Confidence Intervals Methodology

Introduction

The Selected Link report presents each result as a range, for example "4.6% – 6.7%", rather than a single percentage. This page explains why the results are reported this way and how to interpret them.

Overview

1. TomTom data is a sample. The data comes from vehicles that share their position with TomTom. This is a large sample, but it does not include every vehicle on the road.
2. Results are reported as a range. Rather than presenting the sample value as the exact truth, the report provides a range that contains, with 95% confidence, the true share of all traffic.
3. The width of the range reflects the amount of data. A small number of observed trips produces a wide range and indicates high uncertainty. Extending the report to more dates or hours increases the number of observed trips and narrows the range.

How to read the results

A result presented as "A → B: 5.6% [4.6% – 6.7%]" means that, based on the observed data, the true share of all vehicles travelling from A to B lies between 4.6% and 6.7% with 95% confidence, and 5.6% is the most likely value.

Analogy: the election exit poll. Consider an election day on which 10,000 people vote at a polling station. To estimate the share of votes for candidate B, a pollster interviews 100 voters, of whom 56 indicate "B". The pollster does not report that exactly 56% of all voters chose B, because a different sample of 100 voters could have produced 51 or 60 such answers. Instead, the result is reported as "56%, with a margin of error of ±10 points". This margin of error is a confidence interval: a range that, with 95% confidence, contains the true result of all 10,000 voters. Interviewing more voters reduces the margin of error.

How the interval is calculated

Consider the simplest case: road A (the selected link) splits into roads B and C, and the goal is to estimate the share of traffic that continues to B. In a given time range, the following trips are observed:

The calculation proceeds in three steps:

• Trip counting. Out of 1,800 trips observed on A, 100 were observed reaching B. This gives a point estimate of 100 / 1,800 ≈ 5.6% for A → B.
• Treatment of lost trips. 100 trips stopped reporting before reaching either exit, for example due to GPS signal gaps or devices being switched off. These trips are assumed to split between B and C in the same proportions as the observed trips. No assumption is made about where exactly they stopped reporting.
• Conversion into a range. A well-established statistical formula converts the observed counts ("100 out of 1,800") into the interval [4.6% – 6.7%]. The same formula applies regardless of the number of trips on an exit, including exits with zero observed trips.

Junctions with more than two exits are handled in the same way: each exit is evaluated against all remaining exits combined, one at a time.

Statistical details

The share of traffic taking a road is modelled using a Bayesian approach: an uninformative Beta(0.5, 0.5) prior combined with a binomial model of the observed trips yields the posterior distribution:

p ~ Beta( trips on this road + 0.5,  all other trips + 0.5 )

The reported 95% confidence interval is the 2.5%–97.5% quantile range of this distribution. In the example above: p(A → B) ~ Beta(100.5, 1700.5) → [4.6%, 6.7%].

Error interval: lost trips make the counts inconsistent (100 + 1,600 is less than 1,800), and this inconsistency is itself quantified. The share for B can be computed in several defensible ways (e.g. 100/1800 = 5.6%, 100/1700 = 5.9%, or 200/1800 = 11.1% under the assumption that every lost trip continued to B). The minimum and maximum of these values, [5.6%, 11.1%] in this example, indicate the amount of measurement error present at the junction.