The Schwab magazine has an interesting discussion of a marketing research study purportedly showing "less is more" when it comes to consumer choice. They summarized the experimental setup and results in the following succinct graphic:

Schwab jam displays - Jun 4 2017 - 3-45 PM - p3

The data consist of nested proportions. For example, among those seeing display 1, 60% stopped to look at the jams, and among those who stopped, 3% purchased.

The nesting is presented as overlap in this design. The blue figures on pink are those shoppers who stopped as well as purchased. The blue figures with no background are those who stopped but did not purchase. The blue figures disregarding background color include everyone who stopped. What about the gray? Those are the shoppers who did not stop at the jam display, which is not a key number. To understand what proportion of shoppers stopped, the reader must take in the entire set of figures, in effect giving the blue and blue/pink figures a change of clothes.

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In this version, we make it easier to estimate the proportions:

Redo_schwab_jams

Each branch starts with 100 figures. The nesting structure is clearly depicted.

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It turns out that the original design messed up the numbers. They were trying to be precise. The right side (Display 2) had 29 figures on each row, summing to 260, exactly the number of subjects in that treatment cell. The left side had 28 figures per row (one fewer!), summing to 233. However, according to the research paper being cited, they analyzed 242 subjects who saw Display 1. Nine shoppers went missing.

The extra precision, even if correctly rendered, interferes with our comprehension of proportions. Less is more, indeed!

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