Biostatistics: sample size and effect size: practice question

A PSM question in the style of the NEET PG paper. Answer it first, then read why the right option is right and why each of the others is wrong.

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PSM · Biostatistics: sample size and effect size

Sample item

A study is designed to detect a 10 mmHg difference between two mean blood pressures with 80% power. The investigators now decide to detect a difference of only 5 mmHg, keeping the standard deviation, significance level and power the same. What happens to the required sample size?

Original practice item, not a recalled exam question. Nothing here is recorded.

The answer and the reasoning

B. It increases about fourfold

Sample size is inversely proportional to the square of the difference to be detected. Halving the difference from 10 to 5 mmHg multiplies the required sample by (10/5) squared = 4. Smaller effects therefore need much larger studies.

Option by option

  • A. It stays the same

    The detectable difference is a key determinant of sample size, so it cannot stay unchanged.

  • B. It increases about fourfold (correct)

    Correct. The relationship is with the square of the effect size, so halving it needs four times as many.

  • C. It halves

    A smaller detectable difference makes the sample larger, not smaller.

  • D. It doubles

    Doubling would apply if sample size depended linearly on the difference, which it does not.

Source note: Original NextPrep sample item — pending expert review. This item is original practice material awaiting independent expert review, so confirm important facts in a standard textbook.

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Questions about this PSM question

What is the answer to this PSM question?

The best answer is B, It increases about fourfold. Sample size is inversely proportional to the square of the difference to be detected.

Why is "It stays the same" not the answer?

The detectable difference is a key determinant of sample size, so it cannot stay unchanged.

Why is "It halves" not the answer?

A smaller detectable difference makes the sample larger, not smaller.

Why is "It doubles" not the answer?

Doubling would apply if sample size depended linearly on the difference, which it does not.

What concept does this question test?

It tests Biostatistics: sample size and effect size in PSM. Halving the difference from 10 to 5 mmHg multiplies the required sample by (10/5) squared = 4. Smaller effects therefore need much larger studies.

How hard is this question?

We tag it as a multi-step question: it asks you to combine more than one idea. The tag is our own editorial judgement, not an official difficulty rating, so read the reason for every option, not only the answer.

How should I study Biostatistics: sample size and effect size?

Practise biostatistics with small calculations until sensitivity, predictive values and risk measures are automatic. Then use the flashcards and the other PSM questions on this site to test what stuck.

Is this a real NEET PG question?

No. It is an original practice item (editorial status: sample, version 1). NextPrep does not publish recalled or leaked questions, and independent faculty review of this item has not been completed yet, so confirm important facts in a standard textbook.