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Zziggy
1340273.  Tue Jan 07, 2020 8:26 pm Reply with quote

Let's say you live in the US, where 0.3% of the population live with HIV, and, struck with a sudden abundance of caution, you decide to get tested.

"It's bad news," says the doctor. "You tested positive."

"I know itís hard to accept," she continues, "but I'm afraid this test is extremely accurate. It has a specificity of 99 percent."

What are your actual chances of having HIV?

Ans: less than 1 in 4.

Why? Statistics are much easier to understand when we think of them as natural frequencies - think "1 out of every 5 people" rather than "20%". I'm terms of natural frequencies, the problem is the following:

If 0.3 percent of the population is infected, that means for every 1,000 people in the US, three have HIV.

Letís say your doctor's test is so accurate, it never gives false negatives. So, for every three people who are HIV positive, three tests come back positive.

The test has 99 percent specificity, so it gives false positives 1 percent of the time. That means out of the 997 other people who arenít infected, 10 will nevertheless test positive.

So what are the chances that someone who tests positive does, in fact, have HIV? Itís much easier now to see that youíre looking at a chance of only three in 13 Ė about 23 percent.

The weird thing is that while natural frequencies are much easier to understand and work with successfully, nearly half of all test subjects asked to complete a short maths test for an experiment run by the University of Regensburg would translate problems presented as natural frequencies into to percentage format.

When using natural frequencies instead of percentages, respondents' accuracy jumped from 4% to 24%. Nevertheless the more confusing percentage methods won out, thanks mostly, it seems, to a combination of unhelpful schooling and humanity's natural resistance to change (even when it benefits us).

But so what? So we take a little longer to finish our stats homework, or worry unduly over a medical test left un-double-checked. But for at least three women, statistical confusion has cost their freedom.

Quote:
Weber refers to a famous example of the misuse of statistics in court when the prosecution relied heavily on flawed statistical evidence presented by a medical professional. An insufficient understanding of statistical probability led to Sally Clark being wrongly convicted of the murder of her two sons, based on the misjudgment of the probability that they could have died from natural causes.

 
crissdee
1340294.  Wed Jan 08, 2020 6:07 am Reply with quote

Hello Zziggy! Long time no see! I was up in Ipswich over the Christmas break, and was wondering how you were doing.

Interesting post with somewhat disturbing implications.

 
Zziggy
1340327.  Wed Jan 08, 2020 7:40 pm Reply with quote

crissdee wrote:
Hello Zziggy! Long time no see!

Hi! :)
crissdee wrote:
I was up in Ipswich over the Christmas break

So was I, briefly.
crissdee wrote:
and was wondering how you were doing.

I'm fine, I did my PhD and had a baby and I'm now thinking of applying to do a pgce. How have you been, I gather you're no longer a Londoner?

 
crissdee
1340335.  Thu Jan 09, 2020 4:30 am Reply with quote

Nope, I am now an honorary Welshman, posting from a smallish cottage in Builth Wells, increasingly overrun with books and blades.
Mum is in a home in Ippy, as we lost dad in 2018. Hope to get back into work this year.

 
tetsabb
1340350.  Thu Jan 09, 2020 7:20 am Reply with quote

Yay! Zziggy!
PhD and baby! Which was more difficult?
😉

 
PDR
1340352.  Thu Jan 09, 2020 7:57 am Reply with quote

Welcome back Zziggy, and yes, that's intersting stuff! It's similar to getting people to understand the consequences of "system availability" in my field.

A typical availability requirement might be expressed as 99%, which means that the system myst be working for 99% of elapsed time. 99% sounds like a lot, but it isn't - it means that in every year (8,760 hours) the system might only be working for 8,672 hours. So what? Well that means the system may be NOT working for over 87 hours (three and a half days).

One typical response to being told this is to "add nines", so the availability requirement becomes "three nines" (99.9%), "four nines" (99.99%), or more commonly "five nines" (99.999%). Adding a nine looks like a small change, but here we get the opposite problem because people fail to appreciate how diificult the target is. People can't grasp the availability nukmbers, so I turn them around and offer the corresponding down-time limits. I once had a customer demand 99.999% availability for some deplyable runway lighting - that's two 5km rolls of cable with lights every 10m and a pair of central power units. The systems would be rolled out on open ground to mark temporary runways for things like disaster relief aircraft.

Obviously you'd want this stuff to be reliable, but 99.999% - what does that mean? Well in this case the customer defined "unavailable" as being any single light not working. They also specified that redundant bulbs were not allowed (too heavy). The reliability of the available bulbs did not allow us to achieve the availability through bulb reliability alone, so we were supposed to have systems which could be rapidly repaired without any tools or special equipment, and with no support vehicles.

So what does 99.999% mean in terms of downtime? The bulb reliability predicted three bulb failures per year could be expected (five at the lower confidence limit). We were only allowed 63 seconds per repair, and that included time to get from the tent to any failed bulb (which could be 2.5km away) without vehicles. We recommended they emply Usain Bolt as a maintenance tech...

:0)

PDR

 
Zziggy
1340358.  Thu Jan 09, 2020 10:33 am Reply with quote

tetsabb wrote:
Yay! Zziggy!
PhD and baby! Which was more difficult?
😉

At the moment, I'd say the PhD - but then again, that took twelve times as long as the baby has so far...

 
Zziggy
1340359.  Thu Jan 09, 2020 10:35 am Reply with quote

crissdee wrote:
Nope, I am now an honorary Welshman, posting from a smallish cottage in Builth Wells, increasingly overrun with books and blades.
Mum is in a home in Ippy, as we lost dad in 2018. Hope to get back into work this year.

Sorry to hear about your dad :( my nana's moved to a home in Lowestoft now, and we live close to Wales. Seeing her is harder than ideal.

 
crissdee
1340391.  Fri Jan 10, 2020 5:29 am Reply with quote

I know what you mean. Builth to Ipswich by car was 281 miles and took seven hours due to traffic.

 

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