  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.
