The headline problem is this: the Taro Yamane formula that every Nigerian agriculture department expects you to use requires a finite population size, N, and for farmers in a given local government area, no register exists that anyone can hand you on request. Students solve this by writing a round number into Chapter Three and hoping nobody asks. Panels ask.
This piece does two things. First, it names the five sources a Nigerian student can actually cite for a farming population figure, with the vintage of each one stated plainly, because several of the official figures are older than the students using them. Second, it works the calculation through from that figure to a defended, allocated sample.
The five sources you can cite, and how current each one is
| Source | What it gives you | Level of detail | Vintage caution |
|---|---|---|---|
| National Agricultural Sample Census (NBS, with FAO support) | Counts of agricultural households and holdings | National and state | Nigeria’s agricultural census exercises are infrequent; check the publication year on the report you cite and state it |
| General Household Survey — Panel (NBS, with World Bank LSMS) | Proportion of households engaged in agriculture | National and zonal, not LGA | Runs in waves; cite the wave and its reference year |
| State Agricultural Development Programme (ADP) registers | Registered farmers by block, cell and extension zone | LGA and below — the most useful level | Registers count registered farmers only, not all farmers |
| FADAMA and other intervention beneficiary lists | Named beneficiaries by community | Community level | Covers a scheme population, never the whole farming population |
| LGA Department of Agriculture and cooperative unions | Membership rolls, sometimes a local enumeration | LGA and ward | Quality varies enormously; get it in writing on letterhead |
Two rules follow from that table, and both of them are what a good examiner is listening for.
Rule one: name the level your figure describes. A national proportion of agricultural households cannot be your N for a study of yam farmers in one LGA. It can support your background in Chapter One, but your population figure must come from the same level as your study area.
Rule two: define your population by what your source actually counted. If your N came from an ADP register, then your population is registered farmers in that LGA, and you must say so in Chapter Three. Writing “the population of the study comprises all farmers in the LGA” when your number came from a register is a claim your own source does not support. Narrowing the population to match the source is not a weakness — it is precision, and it protects you.
Getting an LGA-level figure in practice
The route that works for most agriculture students takes about a week:
- Ask your supervisor for a letter of introduction addressed to the state ADP or the LGA Department of Agriculture. Departments issue these routinely.
- Visit the ADP zonal office covering your study area and ask for the number of registered farmers in the block or cell you are studying, broken down by ward if possible.
- Ask for it on letterhead, signed and dated. This becomes an appendix and it ends any argument about where your N came from.
- If the ADP cannot help, approach the LGA agriculture desk officer, then the local cooperative union or commodity association.
- Record the date you obtained the figure. You will cite it as a personal communication with that date.
If every route fails and you genuinely cannot obtain a population figure, you have two honest options. Either switch to a sampling approach that does not require N — a purposive or quota sample, defended on its own terms — or state a documented estimate with its source and limitations, and add the limitation to Chapter Five. What you must not do is invent a number. An examiner who has worked in an ADP will recognise a fabricated register size instantly.
The Taro Yamane calculation, worked
Taro Yamane’s formula is the Nigerian standard for a finite population, far more common in undergraduate projects here than Cochran or Slovin:
n = N ÷ (1 + N(e)²)
where n is the sample size, N is the finite population, and e is the level of precision, conventionally 0.05 for a 95 per cent confidence level.
Suppose the ADP zonal office confirms 4,300 registered farmers across the three wards of your study LGA. Then:
- e² = 0.05 × 0.05 = 0.0025
- N(e)² = 4,300 × 0.0025 = 10.75
- 1 + 10.75 = 11.75
- n = 4,300 ÷ 11.75 = 365.96
Round up, never down: n = 366. Rounding down is one of the small errors that invites a correction, because a sample below the calculated minimum no longer carries the precision you claimed.
Two adjustments are worth making before you go to the field. First, add an attrition allowance. Agriculture fieldwork loses questionnaires to rain, to farmers who are not on their plots, and to incomplete returns. Administering 400 to retrieve 366 is realistic; state the retrieval rate in Chapter Four. Second, if your analysis requires comparing subgroups — irrigated against rain-fed, male against female farmers — check that the smallest subgroup will still hold enough cases to analyse. Thirty per cell is a common working minimum.
Allocating the sample across your wards
A sample size is a number; a sampling procedure is a method. Chapter Three needs both, and this is where agriculture projects most often thin out.
Use proportional allocation, sometimes called Bowley’s proportional allocation formula, so that each ward contributes in proportion to its share of the population:
nh = (Nh × n) ÷ N
Continuing the worked example with n = 366 and N = 4,300:
| Ward | Registered farmers (Nh) | Calculation | Sample allocated (nh) |
|---|---|---|---|
| Ward A | 1,900 | (1,900 × 366) ÷ 4,300 | 162 |
| Ward B | 1,500 | (1,500 × 366) ÷ 4,300 | 128 |
| Ward C | 900 | (900 × 366) ÷ 4,300 | 76 |
| Total | 4,300 | 366 |
Then state how individual farmers were selected within each ward — systematic sampling from the register at a fixed interval, or simple random selection from the list. A multistage description reads well for agriculture: state, then LGA, then wards, then farming households, with the selection method named at each stage.
When Taro Yamane is the wrong tool
Three situations where applying it anyway will cost you marks:
- Your population is genuinely unknown. If no register exists at any level, you cannot compute a finite-population formula. Say so, and use a defensible alternative with a stated justification rather than dressing up a guess.
- Your study is qualitative. In-depth interviews with extension officers or focus groups with farming cooperatives are sized by saturation, not by formula. What panels accept as a defence in that case is set out in the piece on how many respondents a qualitative project needs.
- Your unit of analysis is not a person. Field trials, plot experiments, soil sample points and livestock units are sized by experimental design — replications and treatments — not by Yamane. An agronomy trial with four treatments and three replications needs a randomised complete block design, not a survey formula.
What to write in Chapter Three
A paragraph that survives questioning looks like this:
The population of the study comprised 4,300 farmers registered with the [State] Agricultural Development Programme across the three wards of [LGA], as confirmed by the ADP zonal office on 14 March 2026 (see Appendix C). The sample size was determined using the Taro Yamane formula at a 95 per cent confidence level and 0.05 level of precision, giving a minimum sample of 366 respondents. A multistage sampling procedure was adopted. In the first stage, [LGA] was purposively selected because of its predominance of [crop] production. In the second stage, the three wards were included in full. In the third stage, the sample was allocated proportionally across the wards using Bowley’s formula, yielding 162, 128 and 76 respondents respectively. In the final stage, respondents were selected by systematic random sampling from the ADP register at an interval of every kth farmer. Four hundred questionnaires were administered to allow for attrition.
Every claim in that paragraph is traceable. The population has a source and a date, the formula has a stated precision level, the allocation shows its arithmetic, and the selection method is named at each stage. It slots into the wider structure described in the guide to writing Chapter Three section by section.
Two decisions that follow from your sample size deserve early attention. The instrument you administer to those 366 farmers has to be built and validated, and the sequence for that — expert review, content validity index, pilot, reliability coefficient — is the same one used in the guide to designing and validating a survey instrument. And how you administer it matters more in rural areas than anywhere else, because an online form measures who had network that day rather than who farms; the trade-offs are compared in the piece on collecting project data with Google Forms, KoboToolbox or paper.
Two questions the panel will ask about your N
“Where did this population figure come from?” Answer with the institution, the office, the date and the appendix number. Then stop talking. A precise sourcing answer closes the question.
“Why 0.05 and not 0.01?” Because 0.05 corresponds to the 95 per cent confidence level conventional in social and agricultural survey research, and because 0.01 would have required a sample beyond the resources available for an undergraduate project. Saying the second half out loud is fine — examiners prefer an honest constraint to a pretended one.
Get the chapter written while the figures are fresh
The hardest part of an agriculture project is rarely the arithmetic. It is that fieldwork eats weeks, and by the time you return from the wards with four hundred questionnaires in a bag, the writing has not started and the deadline has not moved.
Tesify drafts your chapters from your own topic, population, sampling procedure and instrument, keeps your citations and terminology consistent as the draft grows, and lets you revise a section after supervisor corrections without rebuilding the chapter. It is a way to write your own project faster, not a way to submit someone else’s.
Start your project on Tesify for free and turn your sampling decisions into a finished Chapter Three.
Frequently asked questions
Where can I get the number of farmers in a Nigerian local government area?
The most usable source is the State Agricultural Development Programme zonal office covering your study area, which keeps registers of farmers by block and cell. The LGA Department of Agriculture, FADAMA beneficiary lists and cooperative union rolls are alternatives. Request the figure on letterhead with a date, and reproduce it as an appendix — that document is what answers the panel’s question about your population.
What is the Taro Yamane formula?
n = N ÷ (1 + N(e)²), where n is the required sample size, N is the finite population and e is the level of precision, conventionally 0.05 for 95 per cent confidence. It is the standard sample size formula in Nigerian undergraduate projects and applies only when the population size is known.
What sample size should I use if I cannot find the population of farmers?
Do not apply Taro Yamane to a population you cannot document. Either use a formula for an infinite or unknown population, or adopt purposive or quota sampling with a stated justification and sample size, and record the absence of a sampling frame as a limitation in Chapter Five. Examiners accept a documented constraint; they do not accept an invented N.
Should I round the Taro Yamane result up or down?
Always up. The formula gives a minimum sample for your stated precision, so 365.96 becomes 366. Administering more than the calculated minimum is fine and normal; administering fewer means you no longer have the precision you claimed in Chapter Three.
How do I share my sample across several villages or wards?
Use proportional allocation: multiply each ward’s population by your total sample size and divide by the overall population, so that a ward holding forty per cent of the farmers receives forty per cent of the questionnaires. Show the arithmetic in a table in Chapter Three, and confirm the allocated figures add back to your total sample.
Does Taro Yamane apply to a field experiment or plot trial?
No. Experimental agronomy studies are sized by design — number of treatments, replications and blocks — not by a survey formula. A randomised complete block design with four treatments and three replications gives twelve plots, and the appropriate analysis is analysis of variance rather than descriptive survey statistics.
How recent must my population figure be?
As recent as the source allows, and always cited with its year. Several official Nigerian agricultural datasets are published years after their reference period, so state the reference year explicitly rather than implying the figure is current. An examiner respects “the most recent available figure, published in [year]” far more than an undated number.
