So. About two weeks ago, Your Humble Blogger managed to injure himself badly enough to seek medical care. Having ascertained that nothing was, in fact, broken, the doctor sent me over to a physical therapist, who has been all helpful and stuff. The pain is substantially reduced, range of motion substantially increased, etc etc. Today, my insurer requested that I fill out some forms about my medical condition, which is their right, and I attempted to do so in good faith. However, one of the questions was more or less on a scale of one to ten how severe were your symptoms on average over the last four weeks?
On average?
Over the last four weeks?
Well, doing it by week, that’s two weeks before I had any symptoms so those were zeros, one week that’s about, oh, a six or so, and then this week, let’s call it a four. So, that’s—what—two and a half? Or if they want it by day, I’d say there were, well, let’s call it a dozen zeros, eight or ten fives, a few fours, and three eights. Hm, that’s, um, say, eighty-six over twenty-four, say, three and a half. Hm. Or should I throw out the outliers, and only count from the time I started hurting?
Perhaps, Gentle Reader, the fault was mine, for taking the word average to mean, well, average in a mathematical sense. But then they were asking for a numerical answer. And I honestly don’t have any sense of how to answer their question numerically without doing some sort of averaging. And, you know, I can’t help thinking that somebody somewhere is collating these things, and is going to average the responses. And you know, you can’t average averages. You will get wrong answers. Not just misleading, wrong.
Can we please just give up on averages? I don’t mean that we should abolish averages for people who are doing arithmetic of some kind. In real life, however, away from strictly controlled circumstances, averages almost never tell you anything useful. At least, averages by themselves don’t tell you anything useful; averages with deviation might be helpful in some circumstances. Medians will tell you more, and percentiles (quartiles or quintiles usually) will tell you even more. Why not use them?
Yes, Your Humble Blogger has also, on occasion, used average to mean something like typical or normal, but never (I hope) in situations where it might be understood to be a numerical representation. If I speak of the average citizen, or the average voter, I hope it’s clear that I am speaking crap. Still, I should probably avoid that particular kind of crapspeak, since it does foster the sense that averages are significant and that we should, on the whole, pay some sort of attention to them. We shouldn’t. If you read an article on any kind of statistic that gives you an average and no other details, that article is crap, and you should not only reject its conclusions but find the writer and beat upon him with your fisticuffs and open palms.
Er, metaphorically. In a non-violent manner, and taking into account that writers are generally doing their best. In fact, best to just let these things slide.
Ooh!
chazak, chazak, v’nitchazek,
-Vardibidian.
Well, presumably, before you were injured (and I’m glad you’re feeling better) you didn’t have any symptoms at all (rather than having symptoms of zero severity), so you can throw those out. Which makes the number slightly more meaningful.
More helpfully, what would be a proper way to ask the question? Presumably what they meant is to leave out that moment of level 10 severity when you forgot and put your weight in the wrong place, and leave out the couple hours of level 1 severity when you tried combining extra painkillers with single malt Scotch — how much did you usually hurt?
I don’t remember my stats, which I never took anyway. Is there a way to specify, y’know, the middle? Or do you have to talk about standard deviations and so forth in order to ask the question meaningfully?
Thirty second with Wikipedia later, it seems that when responsible people want to talk about the usual amount, using numbers, they talk about the median (the number that splits the occuring values in the middle). Yes? For example, the median housing price in my home state of Rhode Island currently is, well, more than you’ve got. Presumably that’s more meaningful than the average price, which gets driven up or down (up, in this case) by outliers more than the median does.
But it still leaves out a lot of information. Not that the mode, the other common one, is more helpful (that’s the single most common value). Is there a way to say “the number that the largest number of values are pretty close to” or some such?
Well, and there is, although I can’t remember what it is, and I’m pretty sure looking it up and attempting to explain it falls under behavior proscribed by Prof. Klotz as a condition of my degree.
But even a question of what rating are you most frequently near isn’t really informative. You want to, let’s see, break it into thirds, and say that a third of (the time I was injured) I felt around a seven, a third I felt around a five, and a third I felt a two or below. That tells you (a) that I did have stretches that were relatively pain-free, (2) that the pain never quite hit unbearable, and (iii) that most of the time I was in a fair amount of pain.
Of course, that still won’t give you information you can collate with other people’s information to concoct some sort of ‘average patient’, but if you are, for instance, trying to get a sense of how bad the pain has to be for people to seek medical care, that might conceivably be helpful.
Of course, you would still want to couch your answers carefully, saying something like a third of people won’t see the doctor until they have at least some pain over 7 or three-fifths of people surveyed will see the doctor even if they are experiencing only intermittent pain or such.
Housing prices, by the way, are one of the topics where almost no newspaper information is actually very helpful. The average is, of course, way off, not only because there are enough mansions and McMansions to throw off the average, but the market cuts off below a certain point. That is, there are no outliers below $5,000 to push the average down, the way that a $5,000,000 house pushes the average up. Myself, I would look at the third quartile, which contains the median and a chunk around it. And then I would keep in mind that most houses fall outside that range.
Thanks,
-V.
Apropos of Jacob’s question of “what should they have asked in order to get the information they want”, I’m not even sure what information they want. Why do they care how severe your symptoms have historically been, in some sort of general way?
i think what they meant rather than average was maybe really two things.
1) how often did you feel bad?
2) how bad did you feel when you felt bad?
So, V. How annoyed are you by statistics, ON AVERAGE?
MUHAHAHAHAHAHA!
Like, do 43% of all statistics annoy you, or are you irritated by 100% of all stupid questions, or what?
peace