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Aggregation & Distributional Effects

Primes about how aggregate statistics can diverge from or misrepresent unit-level reality — aggregate-marginal divergence, distributional effects, the modifiable areal unit problem, and partition dependence — plus the underlying measures of spread, effect size, and variability being aggregated.

13 primes in this family — primes that sit near one another in abstraction space (k-means over structural-signature embeddings). Each is shown with its short description.

  • Aggregate-Marginal Divergence — The aggregate trends one way while the next unit's contribution trends the other.
  • Bimodality — A distribution has two separated local maxima with a lower-density interval between them, a shape that constrains but does not by itself identify the process that produced the two modes.
  • Dispersion — A co-launched bundle separates because propagation rate depends on a per-component property.
  • Distributional Effects — An aggregate outcome conceals systematically heterogeneous, unit-level changes.
  • Effect Size — Magnitude of effect.
  • Latent Service Bundle — A sustaining system silently renders a multi-category bundle of benefits to diffuse, unbilled beneficiaries, and because no single category sits on a price ledger the bundle is invisible to decision-makers who consult only the invoice and so systematically under-value it.
  • Law of Large Numbers — As observations accumulate under a stable probabilistic generating process, their empirical average or relative frequency converges to the corresponding expectation, without imposing any balancing obligation on a particular finite sample or next trial.
  • Modifiable Areal Unit Problem — Statistics computed on aggregated data change, sometimes reversing sign, when the boundaries used to aggregate are redrawn — the partition is a non-neutral analytical input.
  • Pareto Effect (80/20 Rule) — 80/20 distribution.
  • Partition Dependence of Aggregates — Any statistic computed on partition-aggregated data is a function of the partition itself, not solely of the underlying data.
  • Stationarity — Stable statistical properties.
  • Variability — Differences across instances.
  • Variation and Sociolect — Group-based language variation.