++ ATOT official NEF thread part IV ++

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busydude

Diamond Member
Feb 5, 2010
8,793
5
76
For diagnostic testing, let​
X = true status (1 = disease, 2 = no disease)
and
Y = diagnosis (1 = positive, 2 = negative). Let πi = P(Y = 1|X = i),

i​
= 1, 2.

a.​
Explain why sensitivity = π1 and specificity = 1 − π2.

b.​
Let γ denote the probability that a subject has the disease. Given that the
diagnosis is positive, use Bayes’s theorem to show that the probability a
subject truly has the disease is

π​
1γ/[π1γ + π2(1 − γ )]

c.​
For mammograms for detecting breast cancer, suppose γ = 0.01,
sensitivity
= 0.86, and specificity = 0.88. Given a positive test result, find
the probability that the woman truly has breast cancer.

d.​
To better understand the answer in (c), find the joint probabilities for the
2
× 2 cross classification of X and Y . Discuss their relative sizes in the two

cells that refer to a positive test result.
 

IndyColtsFan

Lifer
Sep 22, 2007
33,656
687
126
Eli thread is becoming fun!

Cleaner is just now vacuuming, it's been more than two hours.

I just jumped into that thread after opening a can of worms in the Peyton thread about Baltimore's hypocrisy and their insane attempts at rationalizing it.
 

IndyColtsFan

Lifer
Sep 22, 2007
33,656
687
126
I've been watching them applying this the last few days:

bilde
 

IndyColtsFan

Lifer
Sep 22, 2007
33,656
687
126
Oh wait, nevermind. The football on the trophy was completely done this morning and looking at that photo, it isn't done there.