Game 11 · Testing and estimation
How many patients does the study need?
Type I and type II errors, power, and what drives sample size.
Read with: Sample size, Hypothesis testing72 DNB questions
Play
Find the smallest trial that is big enough
Set the number of patients per group, run 100 simulated trials and see what share come out significant: that share is the power. Lock in the smallest n that reaches the target. Other rounds change one planning input and ask for the new n, or ask you to name the error in a described result. You have three lives.
3 lives leftRound 1Score 0Streak 0Best 0
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Two ways to be wrong
Type I and type II errors
| Decision | No real difference (H₀ true) | Real difference (H₀ false) |
|---|---|---|
| Reject H₀ (significant) | Type I error, probability α | Correct, probability 1 − β (power) |
| Do not reject H₀ | Correct, probability 1 − α | Type II error, probability β |
| Feature | Type I error (α error) | Type II error (β error) |
|---|---|---|
| What happens | You report a difference that is not there (false positive) | You miss a difference that is there (false negative) |
| Probability | α, set by you, usually 0.05 | β. Power = 1 − β, usually planned at 80% or 90% |
| Example | A trial concludes that a drug lowers blood pressure when it does not | A 20-patient trial finds "no significant difference" for a drug that works |
| Made more likely by | Multiple testing, repeated interim looks, choosing the analysis after seeing the data | Small sample, large variability, small true effect, strict α |
Memory trick
Type I: you report a difference that is not there. Type II: you miss a difference that is there.
The formula
Comparing two means
n per group = 2 × (Zα/2 + Zβ)² × SD² ÷ d²
- Z α/2
- 1.96 for a two-sided α of 5% (2.58 for 1%)
- Z β
- 0.84 for 80% power, 1.28 for 90%
- SD
- standard deviation of the outcome, from an earlier study or a pilot
- d
- smallest difference worth detecting (the MCID)
2 × (1.96 + 0.84)² × 2² ÷ 1² = 62.7 → 63 per group
Always round up. A quick check at α 5% and 80% power: n per group is about 16 × (SD ÷ d)². In the game the simulated power at the formula n is close to the target. It can fall a point or two short at small n, because the formula uses z while the analysis uses the t-test.
What changes n
Each input pushes n up or down
| Input | If it increases, n… | Teaching example (SD 2, d 1) |
|---|---|---|
| Difference to detect (d) | falls: half d → n × 4 | d 0.5 → 252 per group |
| Variability (SD) | rises: double SD → n × 4 | SD 4 → 252 per group |
| Power (1 − β) | rises | 90% power → 85 per group |
| Strictness of α (5% → 1%) | rises | α 1% → 94 per group |
| Expected dropout | rises: recruit n ÷ (1 − rate) | 20% dropout → 79 per group |
Choose d as the smallest difference that matters to patients, not the difference you hope for. A hoped-for large effect gives a small, cheap study that then misses smaller effects that still matter.
Memory trick
More spread, higher power, a stricter α and more dropouts increase n. A larger difference decreases n.
After the formula
Divide by the share who stay, do not add a percentage
Recruit = n ÷ (1 − dropout rate) → 63 ÷ 0.8 = 79 per group
Adding 20% (63 × 1.2 = 76) leaves the study short: 20% of 76 drop out and only 61 remain. Dividing by 0.8 leaves 63. The formula also assumes independent patients. Patients sampled in clusters (villages, wards) need a design effect, covered in the Sample size chapter with the formulas for proportions, case–control studies and survival.
Writing the answer
How to write this in a 10-mark DNB answer
- Define sample size and say why it matters: too small misses real effects (type II error), too large wastes resources and exposes extra patients.
- Draw the 2 × 2 table of decision against truth and define α, β and power, with one clinical example of each error.
- List the inputs: α, power, SD (from a pilot or earlier study), the MCID, and the expected dropout.
- Write the formula for the study type asked (two means, two proportions, one proportion for a survey) with its legend.
- Work one example with round numbers: SD 2, d 1, α 5%, power 80% gives 63 per group, 79 after 20% dropout.
- End with a table of what increases n, and name software (OpenEpi, G*Power) used to check the calculation.
The one thing to remember
Power is the share of identical trials that would detect the real difference. The sample size is chosen to make that share 80% or 90%.
Past papers
DNB questions this game helps you answer
Questions from NBE theory papers for DNB, DrNB and Diploma courses, most often asked first. The tag after each question is the specialty and the year it was set.
- ×3Sample size determination.
- ×2Calculation of sample size for research study.
- ×1Alpha error in research study.
- ×1Define type 1 and type 2 errors.
- ×1Type 1 and Type 2 errors in statistical hypothesis.
- ×1Type 1 and type 2 error in research.
- ×1Type 1 error. [2.5]
- ×1Calculation of sample size in research.
- ×1Define Null hypothesis and Alternate hypothesis respectively with special reference to their significance in clinical trials. Explain type I and type II errors with examples.
- ×1Write briefly about the 'Power of a study' and its significance.
- ×1Describe different type of sampling in psychiatric research. What is the sample size? Describe principle and essential components of sample size calculation for any two types of research designs?
- ×1Describe the process of determining sample size in healthcare research. Illustrate with suitable examples, various factors which can influence sample size calculation.
- ×1Describe various scientific methods for calculation of sample size in a research setting.
- ×1How do you calculate sample size in observational studies?
- ×1Sample size calculation in research methodology.
- ×1Sample size estimation.
- ×1What is the importance of sample size in clinical trials? Describe the methods for sample size calculation for clinical trials.
- ×1a) Confidence interval. b) Tests to evaluate normal distribution of data. c) Sample size calculation.
- ×1a) Study design in biomedical research. b) Describe the methods of types of study and calculating sample size prior to a clinical study.
- ×1Type I and Type II errors.
- ×1Sample size: how to calculate and what is its significance.
- ×1Explain Type I and type II errors.
- ×1Calculation of sample size in medical research.
- ×1Discuss the principles behind calculation of sample size in clinical trials.
- ×1How do you calculate sample size?
- ×1What is a good sample size for clinical trials?
- ×1Discuss Type II error with an example.
- ×1Null hypothesis and Type I & Type II errors.
- ×1Formulae to calculate sample size for thesis project.
- ×1How do you determine sample size for a study?
- ×1Write about sample size calculation for case control studies.
- ×1What are the Type I and Type II error of hypothesis testing?
- ×1What information is needed to calculate the sample size and power of a study?
- ×1What is null and alternate hypothesis in superiority and non-inferiority clinical trials? Explain type I and type II errors with examples.
- ×1Calculation of sample size in animal studies.
- ×1Describe the sample size calculation and statistical analysis that you will perform for a study to compare a new drug with Eltrombopag in the treatment of immune thrombocytopenia.
- ×1Sample size calculation for a research project.
- ×1Sample size calculation for a study.
- ×1Sample size calculation in clinical trials.
- ×1Sample size for scientific study.
- ×1Write short notes on: Sample size calculation for a research study in ED.
- ×1a) Write the difference between correlation and regression analysis. b) List the types of observational study design. c) How is sample size calculated in case-control study?
- ×1How do you calculate the sample size for a case control study?
- ×1Sample size calculation for a drug intervention study for type 10 diabetes.
- ×1Estimation of sample size.
- ×1How to calculate sample size for a study?
- ×1Sample size calculation
- ×1Sample size calculation in a cross sectional study.
- ×1Sample size.
- ×1Various formulae for calculating sample size.
- ×1Mention and justify the statistical tests which would be most appropriate for the following data: a. Comparison of two groups of sample size 150 each where the parameter /data is a continuous variable and is normally distributed. b. Comparison of two different groups of sample size 20 each where the data is a continuous variable but is not normally distributed. c. Comparison of bilirubin values pre and post therapy (4 weeks) in patients with acute hepatitis E who are given an experimental new drug. Sample size is 200 patients. d. Comparison of outcome (alive or dead) in patients given an experimental drug for severe enteric fever. The control group was given inj. Ceftriaxone. Sample size 50 in each group.
- ×1Method of calculation of sample size for a therapeutic trial.
- ×1Sample size collection formula for thesis
- ×1a) How do you calculate sample size for a research study? b) What is the difference between consent form and assent form? c) What is the difference between 'review article' and 'metanalysis'? d) Double-blinding in research studies.
- ×1What is the power of study?
- ×1With reference to medical Statistics, define:- i) Null hypothesis ii) Power of a study.
- ×1Define sample size and its importance in research methodology.
- ×1How does confidence interval change ‘the sample size’?
- ×1How to test sample size for a research project? How can one derive a value of statistical significance in a research project?
- ×1How will you calculate a sample size while doing a research on nephrotoxicity due to snake bite?
- ×1How would you calculate sample size?
- ×1How would you calculate the sample size for a proper statistical analysis?
- ×1How would you determine the sample size?
- ×1Type I and type II error.
- ×1How do you calculate the sample size of a therapeutic trial?
- ×1Sample size calculation for a clinical study.
- ×1Discuss the following: a) Student's 't' test b) Sample size c) Ethics in research
- ×1What is 'Land mark Analysis'? How will you calculate 'sample size' to study impact of a new drug in advanced Lung cancer?
- ×1Write in brief about the various types of studies in Research Methodology? What is sample size and its importance?
- ×1Type I & Type II errors in Biostatistics
- ×1Discuss the sampling methodology covering: a) Sample size, b) Adjustment of sample size, c) Sample design, d) Sample selection, and e) Mapping and listing operation, in context of National Family Health Survey (NFHS) Round 3.
- ×1Discuss the sampling methodology covering: a. Sample size, b. Adjustment of sample size, c. Sample design, d. Sample selection, and e. Mapping and listing operation, in context of National Family Health Survey (NFHS) Round 3.
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