Subtext is not invariant under linear transformations

by PhilGoetz 1 min read23rd Mar 201013 comments


You can download the audio and PDFs from the 2007 Cognitive Aging Summit in Washington DC here; they're good listening.  But I want to draw your attention to the graphs on page 6 of Archana Singh-Manoux's presentation.  It shows the "social gradient" of intelligence.  The X-axis is decreasing socioeconomic status (SES); the Y-axis is increasing performance on tests of reasoning, memory, phonemic fluency, and vocabulary.  Each graph shows a line sloping from the upper left (high SES, high performance) downwards and to the right.

Does anything leap out at you as strange about these graphs?

What leapt out at me was, "Why the hell would anybody make a graph with their independent variable decreasing along the X-axis?"

Socio-economic status (SES) basically means income.  It has a natural zero.  The obvious thing to do would be to put it on the X-axis with zero towards the left, increasing towards the right.  These graphs have zero off somewhere on the right, with income increasing towards the left.  That's so weird that it couldn't happen by accident.  It would be like "accidentally" drawing the graph with the Y-axis flipped.

What could be the intent behind flipping the X-axis when presenting the data?

If you drew the data the normal way, it would suggest that there's a natural zero-level to both SES and cognition; and that increasing SES increases cognition, possibly without limit.

But when you flip the X-axis, you're limited.  You can't go too far to the right, or you'd hit zero.  And you can't go off to the left, because we don't think that way in the West.  We start at the left and move right.

By flipping the X-axis, the presenter has communicated that SES and intelligence have natural bounds.  Instead of communicating the idea that higher SES is a good thing that leads to higher intelligence, this presentation of the data suggests that the leftmost point on each graph (the anchoring point) is "normal", and a lack of wealth has caused a deficiency in people of lower SES.

(And, of course, rotating around the line Y=X would suggest that intelligence makes you rich.)