A little maths problem

[vegyjones]

You're all just clearly jealous of my cleveressness!

[TheOldhamWhisper]

Ok, here goes:

The minimum acceptable sample is 1 million (otherwise we cannot get a potential 100 people who have the disease).

Of the 100 people who have the disease, 99 will test positive whilst 1 person will wrongly be diagnosed as negative.

There will be 999,900 people who do not have the disease of which 9999 people will be wrongly diagnosed as positive.

In total, 10098 people test positive out of 1 million people with (potentially) 1010 people wrongly diagnosed (rounded). This leaves a 'true' chance of being diagnosed positive AND actually having the disease as 1,000,000/9088 = 1:110.

The chance of any single test being 99% accurate cannot be used because the sample is too small to produce statistical accuracy.

(Lies, damned lies and..... )

[vegyjones]

Of the 100 people who have the disease, 99 will test positive whilst 1 person will wrongly be diagnosed as negative.

I thought we'd already decided that these two statements were completely independant of each other and the fact that a test is 99% accurate doesn't mean that out of 100 people, 1 will get a negative result.

[TheOldhamWhisper]

The only facts we are given are: 1 person in 10000 gets the disease and the test is 99% accurate for both positive and negative tests. The statements are mutually exclusive but as they are the only facts we have, we need to extrapolate the data from them.

Given that we need a minimum of 100 people to be able to prove the positive aspect of the second statement, we can deduce that we need a minimum of 1 million people are needed for the sample (as per the first statement). The rest is perfectly accurate (statistically). :)

[GlosRFC]

I don't understand why you're arguing about this....


...if you'd stayed away from Vegy in the first place, you wouldn't have caught the disease!

[TheOldhamWhisper]

...if you'd stayed away from Vegy in the first place, you wouldn't have caught the disease!

- that gets you some TOW rep!

[vegyjones]

Don't make me hungry.
You won't like me when I'm hungry!

[bigcumba]

The incredible sulk :)