Explain Trend Shift in Incident Rates

Business Context

You are the lead data scientist embedded with a joint military logistics task force responsible for convoy operations across multiple regions. The commander is deciding whether to change routing policy and allocate additional electronic countermeasure (ECM) equipment. A dashboard shows that the weekly rate of roadside incidents per 1,000 convoy-miles dropped after a new route-planning protocol was introduced, but the commander is skeptical: “Is this real improvement or just random fluctuation?”

You have 16 weeks of data: 8 weeks before the protocol and 8 weeks after. The number of convoy-miles varies week to week, so you should compare rates, not raw counts.

Problem Statement

1. Quantify whether the post-change incident rate is meaningfully lower than the pre-change rate.

2. Build a commander-friendly explanation that communicates: (a) the size of the effect, (b) uncertainty, and (c) what decision the data supports.

You may assume incidents are rare relative to miles traveled and can be modeled as a Poisson process with exposure (miles). Treat the two periods as independent.

Given Data

Use a one-sided test at α = 0.05 (we only care if the rate decreased).

Requirements

1. Define the metric precisely (incident rate per mile and per 1,000 miles) and explain why exposure adjustment matters.
2. State hypotheses for a Poisson rate comparison.
3. Compute the rate ratio (post vs pre) and a 95% confidence interval for the rate ratio using a log approximation.
4. Perform a one-sided hypothesis test for whether the post rate is lower (derive a z-statistic on the log rate ratio and compute the p-value).
5. Translate the result into an operational statement: expected incidents avoided per 100,000 miles.
6. Draft a 30-second verbal explanation suitable for a commander with no stats background. It must include one analogy and one explicit caveat.

Assumptions and Constraints

• Incidents follow a Poisson process within each period (independent events, constant underlying rate within period).
• Miles are measured accurately; classification of “incident” is consistent pre vs post.
• No major unmodeled confounders (e.g., threat level, weather, mission mix) changed sharply at the same time; if they did, call it out as a limitation.