69% of statistics are not made up on the spot. But they might as well be.
People do not understand statistics. The most basic elements of statistical analysis, the most elementary logic concerning odds, appears to be beyond every non-technical person on the planet, and some of the technical ones. I once had an argument with a friend about the existence of God. Always a touchy subject, but in this case she used a particularly annoying argument, all the more annoying because I knew it was wrong at the time but took days to realise why. At the time I was arguing for the side of atheism, and she was Christian.
The argument she gave was a huge bunch of statistics on the projected odds of life ever beginning on the earth, how rare the circumstances were, how astoundingly coincidental that they had all managed to combine. She cited this as logical proof that this had not come about by chance, that odds this low clearly constituted a miracle. I found this deeply irritating. What the hell is a miracle? Surely it is the doing of the impossible, not the improbable? If I toss a die and get a 6, that’s not a miracle. If that die has a million sides, its still not a miracle. A miracle would be if I got, for example, a zero.
I witnessed a debate in work a few months ago on the likelihood of a certain set of numbers coming up in the lottery. Everyone was sure that it was less likely that a sequence of consecutive numbers would come up than any other sequence of numbers. Bull. Shit. Human pattern matching does not have an influence on which way little coloured balls turn.
If I flip a coin a hundred time, and every time it comes up heads, what are the chances of it coming up heads the hundred and first time? 50/50. Past performance is not an indication of future performance. The coin doesn’t know about the statistical anomaly it is creating. Statistics are meaningless. Ever heard the one that says you are more likely to be killed by falling off a donkey than in a plane crash? Absolute nonsense. The fact that more people one year were killed falling off donkeys, or being hit by lightning, or whatever, than died in plane crashes, does not make it any more likely that I, a person who has never travelled via donkey in my life, but frequently takes planes, will be killed in a donkey related accident rather than plunging to my demise in a burning aircraft.
Use some of the other 85% (apparently) of your brains, kids. Maths, much like life, just doesn’t work that way.
January 25th, 2006 at 4:20 pm
True, but it can be great fun winding them up about their ’statistics’ when you tell them that events aren’t related.
Though I could refer you to Dewy’s lucky sweater in Malcom in the middle, I dunno, that sweater was a pretty good argument on the side of luck, and made a fool of the oh-so-logical Malcom. But then again, thats an entertaing TV show, and not reality.
January 25th, 2006 at 5:31 pm
re: flipping coin coming up 100 times heads, indeed. It makes you wonder how you prove that a random number generator is… random. I suspect it’s not actually provable, given that theres no reason it couldn’t produce 1 -> 100000 sequentially, etc, it’s just unlikely.
Steve
January 25th, 2006 at 8:28 pm
I don’t know what I’d do without your little rants, they never fail to make me smile!
Also, I’ll remember never to try and calm you down with comforting stats in future :)
January 31st, 2006 at 2:30 pm
Just as an asside to Steve’s post, it reminds me of the dilbert cartoon mikael used to have pinned to his door in the CSIS building when the IDC was there. The company’s random number generator was a guy/creature standing in the corner going “9″, “9″, “9″ repeatedly. When asked about it they came up with the exact same point as Steve has just made. :-)
June 27th, 2006 at 12:11 pm
As a Christian I find this “what are the odds” crap rather irritating for the following reasons:
1. We are not aware of all the of possibilities therefor probability theory doesn’t work in this case.
2. Retrospectively the way any 5 player poker game had its cards dealt out was improbable. So if thats your standards for a miracle????
3. It is similar to flipping a coin a million times and counting the number of heads and tails you have gotten… whats that, you got an almost equal amount of both? Well thats amazing!
Evolution was going to happen, life isn’t random, it was going to happen.
December 25th, 2006 at 9:41 pm
Whilst it is true that getting a specific set of consecutive numbers is equally likely to getting any other specific set of numbers, the probability of getting a remarkable set (for example consecutive numbers) is much less likely than getting a set of “meaningless” numbers (for example, a set of numbers with no obvious relation to each other). In this way, it is very unlikely for the lottery draw to produce all consecutive numbers. That is not saying that you shouldn’t pick consecutive numbers (of course any set of numbers is equally likely), just that if we compare the set which contains all possibilities of seven consecutive numbers to the set of all other combinations (without loss of generality, we can ignore permutations [different ways of arranging the same sequence of numbers]), we can see the order (size) of the “set of consecutives” is a lot smaller than the order of the other set.
So, by that reasoning, the statement:
“it [is] less likely that a sequence of consecutive numbers would come up than any other sequence of numbers”
is in fact true. It does not, however, increase your chances of winning by picking non-consecutive numbers.
January 25th, 2008 at 5:18 pm
>So, by that reasoning, the statement:
>“it [is] less likely that a sequence of consecutive numbers would come up >than any other sequence of numbers�
This is basically exactly the same as saying “It is less likely that this list of sets of randomly chosen numbers will come up, than that any of the other sets will come up”. Technically true, because one set is smaller than the other, but completely irrelevent. The only reason consecutive numbers are viewed as less likely is because there are not as many sets of them.
March 1st, 2008 at 7:06 pm
Looks like Nick needs do over on his math class. He said ““it [is] less likely that a sequence of consecutive numbers would come up than any other sequence of numbersâ€?is in fact true.” This statement is in fact FALSE. When he said “any other sequence of numbers”, that means, for instance, to compare the odds of 1-2-3-4-5-6 and 3-6-9-12-15-18 winning. Do the math buddy, the odds of either set of numbers winning is the same. Likewise, compare the sequence 1-2-3-4-5-6 to the sequence 45-12-9-25-31-8 (random sequence but a specific set). Odds again are the same. Now had you said “it [is] less likely that a sequence of consecutive numbers would come up vs a sequence of nonconsecutive numbers”, that statement would be true. Dah…