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interpolation_error
Interpolation error occurs when values between observed data points are estimated by assuming a particular functional relationship, such as a straight line or smooth curve, without sufficient evidence for that assumption. While generally safer than extrapolation, interpolation can still produce misleading results when the true relationship has features — such as peaks, thresholds, or discontinuities — that fall between measurement points and are therefore invisible.
A river's water level is measured at 6 AM and 6 PM, showing similar readings both times. Linear interpolation suggests a stable water level all day. In reality, a flash flood peaked at noon, causing severe but unrecorded flooding between measurements.
Air quality sensors in a city record pollution levels at 8 AM and 8 PM each day. Linear interpolation between these readings suggests moderate, stable pollution throughout the day. In reality, a sharp midday traffic peak causes pollution to spike to hazardous levels for several hours — a pattern entirely invisible to the interpolation.
A climate researcher has temperature proxy data from ice cores at roughly 500-year intervals. Connecting these points with straight lines implies gradual, continuous temperature change between measurements. However, abrupt century-scale warming events occurred between sample points and are completely smoothed away by the linear interpolation.
Binary (yes/no) questions an LLM must answer to identify this aspect:
Are estimates being made between observed data points using an assumed functional form?
Type: binaryIs the assumed relationship between data points (e.g., linear, smooth) justified by evidence?
Type: binaryCould the true relationship have features (peaks, dips, discontinuities) between the observed points?
Type: binaryAre the data points spaced widely enough that important variation could be missed between them?
Type: binaryInterpolation error occurs when values between observed data points are estimated by assuming a particular functional relationship, such as a straight line or smooth curve, without sufficient evidence for that assumption. While generally safer than extrapolation, interpolation can still produce misleading results when the true relationship has features — such as peaks, thresholds, or discontinuities — that fall between measurement points and are therefore invisible.
The assumption that data varies smoothly between observations seems reasonable and is computationally convenient. However, real-world processes can be erratic, and sparse measurements may miss important events or nonlinear behavior between observation points.
Increase the density of observations in critical regions. Use domain knowledge to select appropriate interpolation methods. Validate interpolated values against independently collected data. Report the assumptions underlying interpolation and assess their plausibility.
Occurs in environmental monitoring with infrequent sampling, in medical records between clinic visits, in economic data released quarterly when monthly fluctuations matter, and in geophysical surveys with sparse measurement points.
Extending conclusions beyond the range of observed data without justification.
Systematic error in how data are collected, recorded, or classified in a study.
Presenting aggregate statistics (means, totals) that mask important variation or subgroup differences within the data. The aggregate can tell a completely different story than the disaggregated data.
Use these tools to detect, analyze, or train this aspect.