Biostatistics: chi-square calculation: 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: chi-square calculation

Sample item

In a study, 30 of 100 exposed people and 10 of 100 unexposed people developed the disease. What is the chi-square value and its interpretation (critical value 3.84 at 1 degree of freedom, 5% level)?

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

The answer and the reasoning

C. 12.5, significant because it exceeds 3.84

With a = 30, b = 70, c = 10, d = 90 and N = 200, chi-square = N(ad - bc)^2 / [(a+b)(c+d)(a+c)(b+d)]. The numerator is 200 x (2700 - 700)^2 = 800,000,000 and the denominator is 100 x 100 x 40 x 160 = 64,000,000, giving 12.5. This exceeds 3.84, so the association is significant at the 5% level.

Option by option

  • A. 12.5, not significant because the degrees of freedom are 2

    A 2 x 2 table has (2 - 1) x (2 - 1) = 1 degree of freedom, not 2.

  • B. 6.25, significant because it exceeds 3.84

    This omits N or mishandles the arithmetic; the correct value is 12.5.

  • C. 12.5, significant because it exceeds 3.84 (correct)

    Correct. The value is 12.5, well above the critical 3.84 for 1 degree of freedom.

  • D. 0.06, not significant because it is below 3.84

    This omits the multiplication by N and wrongly concludes non-significance.

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 C, 12.5, significant because it exceeds 3.84. With a = 30, b = 70, c = 10, d = 90 and N = 200, chi-square = N(ad - bc)^2 / [(a+b)(c+d)(a+c)(b+d)].

Why is "12.5, not significant because the degrees of freedom are 2" not the answer?

A 2 x 2 table has (2 - 1) x (2 - 1) = 1 degree of freedom, not 2.

Why is "6.25, significant because it exceeds 3.84" not the answer?

This omits N or mishandles the arithmetic; the correct value is 12.5.

Why is "0.06, not significant because it is below 3.84" not the answer?

This omits the multiplication by N and wrongly concludes non-significance.

What concept does this question test?

It tests Biostatistics: chi-square calculation in PSM. The numerator is 200 x (2700 - 700)^2 = 800,000,000 and the denominator is 100 x 100 x 40 x 160 = 64,000,000, giving 12.5. This exceeds 3.84, so the association is significant at the 5% level.

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: chi-square calculation?

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.