“It has attained a certain mystique in the physical and biological sciences because it manages to be both rare and ubiquitous. Examples [...] are found in quasar luminosity, tide and river height, traffic flow, and human heartbeat…” (Gilden & Hannock)
Since the mid-90s, a small group of cognitive psychologists have turned their attention to variability in human performance which cannot be explained by existing theories and appears not to be affected by experimental manipulations. “One-over-f” or “pink” noise refers to one way in which human performance across time correlates with itself: in simple reaction time tasks (as simple as “press the button every time you see an arrow”), reaction times tend to oscillate with frequencies which vary inversely as a function of their power. The variance in reaction times which can be statistically explained as 1/f noise frequently dwarfs other sources of variance in RT data, even those which are the intended experimental manipulation!
In a recent paper, Gilden & Hannock show that healthy undergraduates completing mental rotation tasks show a large amount of 1/f noise in their RT timeseries, whereas subjects with ADHD-like symptoms do not show this pattern: instead, their data is better fit by a large amount of white noise in combination with a random walk model, in which a given RT is merely a preceding trial’s reaction time plus a random increment.
Gilden & Hannock conclude that 1/f noise is a phenomenon generated by the process that enables attentional vigilance – and that high variability subjects, such as those with ADHD-like symptoms, show a corresponding absence of 1/f noise. This interpretation does not clearly mesh with previous hypotheses which posit that 1/f noise is a “long-term memory process,” but previous hypotheses of 1/f noise are themselves fairly contradictory.
Wagenmakers, Farrell & Ratcliff describe several of the problems with this line of research. The first is that the slope of log-transformed frequency to log-transformed power is often outside the range expected by 1/f noise (from .5 to 1.5). Therefore we can’t be sure we’re talking about true 1/f noise in the first place. Secondly, it’s not clear when 1/f noise should be observed – some have argued it occurs only during controlled production of intervals, whereas others have observed it even in simple reaction time tasks. Finally, long-range dependencies such as 1/f noise can in fact result from nested shorter-range dependencies which occur at different time scales. Perhaps the most interesting aspect of this critique is the authors’ suggestion that 1/f noise might result from the slow decay of memory traces from previous trials, which follow a power law pattern, “thus giving rise to an autocorrelation function following a power function.”
It will be important for future work to look at the relationship between long-range dependencies, such as 1/f noise, and higher-level cognitive functions such as controlled attention.