at roughly ±3 percentage points, 1,500 gives ±2.5 and 2,400 gives ±2. The headline number is rarely what decides it. If you need results reported separately by zone, state or segment, each of those needs its own usable base and the total rises accordingly.

Does the population size affect sample size?

Barely, once the population is more than a few thousand. A sample of 1,000 gives roughly the same precision whether the population is 200,000 or 200 million, because precision depends on how many people you asked rather than how many you did not. A finite population correction exists but only matters when your sample is a large fraction of the whole population.

What does a margin of error of plus or minus 3 mean?

It means that if the same survey were repeated many times with the same method, 95 times in 100 the result would fall within 3 percentage points of the figure obtained. It describes sampling variability only. It says nothing about question wording, coverage of the sample frame, or whether respondents answered candidly, and it applies to the full sample rather than to every subgroup in the report.

How big a sample do I need for each state in Nigeria?

If you want all 36 states and the FCT readable at roughly ±7 points, you need about 200 completed interviews per state, which is around 7,400 nationally. At ±5 points per state it is closer to 400 each. State-level reporting is the single biggest driver of cost in Nigerian survey research and should be settled before anything else.

What is a design effect and why does it matter?

Most real surveys cluster respondents geographically and weight the data afterwards, and both reduce statistical efficiency. The design effect quantifies that loss: a design effect of 1.5 means 1,500 interviews behave like 1,000. Margins of error should be calculated on the effective sample size rather than the raw count, and any quote should say which was used.

Is a bigger sample always better?

No. Returns flatten quickly, and precision is not the same as accuracy. A larger sample drawn through a channel that systematically misses rural, older or lower-income respondents produces a tighter confidence interval around a biased number. Spending the extra budget on reaching harder-to-reach respondents usually buys more than spending it on additional interviews with easy ones.

How does non-response affect sample size?

You must plan for the completion rate, because the figure that matters is completed interviews rather than contacts attempted. Completion varies sharply by mode, from low single digits on cold SMS to much higher on in-person fieldwork. People who do not respond are also rarely a random slice of those who do, which is a bias that no increase in sample size corrects.