PLATSUM report – Data analysis and inference
Distribution of gender and personality traits:
M F
T 97 10
F 25 5
Usually F is dominating among women, but here 66% of the females are of type T (thinking) which is
likely for this technological study. The strong dominance of T (78%) in general is as expected.
M F
I 87 13
E 35 2
73% of the students are Introverted, which is another expected result since mathematics and technology studies tend to suit these types better than the Extroverted.
M
S 69
N 53
F
7
8
The distribution between iNtuitives and Sensing is more even for both genders, but a slight overweight of hands-on Sensing students among the males. Undergraduate mathematics courses tend in
the structure and teaching to be more adopted to S than N people traditionally, whereas higher level
mathematics require a higher level of abstraction which on average suits iNtuitives better.
M
J 92
P 30
F
9
6
There is an overweight of Judging types (74%), which is also as expected since engineering and math
ematics are subjects that often require firm structure, detail focus, discipline and order. The Perceive
rs thrive better with flexible structures, explorative teaching and complexity, which again is more suit
ed for more theoretically oriented subjects in mathematics.
From these summaries we can see that the most probable personality type among the students is th
e ISTJ (in terms of the Myers-Briggs Type Inventory). Below are summary numbers for the 16 persona
lity types and a barplot in Figure 1 supporting this. In total 46.7% of the students belong to either the
ISTJ or the INTJ types, which is a heavy over-representation compared to a normal population.
Counts
ENFJ ENFP ENTJ ENTP ESFJ ESTJ ESTP INFJ INFP INTJ INTP ISFJ ISFP ISTJ ISTP
7
2
5
9
2
9
3
5
3
22
8
9
2
42
9
Percentages
ENFJ ENFP ENTJ ENTP ESFJ ESTJ ESTP INFJ INFP INTJ INTP ISFJ ISFP ISTJ ISTP
0.05 0.01 0.04 0.07 0.01 0.07 0.02 0.04 0.02 0.16 0.06 0.07 0.01 0.31 0.07
Figure 1: Counts for the 16 personality types among the 137 students. The ISTJ and the INTJ are the
most dominating types among the students on these courses.
The effect of personality trait on expected exam scores
Based on the findings of Sæbø et al., 2015, it is expected that traditional teaching in mathematics sho
uld favorize (in terms of leading to better exam results)
I over E, J over P and T over F. They did not find any difference between N and S.
With regard to expected grade for introverts and
for extroverts, we therefore test the hypoth
eses:
versus
Since lower grade is better.
We will do this separately for each of four mathematics courses. Below are the test statistics (Two-sa
mple T-test, equal variances in both groups) and p-values.
Mathematics 1 (M1):
T = - 0.54736,
p-value = 0.29,
df = 52
Mathematics 2 (M2):
T = 0.27,
p-value = 0.61,
df = 52
Discrete mathematics (DM): T = -2.25,
p-value = 0.014,
df = 81
Mathematical analysis (MA): T = -1.48,
p-value = 0.07,
df = 81
M1 and M2 are taught at Faculty of Electrical Engineering and Communication, whereas DM and MA
are taught for students at Faculty of Information Technology. Only DM shows a significant better (tes
t level 5%) expected exam score for introverts than for extroverts, although the test for MA is border
line to be significant. It appears that the I/E difference matters for the information technology studen
ts, but not for the engineering students in the given subjects.
Similarly we test for expected scores of J versus P:
versus
Mathematics 1 (M1):
T = - 2.15,
Mathematics 2 (M2):
T = -0.75,
Discrete mathematics (DM): T = -0.69,
Mathematical analysis (MA): T = 0.25,
p-value = 0.018,
p-value = 0.23,
p-value = 0.25,
p-value = 0.60,
df = 52
df = 52
df = 81
df = 81
Only for M1 the null-hypothesis is rejected, hence for the other courses there is no significant differe
nce in expected exam score between judging and perceiving types. The judging types appears to do b
etter in M1.
For expected scores of T versus F:
versus
Mathematics 1 (M1):
T = - 0.15,
Mathematics 2 (M2):
T = 0.63,
Discrete mathematics (DM): T = -3.05,
Mathematical analysis (MA): T = -2.33,
p-value = 0.44,
p-value = 0.73,
p-value = 0.0015,
p-value = 0.011,
df = 52
df = 52
df = 81
df = 81
Here for both courses lectured for the information technology students, there is a significant better e
xpected grade for Thinking types than for the Feeling types. We should keep in mind that the numbe
r of Fs is small in the data set, although the tendency is quite clear.
For the difference between N and S the study of Sæbø et al. 2015 showed no difference in expected g
rade, but the results there pointed in the direction of better grades for S than N. Here we test this dif
ference with a two-sided alternative:
versus
Mathematics 1 (M1):
T = - 0.37,
p-value = 0.36,
df = 52
Mathematics 2 (M2):
T = 0.22,
p-value = 0.59,
df = 52
Discrete mathematics (DM): T = 0.73,
p-value = 0.47,
df = 81
Mathematical analysis (MA): T = 0.61,
p-value = 0.55,
df = 81
In accordance with Sæbø et al. 2015, we find no significant effect of the N/S trait on the expected ex
am scores in the given subjects.
Summary:
We can see that these results are somewhat in accordance with the results of Sæbø et al. for the DM
and MA courses taught at Faculty of Information Technology. The engineering students at Faculty of E
lectrical Engineering and Communication show less effect of personality trait on expected exam score
with M1 as the only exception for which the Judging types do better than the Perceivers. The thinking
types tend to make decisions based on pure logic, and information technology is a subject purely base
d on logics. There is probably more room for the Feeling types in engineering mathematics, although t
hey are outnumbered by the T’s in general. Sæbø et al. found that I, T and J’s tend to do better in und
ergraduate courses in mathematics and statistics, and as far as there are significant findings here, the
y are in accordance with Sæbø et al. They concluded that the reason why these types do better may b
e that their cognitive styles are favored by the manner these courses are taught. A more dialogue bas
ed, explorative, motivation driven lecturing style may suit the E, F and P types better.
Do the attendance on lectures depend on personality trait?
A contingency test was run with the attendance levels (1,2,3,4) and trait (I,E) as factors. The nullhypothesis to be tested is the independence between these two factors. If the null is rejected there is
a difference between traits with regard to attendance on lectures.
The 2 by 4 frequency table for these factors are in the autumn courses (M1 and MD) is as follows. The
column factor is the attendance level where 1 = attending all lectures, 2 = more than half, 3 = less than
half, and 4 = no lectures. (The results are approximate due to low counts for level 4 of attendance.)
Frequency table:
1 2 3 4
I 51 36 11 2
E 17 13 4 3
The Pearson test statistic was Q = 2.90, p-value = 0.41. There appears to be no difference in Lecture
attendance between Introverts and Extroverts.
For the spring courses M2 and MA the results were:
Frequency table:
1 2 3 4
I 43 26 18 13
E 11 12 11 3
Q = 3.92, p-value = 0.27. No significant difference between I and E.
For J versus P for M1 and MD:
Frequency table:
1 2 3 4
J 56 36 5 4
P 12 13 10 1
Q = 15.35, p-value = 0.0015. The null-hypothesis is rejected at all reasonable test levels indicating that
Judging and Perceiving students attend lectures at a different extent. Inspecting the differences
between expected (under the null hypothesis) and the observed reveals that the main difference is
due to the high number of Perceiving students that attend less than half of the lectures (10 observed
versus 4 expected).
For J versus P for M2 and MA:
Frequency table:
1 2 3 4
J 46 28 19 8
P 8 10 10 8
Q = 9.32, p-value = 0.025. Also here the Perceivers attend lectures at a lower level than the Judging
types.
For F versus T for M1 and MD:
Frequency table:
1 2 3 4
T 56 36 12 3
F 12 13 3 2
Q=2.32, p-value = 0.51. No difference between F and T with regard to attendance.
For F versus T for M2 and MA:
Frequency table:
1 2 3 4
T 42 29 24 12
F 12 9 5 4
Q=0.53, p-value = 0.91. No difference between F and T with regard to attendance.
For N versus S for M1 and MD:
Frequency table:
1 2 3 4
S 39 31 5 1
N 29 18 10 4
Q=6.83, p-value = 0.07. Borderline to be significant at 5% test level. A tendency to N’s attending class
to a lesser extent.
For N versus S for M2 and MA:
Frequency table:
1 2 3 4
S 28 25 15 8
N 26 13 14 8
Q=2.28, p-value = 0.52. No difference between N and S with regard to attendance.
With regard to attendance to exercises there was no differences between introverts and extroverts
for any course. However there was a significant (p=0.011) tendency that Thinkers attend exercises
more than the Feeling types for courses taught in the spring (M2 and MA). Also Judging types tend to
attend exercises significantly more than the Perceivers in both autumn and spring courses (p = 0.007
and p<0.001). For the N/S trait there were no significant differences in any course (Results not shown).
Summary: The main difference in attendance level at lectures and exercises is between the Judging
types and the Perceiving types. The Judging types tend to appreciate structure and order, which they
probably find in the way most mathematics courses are taught. The Perceivers thrive better if teaching
is more flexible and driven by exploration and motivation, less by listings of theorems and computation
formulas. They tend to be a bit bored by too much external structure and order and tend to dislike
repetitive work like solving numerous similar exercises. The P’s often understand quickly what is
lectured, but they often lack the discipline needed for automation of new knowledge. They need the
repetition through solving exercises just as much as the Judging types, but they need to be “tricked”
into it. Also they tend to procrastinate more than the J’s, hence they may postpone studies for later
and for self-study. The other personality traits showed no significant differences with regard to
attendance level on lectures.
How do people prefer to be taught?
In the study by Sæbø et.al they found that preferred learning style was tightly connected to the
personality traits. The Feeling types tend to prefer a learning style where the teacher is an Integrator
that through dialogue inspires and motivates the students. The iNtuitives, Perceivers and Extroverted
tend to be inspired by teachers that are Entrepreneurs that nourish their creativity to be designers and
to invent or discover the topic on their own without top-down control from the teacher. This is in
contrast to the Judging, Sensing, Thinking and Introverted types which thrive better under a control
regime with a firmer leadership and teacher instruction where the teacher is more a Producer or an
Administrator.
We compared trait with respect to expected scores for the preference for the various learning styles
using two-sample t-tests. Hypothesis tests with two-sided alternative and assumed equal variances in
both groups were used.
The results are summarized as follows:




Introverts have a higher expected score on Administrator than extroverts (p=0.003), whereas
Extroverts tend to have a higher expected score on Entrepreneur (borderline significant,
p=0.06) than introverts.
For Judging versus Perceiving types we found no significant differences in preferred learning
style.
Feeling types have higher expected score than Thinking types on Integrator (p=0.007)
Sensing types had a higher expected score on Administrator (p<0.001) and a lower expected
score on Entrepreneur (p<0.001) than the iNtuitive types.
These findings were supported by a Principal Component Analysis on the data matrix containing the
personality scores and the learning style preferences. A combined score and loadingsplot is shown in
Figure 2. The first principal axis is plotted vertically and the second principal axis on the horizontal in
order to make the plot comparable to the corresponding plot in Sæbø et al. 2015 and the illustrations
in Brovold 2014. Scores (downscaled by a factor of 6.7 to fit into the range of the loadings) of each
student is marked with the four letter MBTI type in grey color. We observe the clear clustering of
students with similar types, with ENTP up to the right, ISTJ down to the right, ISFJ down to the left and
ENFJ up to the left, for instance. The placements relative to the origin is in high accordance with what
was expected according to the findings in Brovold 2014 and Sæbø et al., 2015. In red color the loadings
(variable weights) defining the principal components are superimposed on the scores, and the type
indicators are located in the same relative directions from the origin as the MBTI type clusters of the
students. In blue color the loadings of the preferred learning styles are also plotted. We observe that
Administrator style (Adm) is associated with the I, J and S types in the lower part of the plot. The
Integrator (Int) style is associated with the F type on the left, and the Entrepreneur (Ent) is associated
with the E, N and P types. The Producer type is close to the origin with no clear association to any
personality trait.
Figure 2: Scores- and loadingsplot from a PCA on personality types and scores for preferred learning
styles.
Summary:
All the significant differences between personality types with regard to preferred learning style is in
accordance with the results found by Sæbø et al., 2015. It is an open question for further research
whether the preferred learning style actually leads to best learning, but insofar as students have the
ability to choose the learning style they believe is the best, and these styles and personality types show
consistent patterns across this and previous studies, it is reasonable to believe that there is a difference
between personality types with regard to good learning.
References:
Sæbø, S., Almøy, T., and Brovold, H. (2015) Does academia disfavor contextual and extraverted
students? UNIPED, 38(4) p. 274-283
Brovold, H. (2014) Invarians drøftet i et nevropsykologisk perspektiv med spesiell referanse til
realfaglig kognisjon. (The problem of invariance/permanence in a neuropsychological perspective with
special reference to mathematical cognition). Ph.D. thesis, Psykologisk Institutt, NTNU, 2014