Mental Fatigue Data

Submitted by Stephen J. Guastello

Early 20th Century psychologists were greatly interested in the dynamics
of physical fatigue. This work was socially influential because it 
convinced factory employers that productivity would increase if workers
were given work breaks! The dynamics indicated that there was a system
of work curves that was characterized by a cubic polynomial. It took
just a trick of the pencil, plus 60 years to determine that the underlying
dynamics were those of the cusp catastrophe (Guastello, 1995; Guastello
& McGee, 1987).

It was also proposed that mental fatigue followed the same dynamics.
Ash (1914) conducted such experiments and, fortunately, reported the
original data points. He found the basic work curve that characterized
physical work in mental work data. This function was later shown to
follow a cusp catastrophe regime also (Guastello, 1995). The mental
fatigue problem has a special quirk in that the repeated tasks that
contribute to fatigue, which translates into an increase in response
time, also constitutes practice, which translates into a decrease in
response time. A different dynamical perspective on this interesting
problem has been recently undertaken by Aks & Sprott (in press).

An annotated SPSS control program, which operates the data set,
appears below. It is written in mainframe syntax, which is how
the data were analyzed for the publications. The fourth program
line defines the name of the variables and the spaces that they
occupy within a line of data.

Subjects in the experiment were university professors. They were
presented with Necker Cubes and Necker Pyramids; their task was to
produce a reversal of the figure and hit a response button. Response
time was measured in seconds. Response times were averages of several
trials, although the exact numbers of trials was never stated in the
original document. The elaped amount of mental work was hours of
exam grading during final exam week.

The data set was compiled by SJG from tables published in Ash (1914),
and was the basis of the analyses described in Guastello (1995, p. 184-
185, 201-104). The variables are: NAME = initials of the human subject;
names are not known, and do not figure into the analysis. STIM refers
to the cube or pyramid. The numerical value "12" refers to the pyramid,
and "9" to the cube. The SPSS control program converts those values 
into 1 and 0, repectively. RTBEF is response time to reverse a figure
before a fatiguing work set. RTAFT is the response time after the work
set. FATUN, or fatigue units, is the number of hours of exam grading
that transpired between the before and after measures. PRAC indicates
whether a subject had participated in a previous before-work-after
session; 0 = had not done so, 1 = did do so.

REFERENCES

Aks, D. J., & Sprott, J. C. (in press). The role of depth and 1/f
in perceiving reversible figures. Nonlinear Dynamics, Psychology,
and Life Sciences, 7.

Ash, I. E. (1914). Fatigue and its effects upon control. Archives
of Psychology, v. 31.

Guastello, S. J. (1995). Chaos, catastrophe, and human affairs:
Applications of nonlinear dynamics to work, organizations, and 
social evolution. Mahwah, NJ: Lawrence Erlbaum Associates.

Guastello, S. J., & McGee, D. M. (1987). Catastrophe modeling of
fatigue in physically demanding jobs. Journal of Mathematical
Psychology, 31, 248-269.

SPSS:

title ash fatigue all p. 38 + 41, cusp and nl
file handle datafile  name='mfatigue1a.dat'
data list file=datafile records =1
 /1 name 1-4(a) stim 6-7 rtbef 9-12 rtaft 14-17 fatun 19-21 prac 23
recode stim (9=0) (12=1)
COMMENT NAME consists of the initials of subjects who were university
 professors. The mental work that they did between response time se
*temporary 
*select if (prac =0)
*condescriptives rtbef rtaft
*temporary
*select if (prac =1)
*condescriptives rtbef rtaft
regression descriptives/ missing=pairwise
 /variables stim to prac
 /dependent = rtaft
 /enter rtbef stim fatun prac
compute dy = rtaft - rtbef
regression descriptives/ missing=pairwise
 /variables = stim fatun prac dy
 /dependent = dy
 /enter stim fatun prac
compute zbef0 = (rtbef - .69)/ 0.46
compute zaft0 = (rtaft - .69)/ 0.77
compute zbef1 = (rtbef - .69)/ 0.31
compute zaft1 = (rtaft - .69)/ 0.57
if (prac = 0) z1 = zbef0
if (prac = 0) z2 = zaft0
if (prac = 1) z1 = zbef1
if (prac = 1) z2 = zaft1
compute dz = z2 - z1
compute zpow3 =  z1**3
compute zpow2 =  z1**2
compute nfatun = fatun/ 0.886
compute bifur =  z1*nfatun
regression descriptives/missing=pairwise
 /variables = zpow3 zpow2 bifur prac dz
 /dependent = dz
 /enter zpow3 to prac