Removal of zero-point drift from AB data and the statistical cost

TL;DR

This paper introduces a post-hoc analysis method to remove zero-point drift bias from AB measurement data, demonstrating that for sufficiently large data sets, the statistical cost of correction is minimal, thus improving measurement accuracy.

Contribution

It proposes a novel post-hoc analysis technique to eliminate polynomial drift bias in AB data, along with a cost function to evaluate the trade-off between data size and correction order.

Findings

Bias removal effective for polynomial drift up to order p

Statistical cost is negligible for data sets larger than 30 points

Trade-off between data set size and filter order p is characterized

Abstract

Often the result of a scientific experiment is given by the difference of measurements in two configurations, denoted by A and B. Since the measurements are not obtained simultaneously, drift of the zero-point can bias the result. In practice measurement patterns are used to minimize this bias. The time sequence AB followed by BA, for example, would cancel a linear drift in the average difference A-B. We propose taking data with an alternating series ABAB.., and removing drift with a post-hoc analysis. We present an analysis method that removes bias from the result for drift up to polynomial order p. A statistical cost function c(N) is introduced to compare the uncertainty in the end result with that from using a raw data average. For a data set size N>30 the statistical cost is negligible. For N<30 the cost is plotted as a function of N and filter order p and the trade off between the size of the data set and p is discussed.