Transcript Brain Teasers - Mathematics Department : Welcome

Brain Teasers
 Brought to you
by:
Are Dartmouth students
this anxious under time
pressure?
 Yifat Tamir
 David Anderson
 Kaylie Dienelt
 Mirelle Phillips
Introduction
•
Getting admitted to
Dartmouth College requires
the combination of high SAT
scores, strong grades, and
involvement in extracurricular activities.
•
Performing well on a test
such as the SAT correlates
with an ability to maintain
high performance under time
pressure.
•
But does time pressure help
or hinder cognitive
performance?
•
The Test: Nervous yet?
Choosing the Brain Teaser Task:
Selection of Participants:
– Somewhat cerebral, but still
fairly simple
– Short and sweet
– Lack of associated prior
sense of anxiety
– Two experimenters assigned
to each subject group
•
Two groups: one low-pressure
(untimed) and one high-pressure (time
limit)
•
HP group was told the mean time
needed to complete brain teaser task
for participants in LP scenario.
– Random selection of
participants across a number
of campus locations (collis,
hop, baker, novack)
•
Does this foster a sense of
competition or anxiety?
– 30 LP, 30 HP subjects
– Each participant tested
individually so as not to
increase any group-oriented
competitiveness
– Results would be analyzed
both for time and response
accuracy
The Test: Exposed
0
________________
Ph.D.
B.Sc.
B.A.
123safety456
Hypotheses: Will they freak out??
 Null Hypothesis:
There will be no difference
in the mean amount of time
it takes for each group to
complete the task.
 Alternate
Hypothesis: There will
actually be a difference in
the mean amount of time it
takes for each group to
complete the task.
Our Beautiful Thoughts: Can they
handle the PRESSURE?

We hypothesized two
possibilities for the effects of
pressure:

Subjects may take more
time to complete the task
due to anxiety induced by
time-pressure

Subjects may take less time
to complete the task because
they are already motivated
to perform well in highpressure, competitive
situations (by virtue of being
Dartmouth students).

These effects could have
confounded each other,
confusing the difference
between our means and
increasing variance.
Holy Platypus! What Brilliance!
But are there any significant
effects?
Results:
• The average time for the LP
group was 198 seconds (3
min. 18 sec.) with a standard
deviation of 89 seconds.
• Average time for HP group
(once told the average for LP)
was 221 seconds (3 min. 41
sec.) with a standard dev. of
144 seconds.
• But what about accuracy?!
Mathematical Shizzy:
Graphical
Comparison of Performance across Subject Groups
Times for High-Pressure Trial
900
900
800
800
700
700
Time (seconds)
Times (seconds)
Times for the Low-Pressure Trial
600
500
400
300
600
500
400
300
200
200
100
100
0
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29
Subjects
1
3
5
7
9
11 13 15 17 19 21 23 25 27
Subjects
Shooting in the Dark: Accuracy
across experimental situations
Correct Answers in High-Pressure Trial
8
8
7
7
Number of Correct Answers
Number of Correct Answers
Correct Answers in Low-Pressure Trial
6
5
4
3
2
1
0
6
5
4
3
2
1
0
1
3
5
7
9
11
13
15
17
Subjects
19
21
23
25
27
29
1
3
5
7
9
11
13
15
Subjects
17
19
21
23
25
27
Accuracy Issues:
Did some punks like to hit it
and quit it, or did they like to stay and play?
Average number of correct
answers in the low-pressure
group was 5.13 (out of 7)
with a standard deviation of
1.5.
 Average number of correct
answers in the high pressure
group was 5 with a standard
deviation of 1.5.


No real statistically significant
difference between group
accuracy
Our friend
Sir Mix-a-Lot
*******************************
•Had to remove one subject from
LP group: only answered two
teasers
•Removed three subjects from HP
group: two only answered a limited
number of teasers, and one was a
huge outlier (4 standard deviations
away from mean)
•Subject pool became 29 for LP
and 27 for HP.
Significance: means and sd’s- F-test
and t-test






To calculate the t-score for the difference
between two means, we used t = (x1 – x2)/ (s12/n 1
+ s2.52/ n2.5)
Our critical region required that t ≤ +1.671 or t ≥ 1.671
t = 0 = No significance
To calculate the difference in variance between the
two samples, we used F = s12/ s22
To be significant at a 5% level, F would have to be in
the range of 1.87-1.91
F = 1.27 = No significance
Discussion: Robbed of rightful results with the rebus

The problem with the “3 degrees below
zero” rebus.
0
________________

How the rebus might have skewed the
data in two directions:
–
–

students who spent too much time on one
rebus (more time)
students who just gave up (less time)
Perhaps we need a cognitive measure
that would make time much more of a
salient factor than accuracy.
Ph.D.
B.Sc.
B.A.
Ridiculous Rebus
Discussion Part Deux:
Faster, Hotter, and More All-Encompassing

Sampling Problems

Self-Selection:


After seeing the task, people could choose not to participate
and it is likely that people who are not familiar with or do not
like brain teasers would opt not to participate
Location:


Public area, Presence of other students: increased sense of
anxiety or competition (respectively)
Ideally, subjects would be isolated in a small room
Conclusion:
Overly verbose
suggestions for further, equally-awesome
projects
The results of the study indicate that applying pressure in the form of an
implied time constraint does not significantly affect cognitive
performance.
•
Potential mplications for the SAT and other high-stakes testing,
suggesting that there is not much truth to the claim that cognitive
performance is negatively affected by time constraints. On the other
hand, no one was really invested in our little task, so who really knows
what would happen under real pressure.
•
However, certain common characteristics of our participants should be
noted. As we might be able to assume at Dartmouth, the participants in
such an elite academic environment tend to have been trained to perform
well under timed conditions.
•
Therefore, we would recommend that future projects be performed on a
large population of students from many different grade-levels and
institutions, that a more time-oriented cognitive task be chosen, and that
the subjects be truly isolated in the testing situation.