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06 February 2009 @ 04:32 pm
"This is a numerator. Without a denominator, it tells me /n/o/t/h/i/n/g/ very little."  
I can't remember where I first heard that (although I have a vague impression that it might have been alt.poly), but it's very useful when evaluating scare stories in the media. "Twenty-eight people have been killed in medical evacuation helicopter crashes in the last two years! The FAA must take action to better regulate these flights!" I'm honestly sorry to hear that, and my sympathy to their families, but how many flights were there? How many people were transported safely? Is this really a crisis? I don't know. I have a numerator, but no denominator.

Related to this, you cannot compare numbers and percentages and expect any kind of valid results. It makes no sense whatsoever to say, "15% of the people in Department A were laid off, but only 2 people in Department B were laid off." (This is an argument that I had, repeatedly, with a lawyer I used to work for.) In many cases, you can't really compare numbers with numbers, even; you need to compare percentages.

ETA: Changed the subject line slightly; redbird pointed out that the difference between "numerator = 0 --> nothing has happened" and "numerator != 0 --> something has happened" can be useful information.
Villiers: Martian snow cloudsdianavilliers on February 6th, 2009 10:21 pm (UTC)
Yes, this is something that occurs fairly frequently at work where we have to explain to someone that we can give them either the number they've asked for or the information they actually want. The trick is to do this before giving them a definitive answer, so they are motivated to understand the difference.
Traveler Farlandertwfarlan on February 6th, 2009 11:35 pm (UTC)
Related quote: "There are lies, damn lies, and then there are statistics."
Janet Miles, CAP-OMjanetmiles on February 7th, 2009 12:19 am (UTC)
And "You can lie with statistics, but not to a statistician."
A Wandering Hobbitredbird on February 7th, 2009 12:00 am (UTC)
The mathematical nitpicker in me notes that a numerator either is or is not zero, and that difference can be meaningful information, but mostly I agree with you.
Janet Miles, CAP-OMjanetmiles on February 7th, 2009 12:19 am (UTC)
I'm not sure I understand the nits you are picking. If you don't mind, would you unpack it a bit, please?
Peter Engdornbeast on February 7th, 2009 12:26 am (UTC)
So you're saying that a numerator is useful data, but only for "something has happened" versus "nothing has happened."

And it takes a denominator to make a nonzero numerator any more useful than "something has happened."
Janet Miles, CAP-OMjanetmiles on February 7th, 2009 12:39 am (UTC)
Ah! Now I understand.
Elizabeth Barretteysabetwordsmith on February 7th, 2009 01:17 am (UTC)
Thank you!
This elucidates one of the more common reasons I balk at people's numbers: they're incomplete. I'll probably forget this explanation, but it's gratifying to read.
Janet Miles, CAP-OMjanetmiles on February 7th, 2009 04:09 am (UTC)
Re: Thank you!
Well, it'll be here if you need it. :-)
Ayesha: debbie's mebrowngirl on February 7th, 2009 02:19 am (UTC)
I had been thinking about this problem recently; I like your way of phrasing it.
Janet Miles, CAP-OMjanetmiles on February 7th, 2009 03:09 am (UTC)
I wish I could claim credit for inventing it, but it's only remembered. :-)
Shadow/Brookekengr on February 7th, 2009 06:24 am (UTC)
and then there's "the incidence of X has doubled" (or "the incidence is 10 times higher at A as opposed to B")

Ratios are useless without numbers.

If "ten times as much" is versus 0.0000001% it's not worth worrying about in most cases. If it's 10% versus 1%, you've probably got a problem.

I once had to maintain a program to produced QA reports for orders being shipped to customers. Alas, they were utter nonsense once I actually looked at them.

Y'see, each shipment was made up of items from multiple production lots. And the data the program used as input were the results of testing samples from the lots.

Regardless of how many items from a given lot were in the shipment, it took the readings from the samples for each lot and combined them as if they were a sample of the entire *shipment*.

As I commented to the head of QA when I noticed this, this produces utter nonsense statistically speaking.

His comment was that he'd tried telling management that. And been ignored.

Best I can figure the "right" way to do it would have been to take the entirety of a lot, print out the pretty graphs and figures for that, and make it part of shipment. If the lot was bigger than the number to be shipped, just save the extras for the next shipment. If it was smaller, grab from another lot and generated the paprers for it. etc.

But that'd be harder on shipping. And might show figures the customer wouldn't like as much. :-(
Terry Karneypecunium on February 7th, 2009 09:09 pm (UTC)
Percentages are also suspect, absent context.

Laying 10 people off in one dept, and 2 in another, can be fairly described as, 10 percent, in two very different cases.

They can also be described as 50 percent/60 percent, with very different effcts on the depts in question.
Janet Miles, CAP-OMjanetmiles on February 8th, 2009 12:08 am (UTC)