Check an aggregate comparison against its group composition
Two collections can reverse their comparison when their groups are pooled. Check the arithmetic together before deciding what the total means. This manual exercise uses invented counts in an ordinary shared document; a Kiguri office can be the discussion setting, but no product analytics or real team outcome is involved.
Keep the groups and outcomes explicit
Define a completed outcome and two fictional case groups, simple and complex. Collection A contains one completed outcome from one simple case and one from four complex cases. Collection B contains three completed outcomes from four simple cases and zero from one complex case.
Keep the completed count and total count beside each group name. Both collections contain five cases overall. Their group composition differs: A has four complex cases, while B has four simple cases. Treat the labels as definitions for this exercise, not as measured descriptions of any real work or proof that one type is inherently harder.
Compare matching groups first
For simple cases, A has 1/1 and B has 3/4. For complex cases, A has 1/4 and B has 0/1. A's fraction exceeds B's within both defined groups.
Write those comparisons in a register that names the group and the two fractions. Do not substitute the total collection count as a denominator for a group-specific result. Ask another reviewer to reconstruct each fraction from the supplied counts. This catches a copied denominator or a silently omitted zero before discussion moves toward explanations.
Pool counts rather than averaging fractions
A has two completed outcomes from five cases overall, so its pooled fraction is 2/5. B has three from five, giving 3/5. The pooled comparison favors B even though both group-specific comparisons favor A.
The arithmetic is consistent. A includes more cases from the group with the smaller fractions in this fixture; B includes more from the group with the larger fractions. Adding numerators and denominators preserves that composition. Taking an unweighted average of each collection's two group fractions would answer a different question and would not reproduce the pooled count. Keep the group sizes visible rather than forcing the two calculations to agree.
State two bounded conclusions
One conclusion is that B has the larger completed fraction across its five supplied cases. Another is that A has the larger completed fraction within each matching fictional group. Neither sentence should silently become a claim that a real process is superior or that group composition caused an observed business change.
Choose the comparison relevant to the original question. If the question concerns the supplied collection as a whole, the pooled result matters. If it concerns performance within a specified case group, inspect that group. When the intended comparison is unclear, clarify it before choosing whichever result supports a preferred option.
Preserve the reversal in the review record
Keep the original counts, four group fractions, two pooled fractions, and group proportions together. Have another participant explain why the reversal does not indicate an arithmetic error. If the summary says A wins everywhere or B is always better, reopen the wording.
This tiny fixture supplies no statistical generalization, causal finding, or customer result. Its useful lesson is a checkable distinction between two questions. A clear record allows the next discussion to use the right comparison while retaining what the other comparison actually establishes.
