1

CRITERIA AND PROCEDURES FOR VALIDATING 

BIOMATHEMATICAL MODELS OF HUMAN PERFORMANCE 

AND FATIGUE: 

PROCEDURES FOR ANALYSIS OF WORK SCHEDULES

Each railroad covered by 49 CFR 228.407 must perform an analysis of the work 

schedules of its train employees who are engaged in commuter or intercity rail passenger 

transportation and identify those schedules that, if worked by such a train employee, may 

be at risk for a level of fatigue at which safety may be compromised. A level of fatigue at 

which safety may be compromised, the fatigue threshold, shall be determined by 

procedures that use a scientifically valid, biomathematical model of human performance 

and fatigue. This document describes the criteria and procedures that the Federal 

Railroad Administration (FRA) will use for certifying the scientific validity of a 

biomathematical model and for determining a fatigue threshold in a biomathematical 

model. This document also identifies specific such models that are acceptable. 

Furthermore, it describes the procedures that must be used both to analyze work 

schedules and to report FRA those schedules that are at risk for exceeding the fatigue 

threshold.

A. What is a scientifically valid, biomathematical model of human performance and 

fatigue?

FRA will decide that a model of human performance and fatigue is scientifically 

valid and may be used for the analysis of work schedules as required by 49 CFR 228.407, 

if the following two objective criteria are met:

Criterion 1. The model documents sensitivity to circadian, sleep deprivation, 

sleep recovery, and sleep inertia effects on one or more well-known behavioral or 

performance-based indicators of fatigue, including vigilance speed, reaction time, lapses, 

cognitive throughput, alertness, and tendency to fall asleep, similar to that observed in the

sleep and fatigue literature as noted below.

Criterion 2. The model is able to demonstrate sensitivity to rail operations human 

factors accident risk by--

(a) using the Fatigue Accident Validation (FAV) Database to contrast 

human factor (HF) and nonhuman factor (NHF) accidents 

(http://www.fra.dot.gov/rpd/policy/1975.shtml); 

(b) demonstrating that HF accident risk is a statistically reliable function 

of modeled performance; and

(c) demonstrating that NHF accident risk is independent of modeled 

performance.

Criterion 1 requires that a model of human performance and fatigue (model) is 

demonstrated to be consistent with currently established science in the area of human 

performance, sleep, and fatigue. The scientific literature in this area has documented that 

certain patterns of work and/or sleep (model inputs) have known patterns of effects on 
2

behavioral or performance-based indicators of fatigue (model outputs). Consequently, 

model inputs such as—

• the length of time spent working and/or sleeping over long and short periods of 

time (chronic and acute sleep deprivation or restriction),

• the time of day that work and/or sleep occurs (circadian rhythms), and 

• abrupt changes in the time of day that work and/or sleep occurs (phase changes)–

should affect model outputs such as—

• vigilance speed, 

• reaction time, 

• lapses, 

• cognitive throughput, 

• alertness, and 

• tendency to fall asleep.

In particular, any model should be able to demonstrate that appropriate model inputs 

result in acute and chronic sleep deprivation/restriction effects, circadian and phase 

adjustment effects, sleep recovery effects, and sleep inertia effects with regard to one or 

more of these model outputs. Fidelity to the pattern of time and magnitude of these 

effects, as documented in the scientific literature, is a requirement of Criterion 1.

There are currently six scientific models that allow work schedules to be 

evaluated for the effects of fatigue on performance and alertness:

• Sleep, Activity, Fatigue and Task Effectiveness model [SAFTE (Hursh et al.,

2004)];

• Fatigue Audit InterDyne model [FAID (Roach, Fletcher, and Dawson, 2004)];

• Three-Process model (Akerstedt, Folkard, and Portin, 2004);

• System for Aircrew Fatigue Evaluation [SAFE (Belyavin and Spencer, 2004)]; 

• Two-Process model (Achermann, 2004); and

• Circadian Alertness Simulator [CAS (Moore-Ede, Heitmann, Guttkuhn, 

Trutschel, Aguirre, and Croke, 2004)].

Each of these models has demonstrated sensitivity to circadian, sleep deprivation, 

sleep recovery, and sleep inertia effects on one or more well-known behavioral or 

performance-based indicators of fatigue, including reaction time, cognitive throughput, 

lapses, alertness, and tendency to fall asleep (Balkin, Braun, and Wesensten, 2002; 

Balkin et al., 2000; Bonnet, 1997; Carskadon and Dement, 1977; Dinges, Orne, and Orne, 

1985; Dinges and Powell, 1985; Dinges and Powell, 1989; Folkard and Akerstedt, 1987, 

1992; Froberg, 1977; Harrison and Horne, 1996; Jewett, 1997; Jewett and Kronauer, 

1999; Lumley, Roehrs, and Zorick, 1986; Mitler, Gujavarty, Sampson, and Bowman, 

1982; Monk, 1991; Monk and Embry, 1981; Richardson, Carskadon, and Flagg, 1978;

Thorne, Genser, Sing, and Hegge, 1983; Wesensten, Balkin, and Belenky, 1999). These

models were recognized as adequate representations of the effects of fatigue on human 

performance by inclusion in a 2002 workshop cosponsored by the U.S. Department of 

Transportation on fatigue and performance modeling (Neri, 2004) and are recognized by 

FRA as satisfying Criterion 1. 

Other, equally adequate models of fatigue and performance may have been developed 

since 2002 or were inadvertently not included in the 2002 workshop. To satisfy Criterion 

1, other models should present evidence to FRA in sufficient detail to prove that the 
3

model is consistent with the scientific literature on human performance and sleep/fatigue 

as noted above.

Criterion 1 is considered a minimal requirement for a model to be qualified for in 

the purpose of work schedule analysis as required by 49 CFR 228.407. Failure to satisfy 

Criterion 1 disqualifies that model, and eliminates that model from any further 

consideration.

Criterion 2 requires that any model of fatigue and performance (including the six 

models referenced above), to be qualified for use in evaluating work schedules under 49 

CFR 228.407, demonstrates sensitivity to the risk of a railroad accident in which an HF is 

a contributing cause. Satisfying Criterion 2 will entail use of the FAV Database to 

contrast HF and NHF accidents [http://www.fra.dot.gov/rpd/policy/1975.shtml] (1) to 

demonstrate that HF accident risk is a statistically reliable function of modeled 

performance and (2) to demonstrate that NHF accident risk is independent of modeled 

performance.

FAV serves as the input for models seeking to satisfy Criterion 2. FAV is 

available as a Microsoft Excel file on the FRA Web site at 

http://www.fra.dot.gov/rpd/policy/1975.shtml. FAV contains 30-day work histories for 

locomotive crews prior to involvement in approximately 400 HF accidents and 1,000 

NHF accidents. The data represent the work histories of 2,6731

Models seeking to satisfy Criterion 2 should use the FAV as input to the model to 

determine a level of performance (model output) at the time of each accident for each

employee indicating that the employee was--

crewmembers, of whom

732 were involved in HF accidents and 1,944 were involved in NHF accidents. 

• not fatigued (well-rested), or

• mildly fatigued, or

• moderately fatigued, or

• very fatigued, or

• extremely fatigued, or

• severely fatigued.

The performance bin “not fatigued” is determined by the output of the model when 

sleep occurs or can occur for 8 or more hours, without abrupt phase changes, during the 

circadian trough between 2200 hours (h) (10 p.m.) and 1000 h (10 a.m.). This is similar 

to the amount of fatigue produced by the standard 9 a.m.-5 p.m., Monday-Friday work 

week. The performance bin “severely fatigued” is determined by the output of the model 

when there is total sleep deprivation for 42.5 consecutive hours. This is similar to the 

amount of fatigue produced by a permanent night shift schedule with six consecutive 12-

h work periods, followed by 1 day off. These two bins are the “anchor” bins for the 

model. There may be other operational definitions of “not fatigued” and “severely 

fatigued” that are particularly suited to a model. The use of other operational definitions 

must be approved by FRA prior to use in validating and calibrating a model.

 1 Three employees had two NHF accidents.
4

The method to be used is described in detail in three FRA reports (Hursh et al., 

2006, 2008; Tabak and Raslear, 2010):

STEP A1. The model domain (i.e., the values that the model output can have) is divided 

into six bins of modeled fatigue levels. One bin is used to capture individuals with severe

levels of fatigue. Another bin is used to capture all individuals considered not fatigued 

(but instead well-rested) by the model. For example, if Model X can have fatigue values 

that range from 50 to 150, with scores between 50 and 60 representing individuals who 

are well-rested and with scores greater than 100 representing individuals who are 

severely fatigued, the bins would be as follows:

Not 

Fatigued

Mildly 

Fatigued

Moderately 

Fatigued

Very 

Fatigued

Extremely 

Fatigued

Severely 

Fatigued

<60 61-70 71-80 81-90 91-100 >100

For each accident in FAV, the amount of time (in hours) that each employee 

involved in the accident spends in each bin is calculated from the employee’s work 

history. The total time for all employees in each bin is calculated for all accidents. A 

distribution of the proportion (fraction in decimals or percentages) of employee time as a 

function of modeled fatigue is constructed for all accidents. This represents the modeled 

fatigue exposure for all accidents.
5

EXAMPLE OF STEP A1: FAV has data for 528,782 h of work for the 2,673 employees. 

The FAV data is processed by Model X with the following result:

Employee Work Time in Hours as a Function of Modeled Performance Level

Modeled Performance Level

<60 61-70 71-80 81-90 91-100 >100 Total

211,513 121,620 84,605 63,454 26,439 21,151 528,782

Proportion of Employee (Work) Time as a Function 

of Modeled Performance Level

Modeled Performance Level

<60 61-70 71-80 81-90 91-100 >100

0.4 0.23 0.16 0.12 0.05 0.04

STEP A2. For each accident, the modeled fatigue at the time of the accident is 

calculated for each crewmember. The total number of crewmembers involved in HF and 

NHF accidents in each of the six contiguous modeled fatigue bins is calculated for the 

2,673 crewmembers. A distribution of proportion (or fraction in decimals or percentages) 

of crewmember accidents as a function of modeled fatigue is constructed for HF and 

NHF accidents.

 

0

0.1

0.2

0.3

0.4

0.5

< 60 61-70 71-80 81-90 91-100 > 100

Proportion of 

Employee Time

Performance Level
6

EXAMPLE OF STEP A2: FAV data, processed by Model X produces the following result:

Number of Crewmember Accidents as a Function of Modeled Performance Level

Modeled Performance Level

<60 61-70 71-80 81-90 91-100 >100 Total

HF Accidents 220 146 110 102 73 81 732

NHF Accidents 680 486 389 214 117 58 1,944

Proportion of Accidents as a Function of Modeled Performance Level

Modeled Performance Level

<60 61-70 71-80 81-90 91-100 >100

HF Accidents 0.30 0.20 0.15 0.14 0.10 0.11

NHF Accidents 0.35 0.25 0.20 0.11 0.06 0.03

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

< 60 61-70 71-80 81-90 91-100 > 100

Proportion of Accidents

Model Performance Level

HF

NHF
7

STEP A3. The Accident Risk Ratio is calculated for HF and NHF accidents for each 

modeled fatigue level. 

Accident Risk Ratio is defined as follows:

Proportion of accidents in fatigue bin x 

Proportion of employee work time in fatigue bin x

EXAMPLE OF STEP A3: Results for Model X

Modeled Performance Level

<60 61-70 71-80 81-90 91-100 >100

Proportion

HF Accidents 0.30 0.20 0.15 0.14 0.10 0.11

NHF Accidents 0.35 0.25 0.20 0.11 0.06 0.03

WORK TIME 0.40 0.23 0.16 0.12 0.05 0.04

Risk Ratio

HF Accidents 0.75 0.87 0.93 1.17 2.00 2.75

NHF Accidents 0.88 1.09 1.25 0.92 1.19 0.75
8

STEP A4. Determine whether the model demonstrates a statistically reliable relationship 

between the Accident Risk Ratio and modeled fatigue level for HF accidents and whether

the model demonstrates that the NHF Accident Risk Ratio is statistically independent of 

modeled fatigue level.

EXAMPLE OF STEP A4: Correlation coefficients are calculated for (1) the HF Risk Ratio and modeled performance 

level and (2) the NHF Risk Ratio and modeled performance level. Since the modeled performance is binned, 

midpoints for each bin should be used.

Performance Level 

(midpoints)

HF Risk 

Ratio

NHF Risk 

Ratio

55 0.75 0.88

65 0.87 1.09

75 0.93 1.25

85 1.17 0.92

95 2.00 1.19

125 2.75 0.75

An Excel spreadsheet can be used to compute the correlations. For HF accidents, the correlation is 0.9621. For NHF 

accidents, the correlation is -0.3556. Since there are six pairs (n) of modeled performance and risk ratios for each 

correlation, the number of degrees of freedom for a t-test to determine the statistical significance of each correlation is 

four (n-2). For 4 degrees of freedom, the absolute value of a correlation must be at least 0.811 to be statistically 

significant with a probability of 0.05. The figure below shows a scatter plot of the six pairs of HF and NHF data. A 

least-squares linear regression line is also shown for HF and NHF accidents, along with the equation for each line and 

the value of the squared correlation coefficient. Consequently, the computations demonstrate that a statistically 

reliable relationship exists between the Accident Risk Ratio and modeled fatigue level for HF accidents and that no 

statistically reliable relationship exists between the Accident Risk Ratio and modeled fatigue level for NHF accidents 

(i.e., Accident Risk Ratio and modeled fatigue level for NHF accidents are statistically independent). This means that 

Model X satisfies Criterion 2 for use as a scientifically valid model of human performance and fatigue. 

Any introductory textbook on statistics will have information on correlation and related t-tests of significance (e.g., 

Hays, 1963). It should be noted that this example assumes that fatigue level and risk are linearly related. If inspection 

of the data, plotted as above, does not support a linear relationship, nonlinear correlation and regression methods 

should be used.

y = 0.030x - 1.155

R2 = 0.925

y = -0.002x + 1.246

R2 = 0.126

0

0.5

1

1.5

2

2.5

3

50.00 70.00 90.00 110.00 130.00

Risk Ratio

Fatigue Level (midpoints)

HF
9

STEP A5. Calculate Cumulative Risk for HF accidents as a function of modeled fatigue 

criterion level. Calculate mean Cumulative Risk for NHF accidents

STEP A6. Calculate 95 percent confidence intervals for each Cumulative Risk bin, 

determine Cumulative Risk bin in which HF cumulative risk exceeds both HF Accident 

Risk Ratio = 1 and the mean NHF risk. This is the fatigue threshold for the model. If the 

model does not calibrate by this method, proceed to Step A6a.

EXAMPLE OF STEP A5: Step A5 uses information from Steps A1 and A2 in which the proportion of 

employee time and proportion of HF and NHF accidents was calculated. Six bins are again arranged as 

shown below. Note, however, that the bins are now partitioned between the category “not fatigued” (<60) 

and any level of fatigue (>60). In the table below, 40 percent of the employees’ time is “not fatigued,”

and 60 percent of employees’ time has some fatigue ranging from “mildly fatigued” to “severely 

fatigued.” Cumulative Risk is calculated similarly to the Accident Risk Ratio. Cumulative Risk is 

defined as

Cumulative proportion of accidents in fatigue bin x 

Cumulative proportion of employee work time in fatigue bin x

Modeled Performance Level

<60 >60 >70 >80 >90 >100

Cumulative 

Proportion

Employee Time 0.40 0.60 0.37 0.21 0.09 0.04

HF Accidents 0.30 0.70 0.50 0.35 0.21 0.11

NHF Accidents 0.35 0.65 0.40 0.20 0.09 0.03

Cumulative Risk

HF Accidents 0.75 1.17 1.35 1.67 2.33 2.75

NHF Accidents 0.88 1.08 1.08 0.95 1.00 0.75

NHF Mean 0.96
10

STEP A6a. If a model fails to meet the calibration criteria in STEP A6, calibration may 

alternately be accomplished by demonstrating a statistically reliable correlation with a 

model that has been validated and calibrated as described above. The fatigue threshold 

EXAMPLE OF STEP A6: The 95 percent confidence interval (CI) is as follows:

,

where T = 

P is the proportion of human factor accidents in each bin.

N is the total number of accidents (based on formula 9.26.2, Hays, 1963, p. 291).

S is the cumulative proportion of employee time in each bin. 

Cumulative accidents and cumulative employee hours are determined as in STEP 5. The Cumulative 

Risk for HF accidents, the upper and lower CI, and the mean NHF Cumulative Risk are plotted below 

for visual inspection:

For Model X, the point at which the HF Cumulative Risk 95 percent CI exceeds both Cumulative Risk 

=1 and the mean NHF Cumulative Risk is in the bin >60. For Model X, 60 is the fatigue threshold. 

It is well known from epidemiology (Lilienfeld and Lilienfeld, 1980) that outcome risk is 

determined by both magnitude and duration of exposure. In the present case, HF accident risk should 

therefore be determined by duration of exposure to fatigue as well as fatigue severity. The cumulative 

proportion of work time spent at a Model X score at or greater than 60 is 0.6 (60 percent). 

Consequently, there should be less than 60 percent of work time at a Model X fatigue score above 60. 

On the basis of the same reasoning, calibration results for FAST indicated that there should be less than 

20 percent of work time at a FAST score below 70. For FAID, there should be less than 20 percent of 

work time at a FAID score above 60. 

y = 0.394x + 0.288

R2 = 0.971

0

0.5

1

1.5

2

2.5

3

3.5

< 60 >60 >70 >80 >90 >100

Cumulative Risk

Fatigue Level

HF

Mean NHF

Upper 95% CI

Lower 95% CI

Linear (HF)
11

for the model will be that value that corresponds with the fatigue threshold of the 

validated and calibrated model by use of a regression or other suitable mathematical 

equation. The use of STEP A6a is subject to approval by FRA.
12

B. What are the procedures for determining that a schedule exceeds the fatigue 

threshold?

The procedures for determining that a schedule exceeds the fatigue threshold require the

use of a scientifically valid, biomathematical model of human performance and fatigue 

documented as noted above. 

STEP B1. For each unique schedule, the time on duty, time on interim release, and limbo 

time must be described in a table that shows the time of day spent in each activity, for 

each day of the week, for one complete cycle of the schedule.

STEP B2. Use a validated model to analyze the schedule. Determine the fatigue score 

for every hour of the schedule marked “D.” Determine the number of work hours in bins 

as described in Step A1. Calculate the proportion (fraction in decimals or percent) of 

total work time in bins as described in Step A1.

EXAMPLE OF STEP B1: Schedule A has work periods on Sunday, Monday, Wednesday, Thursday, and 

Friday from 0601 to 1000 and from 1601 to 1900. Schedule A includes a period of interim release from 

1001 to 1600. This schedule repeats every week (one complete cycle occurs in a week). The table below 

shows this schedule using the following symbols:

D – time on duty

R – time on interim release

L – limbo time

Time of Day

DAY

0001 - 01000101 - 02000201 - 03000301 - 04000401 - 05000501 - 06000601 - 07000701 - 08000801 - 09000901 - 10001001 - 11001101 

– 1200

1201 - 13001301 - 14001401 - 15001501 - 16001601 - 17001701 - 18001801 - 19001901 - 20002001 - 21002101 - 22002201 - 23002301 - 2400

Sun D D D D R R R R R R D D D

M D D D D R R R R R R D D D

T

W D D D D R R R R R R D D D

Th D D D D R R R R R R D D D

F D D D D R R R R R R D D D

Sat
13

EXAMPLE OF STEP B2: If Model X, which was validated as in Section A of this Appendix is used, 

the fatigue scores for specific work periods are as shown below:

Time of Day

DAY

0001 - 01000101 - 02000201 - 03000301 - 04000401 

– 0500

0501 - 06000601 - 07000701 - 08000801 - 09000901 - 10001001 - 11001101 

– 1200

1201 - 13001301 - 14001401 - 15001501 - 16001601 - 17001701 - 18001801 - 19001901 - 20002001 - 21002101 - 22002201 - 23002301 - 2400

Sun 55 60 65 69 R R R R R R 60 65 69

M 56 62 67 68 R R R R R R 62 67 68

T

W 55 60 65 69 R R R R R R 60 65 69

Th 54 57 61 65 R R R R R R 64 68 69

F 58 63 67 69 R R R R R R 66 69 71

Sat

The number of work hours in the six bins from Step A1 is shown in the following table:

Employee (work) Time (in hours) as a Function of 

Modeled Performance Level

Modeled Performance Level

<60 61-70 71-80 81-90 91-100 >100 Total

6 28 1 0 0 0 35

The proportion of work hours in each bin is shown in the following table:

Proportion of Work Time as a Function of 

Modeled Performance Level

Modeled Performance Level

<60 61-70 71-80 81-90 91-100 >100

0.17 0.80 0.03 0 0 0
14

Step B3. The fatigue threshold for Model X is >60. The cumulative proportion of work 

time at a score of >60 is 0.8. This schedule is at risk for a level of fatigue at which safety 

may be compromised. Schedules that exceed the fatigue threshold must be reported, 

mitigated by one or more elements of a railroad’s fatigue management plan, and 

approved for use by FRA, as required by § 228.407.
15

Glossary

The 95% Confidence Interval is the range of estimated values (M) of a parameter that 

has a probability of 0.95 of containing the true population value (μ) of that parameter. In 

a normal distribution of sample means, with population mean μ and standard deviation 

σM, the probability is approximately 0.95 that M – 1.96 σM ≤ μ ≤ M + 1.96 σM. In other 

words, the range of values between M ± 1.96 σM is the 95% Confidence Interval for μ.

Alertness is the state of being awake and watchful, of paying close and continuous 

attention to events in the immediate environment.

A Bin is a range of values of a variable defined by two endpoints. Bins are discrete, 

nonoverlapping intervals of a variable. For instance if a variable can have values 

between 11 and 70, bins might be defined as 11-20, 21-30, 31-40, 41-50, 51-60, and 61-

70. 

Binning refers to the grouping of values of a variable in one of several bins.

The Bin Midpoint is the middle point of a bin. It is equidistant from the bin endpoints 

and is often used to represent the whole bin. For example, the midpoint of the bin 11-20 

is 15.5.

Circadian refers to events or processes that have a periodicity of approximately 1 day. 

Cognitive Throughput is a measure of mental processing speed in humans. In a typical 

task, such as serial addition and subtraction,

2

Phase Changes refer to changes in the timing of sleep and wakefulness in circadian 

rhythms. Phase delays (later wake-up and sleep onset) can be induced by exposure to 

bright light 2 h before usual bedtime. Phase advances (earlier wake-up and sleep onset) 

can be induced by exposure to bright light 5 h after usual bedtime. Jet lag (circadian 

desynchonization) is caused by phase changes because of travel to distant time zones in a 

short period of time.

the product of speed and accuracy (correct 

answers per minute) in the task is an index of cognitive throughput.

A Lapse is a brief loss of attention, alertness, or wakefulness. Also known as a 

microsleep, episodes can be as brief as a fraction of a second. In the laboratory, lapses 

are failures to respond in a reaction time task (see below).

Least-squares Linear Regression is a statistical technique for fitting data to a straight 

line (y = mx +b) such that the sum of the squares of the errors is minimized.

3

 2 This task requires a person to add or subtract a value from a previously obtained sum or difference. See 

Thorne, Genser, Sing, and Hegge, 1983. 3 See Klein and Wegmann, 1980. 
16

r, correlation coefficient is a statistical measure of the linear (y = mx + b) dependence 

between two variables. The value of r is +1 when there is a perfect positive (increasing) 

linear relationship. The value of r is -1 when there is a perfect negative (decreasing) 

linear relationship. If r is 0, there is no linear relationship between the variables. 

However, the absence of a linear relationship does not preclude the existence of a 

nonlinear relationship.

r

2

, coefficient of determination is the squared value of the correlation coefficient, r. It is 

the proportion of variance that is accounted for by a linear relationship between the 

variables.

Reaction Time is the time between the presentation of a sensory stimulus and the 

response to that stimulus. It is a measure of mental processing speed. In the laboratory, 

subjects are instructed to respond as fast as possible to the appearance of the stimulus. 

Generally, a maximum duration to respond is set before a trial is ended. Failure to 

respond within the maximum duration is considered a lapse (see above). Reaction time 

should not be confused with response latency, which refers to a response time that is not 

cued for an “as fast as possible” response.4

Sleep Deprivation refers to a person obtaining less than a normal amount of sleep 

(approximately 8 h in a 24-h period).

Sleep Inertia refers to a lack of alertness and a decline in motor dexterity immediately 

following an abrupt awakening. 

Sensitivity means that a fatigue model output is readily affected or changed by variables 

such as sleep deprivation and circadian phase changes.

Sleep Recovery refers to a person obtaining more than a normal amount of sleep 

(approximately 8 h in a 24-h period) following a period of sleep deprivation (see above).

Statistically Reliable has the same meaning as statistically significant (see below).

Statistically Significant in hypothesis testing means that the outcome of a statistical test 

is unlikely to have occurred by chance. Chance is usually defined as a probability less 

than 0.05. 

Vigilance Speed (see Reaction Time above).

 4 See Dinges and Powell, 1985. 
17

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