Going beyond statistics as useless information

A few years ago, when our younger son, Douglas, began to participate in the "Tough Mudder" events, he called to tell us how he did. He told my wife that he finished in, as I recall, something like two hours. My wife responded with great pride.

When she communicated this information to me, she was a bit surprised by my reaction: while it wasn't quite "so what's your point?," it was definitely not the enthus-
iastic reply she anticipated. I wanted to know his time
within some frame of reference: perhaps what the ave-
rage time was, or the range of times, or, the average time for men who competed, or the average time of men in his age group. When I learned some of this I respond-
ed with pride as my wife had (perhaps the additional information really didn't serve any value; or, perhaps she knew more about these events than she let on).

 

Statistics are useless information

without a frame of reference

I think you'll agree that this is a valid statement.

Now, permit me to gloat a bit about my son, before moving on. He has now participated in more than a half-dozen Tough Mudder events (including the "World's Toughest Mudder" (a 24-hour event)), a couple Spartan races, a marathon, and numerous other races. Next weekend he will be in a 28-mile Spartan Race he had to qualify for (to put THAT into perspective, a couple
weekends back he was in a regular Spartan event and his time, coincid-entally, was about two hours (2:07:01, to be precise); he finished 215th out of a total field of almost 3,500 par-
ticipants. The event next weekend will only have around 400. Pretty good, I think, for a fellow who didn't do any sports in school (he's the actor in the family) and only recently discovered that he's a pretty good runner and obstacle course lover.

Well, enough of that. So, what's my point? I kind of made it, I think: statistics without a frame of refer-
ence are useless information. But so often we are exposed to examples of numbers being tossed about without any reference, are we not?

To be given a statistic, all by itself, without the benefit of a frame of reference (again, it can be an average, a range, or similar information), serves no (or at most, limited) purpose. Thus, the reason why in our industry we insist upon seeing benchmarks of some sort. An important thing, of course, is that it's relevant.

I recall in early 2000 seeing a full page advertisement of a mutual fund company celebrating the fact that 29 of their funds outperformed the S&P 500 in 1999. Putting aside the fact that we weren't told how many of their funds failed to accomplish this feat, the list of funds that did included their Large Cap Growth, Euro Develop-
ment, Small Cap Opportunity, Global Aggressive Growth, and International Equity funds. None of these would normally be compared with the S&P 500; knowing that they outperformed is, in a word (actually two words), useless information. Well, almost useless, as I guess knowing this is good from a broad perspective, but doesn't say a whole lot about the success of their large cap growth, etc. managers relative to their respective sector indexes.

To avoid touting useless information, we need a bench-
mark or two, but it (they) has (have) to be relevant, unless they're being shown not from the standpoint of this is how we did but rather in case you were wondering, this is how other markets performed.

And yes, both my wife and I are proud of our son.

p.s., Totally aside from anything to do with perform-
ance, I want to comment on one use of notation. I have the following above:

so what's your point?,

that is, a question mark followed by a comma.

I read a year or so ago about the possible introduction of new forms of punctuation which has, instead of the dot, a comma with the question mark:

 I can create this character using the "overstrike" feature of WordPerfect (yes, I use WordPerfect, not MS/Word, but that's a topic for another time), but if I were to use it, how would readers respond? It's not yet "officially endorsed" notation. But I think it's a great idea. A similar figure may be introduced for the exclamation point.

p.p.s., I also used "statistics are" not "statistics is." I happen to think the latter sounds better, but I confirmed that it's more correct to have the former.

p.p.p.s., Can't make out the details in the above table? Just click on it.