Tag Archives: correlation

What correlation means

From Maria Konnikova’s New Yorker piece on Randall Munroe and what makes science interesting:

In a meta-analysis of sixty-six studies tracking interests over time (the average study followed subjects for seven years), psychologists from the University of Illinois at Urbana–Champaign found that our interests in adolescence had only a point-five correlation with our interests later in life. This means that if a subject filled out a questionnaire about her interests at the age of, say, thirteen, and again at the age of twenty-one, only half of her answers remained consistent on both.

I think it’s totally OK to not say precisely what correlation means.  It’s sort of subtle!  It would be fine to say the correlation was “moderate,” or something like that.

But I don’t think it’s OK to say “This means that…” and then say something which isn’t what it means.  If the questionnaire was a series of yes-or-no questions, and if exactly half the answers stayed the same between age 13 and 21, the correlation would be zero.  As it should be — 50% agreement is what you’d expect if the two questionnaires had nothing to do with each other.  If the questionnaire was of a different kind, say, “rate your interest in the following subjects on a scale of 1 to 5,” then agreement on 50% of the answers would be more suggestive of a positive relationship; but it wouldn’t in any sense be the same thing as 0.5 correlation.  What does the number 0.5 add to the meaning of the piece?  What does the explanation add?  I think nothing, and I think both should have been taken out.

Credit, though — the piece does include a link to the original study, a practice that is sadly not universal!  But demerit — the piece is behind a paywall, leaving most readers just as unable as before to figure out what the study actually measured.  If you’re a journal, is the cost of depaywalling one article really so great that it’s worth forgoing thousands of New Yorker readers actually looking at your science?




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The S&P 500 and the Dow Jones

Adam Davidson in last Sunday’s New York Times Magazine, on the drawbacks of the Dow:

None of these criticisms will come as news to finance professionals, most of whom use far more precise measures — like the S&P 500 or the Wilshire 5000, which cover more companies more precisely — when making investment decisions.

The S&P 500 certainly covers a wider range of companies.  But in a typical 5-day window its correlation with the Dow is more than 95%.  How much more precise could it be?

It’s good to have fine-grained measures, but it’s also good to know at what point extra granularity stops addding new content.


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