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Applying Population Statistics to the Individual

Three statisticians go duck hunting. The first statistician sees a duck and shoots, but aims too high and misses the duck. The second statistician shoots, but aims too low and misses the duck. The third statistician grins and says, "We got it!"

This below-average joke typifies a problem with applying biostatistics to your individual life. Biostatistics refers to the application of statistical methods to biological processes. For example, the Sleep, Activity, Fatigue, and Task Effectiveness (SAFTE™) model has been validated against experimental sleep and cognitive performance under a range of sleep deprivation paradigms and operational environments (Van Dongen 2004, Hursh et al. 2011, Gertler et al. 2012, Roma et al. 2012). These comparisons rely on statistical comparisons between the model and averaged results from experimentally-collected human data. But where does this leave the individual who is trying to apply fatigue risk management practices to their own life?

In the name of science, I have taken people’s blood, tested people’s urine, stressed people out, glued electrodes to people’s scalps, made people stick their hand in ice water, shown people pornography, scratched people’s faces, burned them with heat probes or pepper spray, watched people sleep, and I have asked people a lot of embarrassing questions. Yet never in my years as a human subjects’ researcher have I ever met an average person. There is a lot of variability. Whether you consider yourself within a standard deviation of “normal”, or prefer to think of yourself as an outstanding outlier, it can be difficult to practice a statistically-optimized lifestyle.

Common wisdom says to use your best judgement. However, when it comes to fatigue, this may not be a smart idea. Fatigue has a funny way of affecting judgement. Chronic sleep restriction or deprivation is associated with worsening performance and physiological responses even when the sleep-deprived individual subjectively feels fine (Banks et al. 2007, Simpson et al. 2016). That is to say, someone who is tired doesn’t think they’re tired because they’ve been tired so long that they forget what it feels like to not be tired. A 2021 meta-analysis from a team of researchers at Monash University in Australia examined the ability of sleep-deprived individuals to accurately assess their performance and monitor errors across 11 separate studies which had previously examined whether sleep restriction or total sleep deprivation influenced the accuracy of performance monitoring (Boardman et al. 2021). Findings were mixed. Seven studies reported no effect of sleep loss on performance monitoring (Baranski et al. 1997, Baranski et al. 2002, Baranski 2007, Boardman et al. 2018)(Hsieh et al. 2009, Steward et al. 2009, Hsieh et al. 2010), one found an overestimation of performance (Steward et al. 2009), two reported an underestimation of performance (Hsieh et al. 2009, Hsieh et al. 2010), and one reported accurate performance monitoring (Boardman et al. 2018). Statistics really hit the duck on that one.

What does this mean for actual performance? A study by Van Dongen et al. investigated the impact of individual differences on neurobehavioral performance tasks, including the Psychomotor Vigilance Task (PVT), under sleep deprivation (Van Dongen et al. 2004). The team found that neurobehavioral deficits from sleep loss varied significantly among individuals and were stable within individuals. In other words, some people perform better when sleep-deprived than do other people.

Individuals are different, which includes their need for sleep or their ability to perform well even when fatigued. If you work in a safety-sensitive industry, play it safe! Fatigue risk management is about reducing risk, not taking risks. The easiest way to do that is to allow sufficient time for sleep. One of the goals of using biomathematical modeling software like SAFTE-FAST is to determine whether workers in safety-sensitive industries like aviation, rail, or healthcare are receiving enough time between work events to get that necessary sleep. One benefit to the way that SAFTE-FAST predicts performance is that percent effectiveness is scaled to an individual’s personal best. Person A’s 100% may not be equivalent to Person B’s 100%, but it doesn’t matter, because performing at your own personal best is the goal.

I searched for a second statistics joke to close out this post, but I couldn’t find any. The duck joke seems to constitute the entire population of jokes about statistics (N=1). I thought about making up a second joke myself, but I doubted aNy1 would get it. Before you wonder how much fatigue affects sense of humor, let me assure you that I am fully rested. It’s just that my 100% personal best still isn’t that funny.


Banks, S. and D. F. Dinges (2007). "Behavioral and physiological consequences of sleep restriction." J Clin Sleep Med 3(5): 519-528.

Baranski, J. V. (2007). "Fatigue, sleep loss, and confidence in judgment." J Exp Psychol Appl 13(4): 182-196.

Baranski, J. V., V. Gil, T. M. McLellan, D. Moroz, A. Buguet and M. Radomski (2002). "Effects of Modafinil on Cognitive Performance During 40 Hr of Sleep Deprivation in a Warm Environment." Military Psychology 14(1): 23-47.

Baranski, J. V. and R. A. Pigeau (1997). "Self-monitoring cognitive performance during sleep deprivation: effects of modafinil, d-amphetamine and placebo." J Sleep Res 6(2): 84-91.

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Boardman, J. M., K. Porcheret, J. W. Clark, T. Andrillon, A. W. T. Cai, C. Anderson and S. P. A. Drummond (2021). "The impact of sleep loss on performance monitoring and error-monitoring: A systematic review and meta-analysis." Sleep Med Rev58: 101490.

Gertler, J., S. Hursh, J. Fanzone, T. Raslear and Q. N. America (2012). Validation of FAST model sleep estimates with actigraph measured sleep in locomotive engineers, United States. Federal Railroad Administration.

Hsieh, S., T. H. Li and L. L. Tsai (2010). "Impact of monetary incentives on cognitive performance and error monitoring following sleep deprivation." Sleep 33(4): 499-507.

Hsieh, S., C. Y. Tsai and L. L. Tsai (2009). "Error correction maintains post-error adjustments after one night of total sleep deprivation." J Sleep Res 18(2): 159-166.

Hursh, S., J. Gertler and T. Raslear (2011). "Measurement and Estimation of Sleep in Railroad Worker Employees." Research Results.

Roma, P. G., S. R. Hursh, A. M. Mead and T. E. Nesthus (2012). Flight attendant work/rest patterns, alertness, and performance assessment: Field validation of biomathematical fatigue modeling, Federal Aviation Administration Oklahoma City Ok Civil Aerospace Medical Inst.

Simpson, N. S., M. Diolombi, J. Scott-Sutherland, H. Yang, V. Bhatt, S. Gautam, J. Mullington and M. Haack (2016). "Repeating patterns of sleep restriction and recovery: Do we get used to it?" Brain Behav Immun 58: 142-151.


Van Dongen, H. P. (2004). "Comparison of mathematical model predictions to experimental data of fatigue and performance." Aviat Space Environ Med 75(3 Suppl): A15-36.

Van Dongen, P., M. D. Baynard, G. Maislin and D. F. Dinges (2004). "Systematic interindividual differences in neurobehavioral impairment from sleep loss: evidence of trait-like differential vulnerability." Sleep 27(3): 423-433.


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