Practice: Choosing What the Reader Will Judge

1. The question and the comparison. The board asks about change over time, per product, relative to the others. The reader must therefore trace four trajectories across twelve quarters and compare their directions and separations. That is a position judgement on a shared axis: four lines on one set of axes, quarter on the horizontal, score on the vertical, one line per product, directly labelled at the right-hand end rather than in a legend. Twelve separate pies cannot support it at all, because each pie shows one quarter's composition and nothing about movement between quarters. The reader would have to hold four angles in memory across twelve panels. A defensible alternative is four small multiples, one panel per product with the other three greyed behind it, if the lines overlap badly. That keeps every comparison a position judgement while reducing clutter. 2. The encoding. The pies assign an angle judgement, which is fourth in the measured ordering, below position and length. Being 3-D makes it worse: perspective foreshortens the wedges unequally, so equal shares subtend unequal apparent angles depending on where they sit in the pie. The reader is being asked to do something difficult, on a display that then distorts it. There is also a category error. A pie encodes parts of a whole, and four satisfaction scores are not parts of a whole. They do not sum to anything meaningful, so the shares shown are an artefact of dividing each by the total. Even a perfectly drawn 2-D pie would be answering a question nobody asked. I would use position along a common scale: lines for the trend, and if a single quarter must be compared, a sorted dot plot. 3. The inset baseline. It depends on the encoding, and this is the point most often got wrong in both directions. For bars, the baseline must be zero, because a bar's length is read from the baseline. With scores from $72$ to $88$ against an axis starting at $70$, the visible lengths are $2$ to $18$. A ratio of $9$ where the data give $88/72=1.22$. That is a gross distortion, and it is the same mechanism as the unit's worked case, where values of $102$ and $108$ on a baseline of $100$ produce bar heights in a ratio of $4.0000$ against a true ratio of $1.0588$. But forcing zero into view here would compress all the variation into the top fifth of the plot and hide exactly what the board is asking about. The resolution is to stop encoding with length. On a line chart or dot plot the reader reads positions against a labelled scale rather than comparing lengths from a baseline, so an axis running $70$ to $90$ is entirely honest, provided the axis is clearly labelled and the restricted range is stated rather than left to be noticed. 4. The scale. Linear. A logarithmic axis renders equal ratios as equal distances and suits quantities that grow multiplicatively over a wide range. Satisfaction scores are a bounded index spanning $72$ to $88$, roughly a fifth of a decade; the meaningful comparison is "how many points did this move", which is additive. A logarithmic axis here would add a convention the audience must decode while answering a question nobody has. 5. What the redesign forecloses. The current slide shows each quarter's shares summing to a whole, and my line chart does not. That loss costs nothing, because the shares were an artefact of normalising four independent scores. Neither display shows the sample size or the uncertainty behind each score. If Product C is measured on forty responses and Product A on four hundred, "pulling ahead" may be noise, and nothing on either slide would reveal it. For a board deciding on investment, that is the omission that matters most, and I would add the number of responses per point and an interval, or state plainly that the scores are unadjusted. I would also drop the note "Product C is pulling ahead" unless the redesigned chart shows it, since a caption asserting a conclusion the display does not support is the same failure as the truncated axis: it moves the reader without the data moving.