Don't trust the narrowest interval. Count the votes.
IF&PA fuses measurement results of the form “value ± uncertainty” into one reliable value. Each result votes for the values its interval covers; the votes are aggregated by the Borda rule — giving the preferential median, robust to outliers and to understated uncertainties.
- Everything runs in your browser — your data are not sent anywhere
- Comparison with nine well-known estimators on the same data
- Ready code in Python, R, MATLAB, C++ and JavaScript
What problem the method solves
In short, without formulas
Problem
Many measurements — which value to trust?
The same quantity has been measured several times: in different laboratories, with different instruments, sensors or methods. The results differ, each has its own uncertainty, and some are wrong while looking very precise: their interval is narrow. One value that can be trusted is needed.
IF&PA's answer
Let the results vote
The interval of each result is a vote for all the values inside it. The value voted for by the most intervals wins. A wrong result is just one vote, however narrow its interval.
Where it is used
How it works
Try it — the intervals can be dragged. Details on the Method page
Intervals vote
Each result x ± u votes for all the values inside its interval.
Votes are counted
For each value we count how many intervals cover it — the bars under the axis. The Borda rule picks the values with the largest support; their median is the preferential median.
One interval, one vote
Drag the narrow interval I6 — an outlier — anywhere: the preferential median hardly moves, while the weighted mean follows it.
Laboratory toolkit
Everything runs in your browser
Calculator
Paste your intervals — get the PM, charts, a step-by-step breakdown and a comparison with nine other estimators.
Calculate →Applicability configurator
Set noise, outliers and honesty of uncertainties — and see which estimator is more accurate and why.
Check →Planner
Labour norms from work history and a schedule under limited resources: how an error in norms carries over into the plan.
Plan →Voting
Enter rankings and compare the plurality, Borda, Condorcet and Kemeny rules; the Condorcet paradox in action.
Vote →Applications
Planck constant, interlaboratory comparisons, a sensor network, regression — interactive demos and results of the papers.
Try →Code
One file with no dependencies in Python, JavaScript, R, MATLAB/Octave and C++, test sets with answers.
Copy →Understand the method: interactive lecture · preference aggregation theory · the IF&PA method step by step · publications
When the method helps
From the simulations in the configurator and the planner
IF&PA is more accurate
About the same
- A wide normal spread, as in production records. The MM-estimator and the median are as accurate as IF&PA but overstate the norms — extra reserve in the plan. Check →
Using the method in your work? Please cite: Muravyov S.V., Khudonogova L.I., Emelyanova E.Yu. Interval data fusion with preference aggregation. Measurement, 2018, 116, 621–630. doi:10.1016/j.measurement.2017.08.045
How to cite