Specificity calculation question

[chemistry]

My oldest is struggling with a specificity calculation revision question and, unfortunately, has asked me for help. Unfortunately for me, I'm also stuck and neither of us can't get the correct answer given in the mark scheme. Can anyone point out where we're going wrong? The question is:

A study assesses the validity of the MOCA test in screening for mild cognitive impairment (MCI) in adults with poor literacy. The study consist of 135 individuals, 68 of whom have known MCI. The optimal cutoff score for MCI is determined and a total of 71 individuals score below this, of whom 59 have known MCI.

What is the best estimate for the specificity % of the optimal cutoff score? 80, 82, 84, 86 or 88?

Apparently the correct answer is 82%

My (apparently incorrect) workings are Specificity = (true negatives)/(true negatives + false positives)

True negatives are the total sample (135), less the known true positives (68)

False positives are total positives the test identifies (71), less the actual positives within that sample (59)

Specificity = TN/(TN + FP)

(135-68)/((67)+(71-59)) = 67/(67 + 12) = 67/79 = 84.8%

So I would say the correct answer is C, 84% is the best estimate for the specificity of the optimal cutoff score.

But apparently that's wrong...



Any idea what I'm doing wrong and how to derive the correct answer?

Edited by chemistry on Monday 6th June 10:48

Edited by chemistry on Monday 6th June 10:48

[Mr Pointy]

True Negatives = 55
False Positives = 12

S= TN/(TN+FP) = 55/(55+12) = 55/67 = 0.82 or 82%

[chemistry]

Mr Pointy said:

True Negatives = 55
False Positives = 12

S= TN/(TN+FP) = 55/(55+12) = 55/67 = 0.82 or 82%

Thank you!!!

However - and forgive me for being thick - but where does the 55 come from? If 68 people are known to have MCI (the true/gold standard) then isn't the true negative number 135 - 68 = 67? Isn't this the case irrespective of the negatives that the optimal cutoff score throws up (the screening test results) i.e'. the the fact it 'finds' 12 false positives doesn't affect the number of true negatives, it remains 67 rather than 67-12.

I'm still confused (but grateful).

[chemistry]

Ignore that - I understand now! Thanks again!!!!!!