Sample Size for an MD/MS Thesis Protocol in Nepal: A Worked Calculation

13 October 2026 · 9 min read

The most common reason a postgraduate protocol comes back is a sample size with no working behind it. The review committee is not checking your arithmetic so much as your assumptions: where the expected prevalence came from, what precision you chose and why, and whether your department can actually reach the number in the study period. This post writes one calculation out in full so you can see what a reviewer expects to read.

The numbers below are illustrative. They show the method. Your own figures must come from a cited study, and your biostatistician should confirm the design before it goes to the IRC.

Start from the primary objective

Sample size answers one question, the primary one. Name the primary outcome first. If it is a proportion, for example the prevalence of a condition or the proportion with a complication, you use the single-proportion formula below. If you are comparing two groups, or comparing means, a different formula applies and this one does not. Secondary objectives are reported with whatever precision the sample gives them. They do not enlarge the sample.

The single-proportion formula

For a descriptive study estimating one proportion, the standard formula is n = Z² × p × (1 − p) ÷ d², where:

Z is 1.96 for 95% confidence.
p is the expected proportion, as a fraction, taken from a published study you cite.
d is the absolute precision you will accept, as a fraction. Five percentage points is written 0.05.

Worked example

Suppose a published study from a comparable setting reports a prevalence of 20%, and you want a precision of 5 percentage points at 95% confidence.

n = 1.96² × 0.20 × 0.80 ÷ 0.05²
n = 3.8416 × 0.16 ÷ 0.0025 = 245.9, which rounds up to 246.
Always round up. A sample of 245.9 does not exist.

If you have no usable prior figure, many protocols assume p = 0.5 because it gives the largest possible n. With the same precision that is 1.96² × 0.5 × 0.5 ÷ 0.0025 = 384.2, so 385. Reviewers accept it only when you say plainly that no prior estimate exists, and they will ask you to search harder first.

Small population: the finite population correction

The formula assumes a very large population. A single department often sees far fewer eligible patients than that. When your sample would be a large share of the eligible population, adjust: n adjusted = n ÷ (1 + (n − 1) ÷ N), where N is the number of eligible patients over the study period.

Continue the example with N = 600 eligible patients: 246 ÷ (1 + 245 ÷ 600) = 246 ÷ 1.408 = 174.7, which rounds up to 175.
N must be a real figure from your department’s register for a comparable period, not a guess.

Allow for non-response and exclusions

Some participants will refuse, drop out or fail an exclusion criterion after enrolment. Inflate the sample so the analysable number still meets the target. For a 10% allowance: 175 ÷ 0.90 = 194.4, so 195 would be enrolled. State the percentage and say what it is based on.

What the sample-size paragraph must contain

The primary outcome and the formula, named.
Every input, with the source of p cited in the reference list.
The confidence level and the precision, with a sentence on why that precision is clinically acceptable.
The arithmetic in full, including the rounding.
Any finite-population or non-response adjustment, with the figures.
The final number, and how it fits the study period and your case load.

The feasibility check committees ask about

A correct calculation can still fail on feasibility. If the study period is twelve months and your centre sees ten eligible cases a month, 195 is out of reach, and the fix is to redesign the study, not to shorten the calculation. Work out the monthly case load before you fix d, because precision is the input you can negotiate. Loosening it from five to seven percentage points cuts the unadjusted sample from 246 to 126.

When the formula above is wrong for your study

Comparing two proportions or two means, as in a case-control or randomised design, needs a power calculation with an effect size, significance level and power.
Diagnostic accuracy studies size on sensitivity or specificity and on prevalence.
Studies with clustering, for example patients within wards or villages, need a design-effect adjustment.
Qualitative components are sized by saturation, not by this formula.

Those are the cases to take to your biostatistician at the protocol stage. They are also the cases where a mistake survives to the thesis, because the data are already collected by the time it is found.

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