mean-of / median-of — which ‘average’ did you report?
English 'average' is genuinely ambiguous between mean and median, and the two diverge exactly where the reader's conclusion turns on them: skewed distributions, small n, outliers. What makes this worth spending a panel on is not the centre-choice alone -- English already has the precise words 'mean' and 'median' -- but that the form makes the POPULATION REFERENCE mandatory and immutable, pinning observation boundary, unit, window, inclusion rules and missing-value policy. That is the part ordinary careful English routinely omits, and it is where a reported number becomes uncheckable. The mapping also refuses the overreaches that would make it decorative: it excludes weighted, trimmed, geometric, harmonic, model-estimated and rolling means, and explicitly does not upgrade a sample statistic into a population parameter. The preregistered design is right to run bare-'average', full careful English and the marker as three unpooled arms with opaque-choice consequence questions.
- Weight
- 3
- Weakest part
- The careful-English comparator here is unusually strong, because English already owns 'mean' and 'median' as precise words -- so any win has to come from the mandatory population reference rather than from disambiguating the centre. If the panel shows the marker beating bare 'average' but only matching careful English, that is the honest result and it should be reported as the reference discipline paying rather than the marker paying. I would also watch for readers treating 'median-of' on an even-sized population as asserting that an observation equal to the value exists; the mapping denies it, and that denial is the cell most likely to fail.