What is the probability of being drunk at work and also being tested? Let's find out! Correctly

Analytical skills are in big demand so it is really important not to make the basic, common, mistakes that show you up as a newbie. For example, probability calculations are often performed on binary outcomes such as "What is the probability that a given policy holder will claim?" The result is binary because they will either …

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comes in drunk 12 times per annum

= once a month

weekly testing = 4 ish times per month

20 ish working days per month

odds of catching .. 5.ish to 1

er, right?

"= once a month"

Except for most people that would be:

"Week of birthday - drunk 2 days"

"Week before Christmas - drunk 5 days"

"Week between Christmas and New Year - drunk 5 days"

:-)

They never heard of a Friday working lunch? In the pub natch.

The 'correct' calculation has not factored in the test frequency whatsoever.

If the tests were run on 52 consecutive days, if the drunk managed to miss out on being caught for those his chances for the rest of the year are 100%, even if he comes in drunk on 12 consecutive days.

Also, human behaviour being what it is, isn't it more likely that it will be a Monday that the person would be drunk, or a Friday afternoon for example?

Still, useful article :P

comes in drunk 12 times per annum = once a month

Analytical engine I usually work with suggests it's day after payday.

Re: test frequency

Yes, it has the test *frequency* in: on average once per month or once per year or whatever. It says nothing about how these should be distributed over the year, so the assumption is randomly. This is what frequency means in stats. This is what those people we call "frequentists" strive on.

What you describe is factoring in prior knowledge, and that is something that Bayes' rule can do for you - but not within the scope of that article... (I leave looking up a relevant xkcd as an exercise for the reader).

Mine's the one with the hip flask...

Re: test frequency

If tests were on Friday mornings you may stand a better chance of catching people as they start to let their hair down Friday nights. This would further interfere with the probabilities.

Theres a brilliant book on the history of stats - let me find it . . . blah, bloody Google - its on my Kindle - 2 mins . . . Against the Gods: The Remarkable Story of Risk. Very highly recommended.

Re: test frequency

Sheesh, you guys do love to overcomplicate these things...

Testing happens 1 day in 5 ("weekly"). So each time the target comes in drunk, they've got a 20% chance of being tested that day.

If they do it 12 times a year, their chance of getting away with it every time is (0.8 ^ 12 = ) 6.87%.

Re: test frequency

Just ordered the book. Thanks for the recommendation.

and in the real world

You might not just test on a few decided in advance "random" days, but decide on behavior, breath smell etc of one or more staff on a given day to make that day a "hunch" test day (obviously testing everyone so as to be non discriminatory).

Re: and in the real world

I thought in the real world you only tested people you wanted rid of anyway, in the hope they'd show up drunk and make it easy for you?

Probably less the case with Network Rail (who really don't like there poor employees drinking), but I've heard of it working that way in the private sector, especially banks and the like.

Re: and in the real world

in the real world, drunk guy* will just pull a sickie

somehow, it's always a guy, I've never seen a woman drunk at work

Re: and in the real world

I've seen the fair sex drunk at work many times. On six continents. To be fair, though, the dudes are far far more likely to imbibe to excess during working hours, at least in my experience.

Re: and in the real world

and depending upon your physiology, you can fail a drugs test (morphine) from eating two Poppy Seed covered toasted bagels in the morning.

Don't worry people, your Spy TV/Echo/Bixby in the corner will ensure that your Employer (aka Big Bro) knows how much you are eating and drinking when you are at home. They will make sure that you are tested before you leave home for work. Can't have any liability falling on the Dear Employer now can we?

This, you understand, is a purely interim measure. You job will be replaced by robots/A.I. within 5 years. Then you won't be needed at all.

Re: and in the real world

I would also increase the number of tests on a person if they had already previously tested positive.

Re: and in the real world

@jmch:

" in the real world, drunk guy* will just pull a sickie

somehow, it's always a guy, I've never seen a woman drunk at work "

Does not compute. If you see drunk guys at work, but never drunk women, who do you think is taking sickies again?

Re: and in the real world

Chance of catching a tea teetotaller in a year is 0%... so even the 100% is wrong.

Re: and in the real world

>I would also increase the number of tests on a person if they had already previously tested positive.

Depending on the job, the number of tests after a positive would be zero as they would no longer be employed...

Re: and in the real world

I was going to say... Chances for me are preeeeety much zero. :)

Re: and in the real world

>Chance of catching a tea teetotaller in a year is 0%

Not here stateside. Gave up booze when hit my 30s as well as cigs. Now I am old, almost live like a Mormon minus consuming enough caffeine in a day to kill a horse. Have to feed the addiction side of my brain somehow and one of the safer ways I suppose.

Re: and in the real world

"I thought in the real world you only tested people you wanted rid of anyway, in the hope they'd show up drunk and make it easy for you?"

One of the customers I visit from time to time will grab anyone who is on-site, employee or visitor, for random drug/alcohol testing - it's something you have to agree to to be allowed on-site at all.

Re: and in the real world

Caffeine is now excepted since it came out the Mormons own 5% of coke a cola

Re: and in the real world

.... we get tested EVERY day. - plus for-cause and incident investigations. Not to mention random saliva and urine drug testing from both employer and client.

The system to not get caught is to not to consume - or know how much you can consume and metabolise safely.

At a previous workplace, where they were struggling to keep hold of employees, testing was carried out late in the day, a week into the swing and with the intent of not catching anyone.

260 working days per year

Do those poor bastards not have public holidays?

Re: 260 working days per year

I'm guessing "America"

Re: 260 working days per year

Hold my beer - South Korea

Re: 260 working days per year

Clearly not "France", "Italy" or "Spain", as the number is non-zero.

Re: 260 working days per year

Nah it's typically 10 holidays and then 2-4 weeks of PTO, sometimes split up into vacation/sick. Except for the companies that provide "unlimited" vacation. At my current job, after totaling up holidays, vacation, sick, personal days, and volunteer days, a work year is 225 days.

Re: 0 working days per year

@The Man Who Fell To Earth

Can't comment with any accuracy on non-working practices in Italy or Spain but you are dead right about France. I was employed in France for 30 years, only went in to the office for the jokes and the croissants, salary ok and to top it off I'm now retired on a decent pension*.

The joke is on you.

* My UK pension is spent in the UK, it provides pocket money for holidays.

Precision

"The cumulative probability of getting away with it twice is 0.95 x 0.95 = 0.90 (actually 0.91 if you use greater precision)."

No.

At two significant figures of precision, it's either 0.90 or 0.91 You could claim 0.9 and 0.91 to different levels of precision, but when you show that trailing 0, you are showing that you are being precise to that level.

Besides: 0.95*0.95 = 0.9025 which doesn't round to 0.91 at any precision.

If you use (248/260)*(247/260) for full precision, that comes out as 0.906154 which may be where you get your 0.91 from, but the article doesn't make that clear.

Re: Precision

You forgot the icon for the pedant, but thumb up as the article was attempting to make the point of doing things properly.

Re: Precision

"Besides: 0.95*0.95 = 0.9025 which doesn't round to 0.91 at any precision.

If you use (248/260)*(247/260) for full precision, that comes out as 0.906154 which may be where you get your 0.91 from, but the article doesn't make that clear."

" which doesn't round to 0.91 at any precision"

So does it, or not

Re: Precision

Firstly, your calculation looks wrong to me it should be (248/260) * (247/259) which comes out to 0.909652 which rounded to two decimal places is indeed 0.91

Lastly, when I read the author saying it was 0.91 with greater precision I naturally assumed he meant with all calculations up to that point using greater precision. I don't know how else you could read it since he obviously isn't adding extra precision to the result of 0.95 * 0.95.

First test

"We are testing 52 times a year. What are the chances that, on the first day we perform the test, the person will be sober? "

If the first day the test is performed is the first working day of the ear, th echances are pretty low I would say :)

Re: First test

... the first working day of the ear, th echances are pretty low...

Pissed again? Watch out for the tester.

What's the probablility of being fired after being caught drunk the first time?

Depends what you do for a living:-

Bus driver - 100%

Banker - 0%

I work in an office that, among other things, is currently doing civil engineering design work for a rail project.

Train drivers must be dry, obviously, but there are no train drivers on the design team, and none of us will ever go near a train as anything other than a passenger. However, everyone working on the project must be dry, as a condition of the contract.

Rail projects are funny.

Really? I thought they must have been pissed when they came up with HS2...

Depends what you do for a living:-

Bus driver - 100%

Banker - 0%

Home Secretary - Mandatory for the Job*. so -100%

*Or so it seems

Re: Depends what you do for a living:-

"Home Secretary - Mandatory for the Job"

You say that, but I can't imagine May drinking booze. The blood of the unrighteous perhaps, but not booze.

Re: Depends what you do for a living:-

She has to top up her ant-freeze and motor oil once is a while however

Re: Depends what you do for a living:-

May.

Wine drinker I suspect, probably red wine.

or Gin. Neat.

Re: Rail projects are funny

"Train drivers must be dry, obviously, but there are no train drivers on the design team, and none of us will ever go near a train as anything other than a passenger. However, everyone working on the project must be dry, as a condition of the contract."

Yep. It's been that way since 1991. There was a fatal buffer stop crash at Cannon Street caused by the driver not braking properly. The driver tested positive for cannabis three days later, though it was impossible to determine whether and if so to what extent that might have contributed to the crash. Nevertheless the Chairman of British Rail, Bob Reid II, brought in an immediate ban on the use of drugs and other substances which could impair concentration, including alcohol. Obviously the new rules could have just been applied to drivers and other safety critical workers such as signallers, but Reid thought it wasn't fair to insist that drivers couldn't have a lunchtime pint whilst managers and executives, including himself, still could. So the entire organisation went dry, overnight, right from the very top down. And after British Rail was broken up by the privatisation process, all its successor companies inherited the same policy.

A certain bias, there

"It assumes [..] that an employee is coming in with alcohol in their system (drunk) 12 times in a working year."

If you have one glass of wine with your noon meal, you do have alcohol in your system. You are not necessarily drunk, though.

What this means is that it is apparently considered that 0% is the only acceptable percentage of alcohol in the blood in a working environment. Seems a tad draconian to me, but I'm French, so . .

On the other hand, any level of alcohol when coming in to work in the morning is obviously unacceptable because it means that the person has been drinking on the way to work, which is a clear sign that they need professional help and cannot function normally.

Re: A certain bias, there

The way I heard it, if you have more than four pints of an evening, you're risking being over the drink drive limit in the morning.

So if you have four pints the night before, you will have alcohol in your system, just not enough to lose your driving license over.

( Whether that four pints is actually correct I'm not sure, but you get the picture )

Re: A certain bias, there

Given that your liver should be able to clear one unit of alcohol per hour*, the 4 pints should be gone after 8 hours.

*One-ish unit per hour- changes due to metabolism and/or gender.

Re: A certain bias, there

A lot of beers are significantly more than 2 units/pint. Looking at a couple of bottles conveniently to hand, Glamorgan Welsh Pale at 4.3% is 2.2 units (for 500ml, so about 2.4 for a pint), and Three Tuns Old Scrooge at 6.5% is 3.3 (3.6 for a pint).

But serious kudos (and concern for your liver) if you can manage 4 pints of Old Scrooge in an evening! You'll still be showing the effects at lunchtime (if you make it out of bed)

Re: A certain bias, there

It takes me 10 minutes to get to work.

I could easily down a Pint, come to work, still have it in my system.

Nothing wrong with a Pint before work at 8am! ;)

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