Which sample size formula should I use for my MD/MS thesis?

It depends on your primary objective. Use the single proportion formula for prevalence or descriptive studies, the single mean formula when estimating an average, the two proportions or two means formula for comparative (case-control, cohort, RCT) studies, the diagnostic accuracy formula for sensitivity/specificity studies, and the correlation formula when your primary outcome is a correlation coefficient.

Where do I get the prevalence or standard deviation for the calculation?

From a previously published study with a similar population, ideally Indian data. Cite that study in your synopsis. If no data exist, a small pilot study or the conservative assumption p = 50% (for proportions) can be used.

Is this calculator accepted by ethics committees and thesis guides?

The calculator uses the standard textbook formulas (Lwanga and Lemeshow, WHO 1991; Charan and Biswas, 2013) that Indian medical universities expect. Paste the generated sentence into your synopsis and cite the source of your assumed values.

Sample Size Calculator for Medical Thesis (MD, MS, DNB) – Free

1. Your study details

Pick the design that matches your primary objective, then enter the values from a reference study.

Study design / primary objective

Expected prevalence (%)From a previous study. Use 50 if unknown (largest n).

Absolute precision (%)Margin of error, usually 5% (or 10% of p for relative).

Confidence level / α

Power (1 − β)

Dropout / non-response allowance (%)10% is standard; 0 for retrospective studies.

Finite population N (optional)Only if sampling from a small, known population.

Standard formulas · Lwanga & Lemeshow (WHO, 1991) · Charan & Biswas (2013)

2. Your sample size

Result, working and a synopsis-ready sentence.

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Fill in the details on the left and click Calculate.

The Formulas

Which formula does the calculator use?

These are the same textbook formulas Indian medical universities, DNB and IECs expect to see in a synopsis.

Single proportion (prevalence)

Descriptive / cross-sectional studies

n = Z²_α/2 · p (1 − p) / d²

p = expected prevalence, d = absolute precision. With p = 50% and d = 5% at 95% CI, n = 385 — the classic "385" you see in many theses.

Single mean

Estimating an average in one group

n = (Z_α/2 · σ / d)²

σ = expected SD from literature or pilot, d = absolute precision in the same unit as the outcome.

Two proportions

Case-control, cohort, RCT with a yes/no outcome

n/group = [Z_α/2√(2p̄q̄) + Z_β√(p₁q₁ + p₂q₂)]² / (p₁ − p₂)²

p̄ = (p₁ + p₂)/2, q = 1 − p. Gives the size per group.

Two means

RCT / comparative study with a continuous outcome

n/group = 2 (Z_α/2 + Z_β)² σ² / Δ²

Δ = clinically important difference between the two means, σ = pooled SD. Per group.

Diagnostic accuracy

Sensitivity / specificity studies

n = Z²_α/2 · Se (1 − Se) / d² ÷ prevalence

Buderer's formula. Divide by (1 − prevalence) instead when powering for specificity.

Correlation

Relationship between two continuous variables

n = [(Z_α/2 + Z_β) / C]² + 3, C = ½ ln[(1 + r)/(1 − r)]

r = expected correlation coefficient (Fisher's z transformation).

Lwanga SK, Lemeshow S. Sample size determination in health studies: a practical manual. Geneva: World Health Organization; 1991.
Charan J, Biswas T. How to calculate sample size for different study designs in medical research? Indian J Psychol Med. 2013;35(2):121–6.
Buderer NM. Statistical methodology: I. Incorporating the prevalence of disease into the sample size calculation for sensitivity and specificity. Acad Emerg Med. 1996;3(9):895–900.
Hulley SB, Cummings SR, Browner WS, Grady DG, Newman TB. Designing clinical research. 4th ed. Philadelphia: Lippincott Williams & Wilkins; 2013.

FAQ

Sample size questions students ask

Which formula should I use for my MD/MS thesis?

It depends on your primary objective. Prevalence or descriptive study → single proportion. Estimating an average → single mean. Comparing two groups with a yes/no outcome (cured/not cured, complication/no complication) → two proportions. Comparing two groups with a measured outcome (BP, HbA1c, pain score) → two means. Sensitivity/specificity study → diagnostic accuracy. If your main result is a correlation coefficient → correlation.

Where do I get the prevalence, means or SD to put in?

From a previously published study on a similar population — ideally Indian data. Cite it in your synopsis as the basis of the assumption. If nothing is published, run a small pilot (10–20 patients) or, for proportions, use the conservative p = 50%.

Should I add a dropout allowance?

For prospective and interventional studies, yes — most IECs expect 10–20% for loss to follow-up or non-response. The calculator divides n by (1 − dropout). For retrospective record-based studies set it to 0.

Is this accepted by my ethics committee and guide?

The calculator uses the standard formulas from Lwanga & Lemeshow (WHO) and Charan & Biswas — the same ones taught in community medicine and expected by Indian universities and DNB. Paste the generated sentence into your synopsis and cite the source of your assumed values. Software such as OpenEpi or G*Power gives the same numbers.

My calculated n is more than I can recruit. What now?

Options your guide may accept: relax precision (d from 5% to 7%), use 80% instead of 90% power, choose a larger clinically meaningful difference (with justification), extend the study period, or make it multi-centre. Do not silently reduce n — an underpowered study is a common reason for thesis rejection.

Need the full statistical analysis, not just the sample size?

PubMedico's statisticians handle the complete data analysis for MD, MS, DNB, MDS and nursing theses — with tables, graphs and a written results chapter your guide will approve.

Sample size justification written for your synopsis and IEC
SPSS / STATA / R analysis with the right tests
Publication-quality tables and figures
Results and discussion chapters, Vancouver references

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