Diurnal variation in logical reasoning

Abstract

Subjects performed two tests of logical reasoning at each of six different times of day. In terms of speed, preformance on both tests was found to improve markedly from 08.00 to 14.00 and then to fall off fairly rapidly. Accuracy was found to decrease fairly linearly over the day. The results are interpreted as indicating that the different functions relating performance efficiency to time of day found by previous workers are due to differences in task demands rather than to individual differences. It is suggested that the larger the short-term memory component of a task the earlier in the day performance peaks.

Full text

Br.
J.
Psychol.
(1976),
66,
1,
pp.
1-8
Printed
in
Great Britain
DIURNAL VARIATION IN LOGICAL REASONING
BY
SIMON
FOLKARD
MRC
Applied Psgchology Unit, Laboratory
of
Experimental Psychology,
University
of
Sussex
Subjects performed two tests of logical reasoning at each of six different times of day. In
terms of speed, performance on both tests was found to improve markedly from 08.00
to
14.00 and then to fall off fairly rapidly. Accuracy
was
found to decrease fairly linearly over the
day. The results are interpreted as indicating that the different functions relating performance
efficiency to time of day found by previous workers are due to differences in task demands
rather than to individual differences. It is suggested that the larger the short-term memory
component
of
a task the earlier in the day performance peaks.
While
it
is well established that performance on
a
wide range of tasks varies with
time of day (e.g. Blake,
1967a),
the precise nature of this variation is
a
matter of
continuing debate (Freeman
&
Hovland,
1934;
Kleitman,
1963;
Conroy
&
Mills,
1970;
Colquhoun,
1971;
Hockey
&
Colquhoun,
1972).
Freeman
&
Hovland
(1934)
in an extensive review of the early literature distinguish between four different types
of function that have been found
(a)
a continuous rise through the day,
(b)
a
con-
tinuous fall,
(c)
a
morning rise followed by an afternoon fall, and
(d)
a morning fall
followed by an afternoon rise.
More recently there has been a tendency to dismiss the early work on which these
functions are based as being poor in methodology, using inadequate sample sizes,
or
inadequate
or
inappropriate techniques of performance measurement. Alternatively,
differences between functions have been attributed to individual differences. In this
context the work of Blake
(1967a, 1971)
showing the circadian rhythm of introverts
and extraverts to differ, and that of Patkai
(1971),
which distinguishes between
‘morning’ and ‘evening
’
people, has proved most useful. However, while this
research has proved invaluable in accounting for minor inter-individual differences
it
cannot account for either intra-individual differences between tasks,
or
for inter-
individual differences
as
diverse
as
a
continuous rise
or
fall.
A
more valuable approach, suggested by Hockey
&
Colquhoun
(1972),
is that
performance on different types of task may show different functions. Studies of
time of day effects on short-term memory, probably the most extensively studied
type of task, suggest that performance improves slightly from early to mid-morning
and then shows
a
fairly steady fall over the rest of the day. While
a
number of such
studies have tested
at
only two times of day, e.g. Baddeley
et
al.
(1970)
who found
a decrease in digit span from mid-morning to mid-afternoon, the author has been
unable to find any published studies that are inconsistent with such an interpretation.
Further, this function must be regarded as having considerable generality in that
it has been found with both male and female school children (Winch,
1912a,
b;
Gates,
1916a),
naval ratings (Blake,
1967a)
and undergraduates (Gates,
1916b;
Baddeley
et
al.,
1970),
using a variety of tests ranging from digit span (Blake,
1967a;
Baddeley
et
al.,
1970)
to memory for items within
a
story,
or
to associative
learning (Gates,
191 6
b)
.
I P
s
Y
66

2
SIMON
FOLKARD
Blake
(1967~)
and Baddeley
et
al.
(1970)
account for this mid-morning superiority
of short-term memory in terms of an arousal theory. In doing
so,
they draw on the
suggestion that arousal increases through the day (Kleitman,
1963;
Colquhoun
et
al.,
1968a,
3)
and on the finding that short-term memory is impaired under conditions
of high arousal (e.g. Kleinsmith
&
Kaplan,
1963;
Walker
&
Tarte,
1963;
McLean,
1969).
The suggestion that arousal level increases through the day
is
based on the
finding that both body temperature (Blake,
19673;
Colquhoun,
1971)
and perform-
ance on
a
number of different tasks, such as cancellation, card-sorting and calcula-
tions (Blake,
1967
a),
shows a fairly continuous rise through the day and peaks at about
8p.m. Typically the tasks that show this ‘continuous rise’ involve little if any
memory load and have been characterized by Alluisi
&
Chiles
(1967)
as involving
‘performance stress’ and by Hockey
&
Colquhoun
(1972)
as demanding ‘a more
immediate processing (or “throughput
”)
of information’. Thus they all require sus-
tained attention and in most cases are timed and therefore involve considerable
speed stress. Blake
(1967a)
also noted that in the self-paced tasks used it was speed
rather than errors that proved to be sensitive to time of day.
It
seems reasonable to conclude that performance on tasks with
a
high memory
load that demand little immediate processing shows an effectively continuous
fall through the day, whereas performance on those involving immediate processing
with little memory load shows an effectively continuous rise apart from
a
more or
less pronounced ‘post-lunch’ decrement (Blake,
1967~;
Colquhoun,
1971).
However,
as Hockey
&
Colquhoun
(1972)
point out, most tasks involve both processing and
memory, and tasks of this type have received little attention with respect to time
of day. The present study attempts to remedy this situation using two tests of
logical reasoning ability. The
first
of these was developed by Baddeley
(1968)
and
is
based
on
grammatical transformation. Performance on
this
task has been found
to correlate significantly with
I&
and to be sensitive to
a
variety of different stresses
(Baddeley,
1968).
The task is self-paced and can therefore be regarded as demanding
coiisiderable immediate processing. In addition, Hitch
&
Baddeley
(1 973)
have
shown the task to involve acoustic
or
articulatory coding and the use of some
limited capacity processor that
is
also involved in short-term retention of verbal
material.
It
thus seems reasonable to suppose that this task involves both short-term
memory and immediate processing. This task has not previously been used in time
of day studies.
The second task used involved the separation of true from false syllogisms.
It
was originally developed by Hertzka
&
Guilford
(1955)
and extended
by
Fort
(1968)
for use in
a
time of day study. Unfortunately, the design of this study was such
that the subjects could have been suffering from anything up to
40
hours’ sleep
deprivation at some but not all of the times tested. In view of this unbalanced
design and the fact that Alluisi
&
Chiles
(1967)
report that some of the tests they
used were only sensitive to time of day effects when the subjects were suffering
from sleep deprivation, the results of Fort’s study should be interpreted with
caution. Nevertheless,
it
is
interesting to note that performance on this task was
found to peak earlier in the day than performance on
a
test of motor coordination.

Diurnal variation
in
logical reasoning
3
METHOD
Subjects
The subjects were
19
female and
17
male students from the University of Sussex. They had
an age range of
18-24
years and the experiment was carried out in two stages. In the first stage
18
psychology students were divided into pairs within which they acted
as
experimenter and
subject for one another. These students were not naive
as
to the general effects of time of day
on performance efficiency, but were naive
as
to the specsc predictions made in this study.
In the second stage
18
non-psychologists who were naive
as
to the possible influence of time of
day on performance were tested in pairs by the author. These latter subjects were paid at the
rate of 50p per hour.
Materials
Six different versions of each of the two tests were prepared. An item in the grammatical
transformation test consisted of
a
sentence describing
a
relationship between the letters ‘A’
and ‘B’ followed by either the letter pair AB
or
the letter pair BA. The subject’s task was simply
to decide whether the sentence (e.g.
‘B
is
not preceded by A’) was
a
true
or
false description of
the letter pair that followed. On each of the six versions of the test the
32
possible items were
each represented twice. The six versions differed from one another only in terms
of
the order
of the items.
The logical syllogism items consisted of two statements followed by four possible conclusions
only one of which followed logically (e.g. No birds are insects. All swallows are birds. Therefore
(i)
Some birds are not swallows,
(ii)
All birds are swallows, (iii)
No
swallows are insects, (iv)
No
insects are birds). The subject’s task was to indicate which of the four alternatives followed
logically from the two statements. Each of the six versions
of
this test consisted of
a
different
set of
24
items.
Design and procedure
Each subject was tested
at
each of six different times of day:
08.00,
11.00,
14.00,
17.00,
20.00
and
23.00
hours. A cyclic latin-square design was used in which an equal number of subjects
had their first session at each of the six times.
For
the six subjects that had their first session at
08.00
the experiment
was
completed in
a
single day
(15
hours) while for all other subjects
the testing was spread over two consecutive days
(21
hours) with
a
normal period of sleep allowed
between the two. The use
of
this design allows separate estimates to be made of time of day,
session (i.e. practice and/or fatigue) and interaction effects. However, like all repeated-measure,
latin-square designs
it
suffers from the disadvantage that session effects are assumed to be equal
in each of the six subgroups. Within each subgroup of six subjects, half the subjects always
did the Baddeley reasoning test first, while the other half did the logical syllogisms first with
a
rest of
3
min. allowed between the two.
At the beginning of the first session subjects were given worked examples of both tests and
full written instructions
as
to how to do them. They were told that they would be allowed
3
min.
on each test to complete
aa
many items
as
possible. In the event of
a
subject completing
all the items in less than
3
min. the stopwatch was stopped and the analysis based on an estimate
of the number that could have been completed. They were also told not to waste time on any
one item
as
they would be scored simply on the total number that they had correctly com-
pleted. On subsequent sessions the written instructions were made available if required, and
subjects were simply encouraged to work
as
quickly
as
possible. At the end of each session the
subject’s oral temperature was taken with
a
standard clinical thermometer inserted sublingually
for
exactly
3
min. The subjects were given no practice on either of the two tests before the
first,
or
any subsequent, session. Each subject was given
a
different random order of the six
versions of the two tests.
RESULTS
Preliminary analyses indicated that the results from the two stages of the experi-
ment did not differ significantly and analyses were therefore based on the pooled
1-2

4
SIMON
FOLKARD
36.4
08.00
11.00
14.00 17.00 20.00 23.00
Time
of
day
Fig.
1.
Oral
temperature
as
a
function
of
time
of
day.
results. Separate analyses were based on (i) oral temperature, (ii) the number of
grammatical transformation items attempted,
(iii)
the number of logical syllogisms
attempted, (iv) the percentage of grammatical transformation items correct, and
(v)
the percentage of logical syllogisms correct. Thus the two logical reasoning tests
were analysed in terms of both speed (number attempted) and accuracy (per cent
correct). In
all
cases latin-square repeated measure design analyses of variance
(Winer,
1970,
p.
539,
plan
5)
were used.
The analysis of oral temperature indicated that there was
a
significant time of
day effect
(P
=
26.41;
d.f.
=
5,
150;
P
<
0.001)
and this
is
shown in Fig.
1.
Both
the logical reasoning tasks showed
a
significant time of day effect in terms of the
number attempted (grammatical transformations:
P
=
3.59,
d.f.
=
5,150,
P
<
0.01
;
logical syllogisms:
P
=
2-34,
d.f.
=
5,
150,
P
<
0.05).
These effects are shown in
Fig.
2
and were further analysed using Duncan’s multiple-range test. These tests
indicated that on the grammatical transformation test there was an increase in
speed from
08.00
to both
11.00
(P
<
0.01)
and
14.00
(P
<
0.001),
followed by a
deterioration from
14.00
to
23.00
(P
<
0.05).
Similarly, on the logical syllogisms
test speed improved from
08.00
to both
11.00
(P
<
0.05)
and
14.00
(P
<
0-05)
but
had deteriorated again by
17.00
(P
<
0.05).
No other comparisons were significant.
The percentage of items correct on each of the two logical reasoning tasks is
plotted against time of day in Fig.
3.
Neither of the analyses based
on
these data
showed significant main effects of time of day (grammatical transformation
:
P
=
1.75,
d.f.
=
5,
150,
P
>
0-05;
logical syllogisms:
P
<
1,
d.f.
=
5,
150,
P
>
0.05).
However, linear components were extracted and in both cases these accounted
for
a
large proportion of the variance associated with time of day (grammatical trans-

Diurnal variation
in
logical reasoning
5
g
50
2
.s
49
0
a
2
B
2
48
cj
L
-
3
2
'=
47
E
E
,"
46
0
45
12.0
0
0
a
.-
#
on
0
11.5
.-
3
M
0
L
0
-
08.00 11.00 14.00 17.00 20.00 23.00
Time
of
day
Fig.
2.
Number of
items attempted on the grammatical transformation
(0-0)
and logical syllogisms
(0
-
-
-
0)
tests
as
a
function
of
time of day.
96
v)
C
0
m
.-
Y
s
95
C
i?
*
-
m
.-
3
2
94
6
3
'E
L
0
I
0
e
93
s
92
1
I
I
I
I
I
08.00 11.00 14.00 17.00 20.00 23.00
Time
of
day
Fig.
3.
Percentage
of
items correct on the grammatical transformation
(0-e)
and logical syllogisms
(0
-
- -
0)
tests
as
a
function of time
of
day.

6
SIMON
FOLKARD
formation,
88
per cent; logical syllogisms,
67
per cent) although only in the ca.se of
grammatical transformation did the linear component achieve significance
(F
=
7.70,
d.f.
=
1, 150; P
<
0.01).
DISCUSSION
AND
CONCLUSIONS
It
is clear from the results that, in terms of speed, performance on tests of logical
reasoning is
at
its
best considerably earlier in the day than performance on the
‘immediate processing’ tasks employed by Blake
(19674.
Further, the similarity
between the temperature curve obtained here and that found by Blake
(19673)
suggests that this difference is not due to the use of students as subjects instead of
naval ratings, but to the nature of the tasks employed. Thus
it
seems reasonable to
assume that in terms of speed, tasks involving both ‘immediate processing’ and
memory show what Freeman
&
Hovland
(1934)
characterized as
a
morning rise
followed by an afternoon fall. However, in terms of accuracy the results seem best
described in terms of a continuous fall over the day.
There are several possible explanations of these results. Probably the simplest
explanation is in terms of an inverted-U shaped function relating performance
efficiency to arousal level (Freeman,
1948).
Such
a
concept is used by Colquhoun
(1971)
to account for the findings of Alluisi
&
Chiles
(1967)
that diurnal fluctuations
in performance efficiency are more marked when subjects are suffering from sleep
deprivation. Colquhoun
(1971)
points out that
a
given change in arousal level due
to time
of
day will have a more marked effect on performance when the overall level
of arousal
is
relatively low due to sleep deprivation than when
it
is
near optimal. In
the present case
it
is also necessary to invoke the assumption that the optimal level
of arousal decreases with increasing task complexity. Thus the more complex the
task the earlier in the day it should peak. The difficulties in such an approach
are
that
(a)
it
is
extremely difficult to order an assortment of tasks in terms of ‘com-
plexity’, and
(b)
that
it
cannot account for the decrease in accuracy over the day.
An alternative explanation is that as arousal increases through the day
so
per-
formance on the immediate processing components of
a
task improves while per-
formance on the memory components of
a
task declines. Thus
in
terms of speed,
performance should improve due to increased processing speed with increasing arousal
up to some critical point when the memory capacity has been reduced to such an
extent by the increase in arousal that it is no longer capable of ‘keeping up’ with
the processing rate. If accuracy is seen
as
primarily dependent on the memory
capacity, rather than on the processing capacity, then it follows that as arousal
increases through the day accuracy should decrease.
In view of the suggestion of Folkard
&
Greeman
(1974),
that under high arousal
subvocal articulation
is
inhibited,
a
slight variant on this latter explanation is
possible. Namely, that increasing arousal does not directly affect memory capacity
or rate of decay, but rather acts by inhibiting the articulation which has been shown
to be involved in both short-term memory (Baddeley,
1966;
Murray,
1967, 1968;
Levy,
1971
;
Peterson
&
Johnson,
1971)
and the grammatical transformation test
(Hitch
&
Baddeley,
1973).
In conclusion, it is reasonable to assume that the different functions relating

Diurnal variation
in
logical reasoning
7
performance efficiency to time of day discussed by Freeman
&
Hovland
(1934)
are
attribut,able to differences in task demands rather than to individual differences.
Further, it seems clear from Figs.
2
and
3
that different measures of performance
efficiency (i.e. speed and accuracy) may show very different functions. In general,
it
seems that the higher the memory
or
articulatory component of a task the earlier
in the day performance on such a task peaks. The only function discussed by Freeman
&
Hovland
(1934)
that such a statement cannot account for is the morning fall
followed by an afternoon rise. However, Freeman
&
Hovland cite only eight studies
that fall into this category as opposed to
31,
17
and
14
respectively in the other
three categories. Indeed, of these eight only three report any measure of reliability,
while in at least one
of
these three (Hollingworth,
1914)
Freeman
&
Hovland’s
morning fall followed by an afternoon rise can be better described as a relative lack
of any time of day effect apart from a fairly pronounced post-lunch decrement
(Blake,
1967~;
Colquhoun,
1971).
The first stage of this experiment formed part of an undergraduate human performance
laboratory course.
I
should like to thank Dr Ann Fort and Professor Alan Baddeley for supplying
me with copies
of
their tests.
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