Checking the Statistical Assumptions Underlying the Application of the Standard Deviation and RMS Error to Eye-Movement Time Series: A Comparison between Human and Artificial Eyes

TL;DR

This study critically examines the statistical assumptions behind using standard deviation and RMS error to measure eye-movement precision, revealing widespread violations that challenge their validity.

Contribution

It provides empirical evidence that common metrics like SD and RMS assume stationarity and independence, which are often violated in eye-movement data, questioning their appropriateness.

Findings

Many position signals were multimodal.

No fixation signals were stationary.

All signals showed autocorrelation.

Abstract

Spatial precision is often measured using the standard deviation (SD) of the eye position signal or the RMS of the sample-to-sample differences (StoS) signal during fixation. As both measures emerge from statistical theory applied to time-series, there are certain statistical assumptions that accompany their use. It is intuitively obvious that the SD is most useful when applied to unimodal distributions. Both measures assume stationarity, which means that the statistical properties of the signals are stable over time. Both metrics assume the samples of the signals are independent. The presence of autocorrelation indicates that the samples in the time series are not independent. We tested these assumptions with multiple fixations from two studies, a publicly available dataset that included both human and artificial eyes ("HA Dataset", N=224 fixations), and data from our laboratory of 4 subjects ("TXstate", N=37 fixations). Many position signal distributions were multimodal (HA: median=32%, TXstate: median=100%). No fixation position signals were stationary. All position signals were statistically significantly autocorrelated (p < 0:01). Thus, the statistical assumptions of the SD were not met for any fixation. All StoS signals were unimodal. Some StoS signals were stationary (HA: 34%, TXstate: 24%). Almost all StoS signals were statistically significantly autocorrelated (p < 0:01). For TXstate, 3 of 37 fixations met all assumptions. Thus, the statistical assumptions of the RMS were generally not met. The general failure of these assumptions calls into question the appropriateness of the SD or the RMS-StoS as metrics of precision for eye-trackers.