2F Pros and cons; the Rayleigh example
Chapter 2 · pages 68–72 · 890 words
Lord Rayleigh's 1893-94 measurements of the weight of a standard volume of "nitrogen" prepared from different sources became a famous test case for schematic plots, because they show both what these plots hide and what they reveal. When all 15 weights are lumped into a single batch, the values actually split into two tightly clustered subgroups — a low cluster near 2.299-2.300 and a high cluster near 2.310 — with nothing in between. A dot plot of the batch shows this gap immediately, since every individual value is visible:
Dot plot (single batch of 15)
2.310 | xxx
| x
|
2.305 |
|
2.300 | x
| x
| xxx
| xA schematic plot of that same single batch, by contrast, only draws a box from hinge to hinge and whiskers out to the adjacent values, so the two-cluster structure is almost entirely swallowed up — the median line and box sit in the empty middle, and only unusually short whiskers relative to the box give an alert viewer a hint that something is being hidden. The lesson is that schematic plots are not built to reveal structure near the center of a batch, such as gaps or clusters; for that job a dot plot or a stem-and-leaf display is needed instead.
Where schematic plots do their real work is comparing batches. When Rayleigh's 15 weights are split by their true grouping — 7 weights "from air" versus 8 weights "from other sources" — and each subgroup gets its own schematic plot side by side, the enormous separation between the two batches jumps out, along with secondary features: a slight upward straggle in the "other sources" batch, and a hint that this batch is also more variable. This comparison is exactly what let Rayleigh recognize that air-derived nitrogen differed from chemically-derived nitrogen — a discrepancy that led directly to the discovery of the new element argon. The general principle this illustrates is that aims must drive the choice of plot: a plot can show general behavior (as the two-batch schematic comparison does beautifully) or fine detail near the center (as dot plots or stem-and-leaf do), but usually not both at once, so the analyst must decide which one a given picture needs to deliver.
The Rayleigh example also warns against a common piece of graphical advice: many books on graphical presentation insist that a vertical scale must start at zero, so that bar heights faithfully represent relative size, and treat any convention of exaggerating a scale as a "journalistic" or "political" trick. But if Rayleigh's two batches had been drawn as bar graphs starting at zero, the tiny but real difference between them would have been squashed into invisibility, making the two bars look almost identical — a picture that is neither evidence for a new chemical element nor a basis for a Nobel prize, even though it might be perfectly adequate for someone only interested in freight charges for compressed gas. Zooming the scale to enlarge small but real differences is therefore not dishonest but a vital scientific tool, and schematic plots — used well, with an appropriate scale — earn their place as the standard comparison display precisely because they focus attention where it matters and cut down visual "busyness" enough to let many batches be compared side by side, something stem-and-leaf displays cannot do once more than two or three batches are involved.
Exhibits and original pages (4)
