# Sensitivity &amp; Specificity Confusion

By definition, Sensitivity & Specificity are:
Test Result
Negative          Positive
absent     8660 (a)             960(b)
disease      present       40 (c)             340 (d)

Sensitivity
the probability that a symptom is present (or screening test is positive) given that the person has the disease d/(c+d) 340 / (40+340) = .895. This is also know as the true positive rate.

Specificity
the probability that a symptom is not present (or screening test is negative) given that the person does not have the disease a/(a + b) 8660 / (8660 + 960) = .90. This is also known as true negative rate.

But, in this case,

Pathological diagnosis
Clinical diagnosis           Alzheimer’s disease      Other causes of dementia
Alzheimer’s disease                     1643                                190
Other causes of dementia           127                             228

If the clinical diagnosis is considered a screening test for Alzheimer’s disease,

then the sensitivity of this test would be:

Pr (screen test is present | person has the disease)
= 1643/(1643+127) = 0.928

and the specificity of this test would be:
Pr (screening test is negative | the person does not have the disease)
= 228/(190+228) = 0.545

What I am confused is whay these two have different formula to get sensivitiy and specificity?
Am I missing something here??
ozo

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ethanjohnsons