Cancer Test - Intro to Machine LearningYouTube↗  IA↗(long shot)
Education  51.2K views 28 likes 6 dislikes   23 Feb 2015
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let's use the cancer example for my last
Let's use the cancer example from my last unit.
unit see there's a specific cancer that occurs in 1% of the population and the
Say there's a specific cancer that occurs in one percent of the population.
test for this cancer and with 90% chance
And the test for this cancer.
it is positive if we have this cancer see that's usually called the
And with 90% chance that it's positive if you have this cancer C.
sensitivity of a test but the test
That's usually called the sensitivity But
sometimes is positive even if you don't
the test sometimes is positive even if you don't have C.
have C so let's say with another 90% chance it is negative if you don't have
So let's say with another 90% chance it is negative if you don't have C.
C there's usually called the space C tivity so you as my question without
This usually called the specitivity. So here's my question.
further symptoms you take the test and the test comes back as positive what do
Without further symptoms you take the test, and the test comes back as positive.
you think is now the probability of having that specific type of cancer to
What do you think is now the probability of having that specific type of cancer?
answer this let's draw a diagram so
To answer this let's draw a diagram.
pause these are all the people and some
Suppose these are all the people and
of them exactly 1% health cancer 99% is
some of them; exactly 1%, have cancer 99% is cancer free.
cancer-free we know there is a test that if you have cancer correctly this
We know there's a test that if you have cancer,
diagnosis with 90% chance so if you draw
correctly it is diagnosed with a 90% chance.
the area where the test is positive cancer and test positive then this area over here is 90 percent of the cancer
So if we draw the area where the test is positive, cancer and test positive then this area over here is 90% of the cancer circle.
circle however that isn't the full truth
However that isn't the full truth.
the test Sanders is positive even if the person doesn't have cancer in fact in
The test sentenced is positive even if the person doesn't have cancer.
our case that happen to be in 10% of all
In fact, in our case that happened to be in 10% of all cases.
cases so if you have to add more area is
So you have to add more area.
as big as 10% of this large area there
It's as big as 10% of this large area.
is as big as 10% of this large area where the test might go positive but the
It is as big as 10% of this large area where the test might go positive.
person doesn't have cancer so this blue
But the person doesn't have cancer.
area is 10% of all the area over here -
So this blue area is 10% of all the area
the little small cancer circle and
over here minus the little small cancer circle.
clearly all the area outside these circles corresponds the situation of no cancer and the test is negative so let
And clearly all the area outside these circles corresponds to derivation of no cancer, and the test is negative.
me ask you again
So let me ask you again.
suppose you have a positive test what do
Suppose you have a positive test.
you think with a prior probability of cancer 1% a sensitivity and specificity of 90% do you think your new chances are now 90% or 8% or still just 1%
What do you think? Would the prior probability of cancer of 1%. A sensitivity and specificity of 90%. Do you think your new chances are now 90% or
8% or still just 1%?
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