6  Reading the Numbers

A plain-language guide to the statistics in this book

This chapter is for readers who want to follow the evidence without a statistics background. It covers the five concepts that appear throughout the manual and the dashboard.

6.1 “Causal” versus “correlated”

Wells that inject more sit in different places than wells that inject less — closer to faults, in different formations, with different neighbors. A correlation between injection and earthquakes could just be geography. A causal estimate answers a different question: for the same well, in the same place, what changes if only the volume changes? The methods in this pipeline (targeted learning) adjust for the measurable differences between high- and low-injection wells — fault distance, depth, well age, neighborhood injection — so that the comparison is volume-against-volume, not place-against-place.

6.2 ψ (“psi”) — the effect size

ψ is the answer to a specific what-if: if every well in the band had injected 10% more, how much would expected seismicity change? It is measured in units of expected local magnitude per well-day, which makes the raw number small (e.g. +8.8 × 10⁻⁴) — but small-per-well-day across 800 wells and nine years is a material amount of seismicity. What matters for decisions is the sign (positive = more injection, more quakes), the confidence interval (does it exclude zero?), and the comparison across wells (which wells carry the effect).

6.3 z and p — how sure are we?

The z-score counts how many standard errors the estimate sits away from zero; the p-value translates that into the probability of seeing such an estimate if the true effect were zero. The current basin-scale result (z = 4.25, p ≈ 2 × 10⁻⁵) means: if injection truly had no effect, data like ours would occur about twice in a hundred thousand tries. Individual radii are weaker (z around 1); the strength comes from 13 radii agreeing in direction — which is itself the expected signature of a real physical mechanism operating across a distance band.

6.4 Frequency versus magnitude — the mechanism

Total seismicity can change two ways: more events, or bigger events. The pipeline separates these. The finding — stable in every data vintage — is that volume operates almost entirely on frequency: more injection means more earthquakes, not larger ones. For policy this is good news: event frequency is exactly what reactive curtailment programs trigger on, so volume management reduces the thing the existing system is built to respond to.

6.5 Confidence intervals on the dashboard

Every per-well attribution carries a 95% confidence interval. Reading them honestly:

• CI entirely above zero — the data resolve a positive contribution from this well.
• CI crossing zero — the data cannot distinguish this well’s contribution from nothing. This is not evidence of innocence; it is absence of resolvable evidence.
• Red-shaded regions on dose-response curves mark volumes beyond the 99th percentile of observed data. Estimates there are extrapolation and are displayed only to show where the supported region ends.

6.6 What would change our minds

Good evidence states its falsifiers. The program’s standing list:

1. A data vintage in which the patched pipeline produces a negative pooled pressure-band estimate with stable active sets.
2. A demonstration that the operator-feedback loop (operators cutting volume after nearby events) reverses the sign when modeled longitudinally — this is the next planned methods step.
3. A negative-control failure: detectable “effects” of injection on earthquakes too distant or too early for any physical mechanism.

None of these has occurred. The day one does, the Evidence Scoreboard reports it.