Creativity and innovation
2013 – 2014
Research: a dual pathway to creativity, a
contradiction
T. Michiels1 *, F.S. Nobels1† , M. van der Laan2‡ , S.A. van Laar1#
Abstract
In this research the theory from De Dreu et al. that states that positive and negative activating mood lead to an increase
in creativity and that positive and negative deactivating moods lead to a decrease in creativity. This theory is tested on a
brainstorm group from Balinge that creates ideas on sustainable solutions. There is tested whether mood influences the
quantity of ideas and the variety of ideas. The results were that The positive activating mood was the best mood to create
ideas. In contrast with the hypothesis the positive deactivating moods also showed an increase of creativity. The negative
activating moods did not clearly lead to an increase in creativity of in the number of ideas. And the negative deactivating
moods did very clear lead to an decrease of creativity.
Keywords
Creativity — Dual pathway — Active mood — Deactive mood
1
Faculty of mathematics and natural sciences, University of Groningen, Groningen, The Netherlands
Faculty of Philosophy, University of Groningen, Groningen, The Netherlands
*Corresponding author: [email protected]
†
Corresponding author: [email protected]
‡
Corresponding author: [email protected]
#
Corresponding author: [email protected]
2
Contents
Introduction
1
1
2
Theoretical Background
2 Methods
2
2.1 Method 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Part 1 • Part 2
2.2 Method 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.3 Duurzaam Balinge . . . . . . . . . . . . . . . . . . . . . . . 3
3
3.1
3.2
3.3
Analysis of the data
Creativity coefficient . . . . . . . . . . . . . . . . . . . . . .
part 1 of analysing . . . . . . . . . . . . . . . . . . . . . . .
part 2 of analysing . . . . . . . . . . . . . . . . . . . . . . .
3
3
3
4
4
Results
4
5
5.1
5.2
5.3
Discussion and Conclusion
4
Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Acknowledgments
5
References
5
Introduction
The purpose of this research is to determine whether mood
influences the creativity and innovation in a particular team.
Our research is based on the theory of an article from De
Dreu et al. (2008) “Hedonic Tone and Activation Level in the
Mood–Creativity Link: Toward a Dual Pathway to Creativity
Model”. The main idea of this article is that activating moods,
positive and negative like happiness and angry, influences
the creativity in a positive way and deactivating moods, positive and negative like relaxed and depressed, influences the
creativity in a negative way. The theory also states that the
creative outcome from a positive activating mood differs from
a negative activating mood. The theory will be further defined and conceptualized in the theory section. Based on this
the hypothesis is that positive and negative activating moods
increase creativity and that positive and negative moods decrease negativity and that a positive mood results in different
outcomes than negative moods.
The research is done with a brainstorm group from the
village Balinge. This brainstorm group is a group of residents
of Balinge which generate ideas on sustainable solutions. The
group is chosen, because in the first place their goal is to
create ideas and that is what is investigated in this research.
In the second place this is a voluntary group. This means that
they are motivated to create ideas. And residents does create
ideas and take decisions for their own village and because the
residents are emotionally attached to the village creating ideas
and taking decisions can cause emotional situations.
To determine whether mood influences creativity and innovation some of the members of the brainstorm team are
interviewed. In this interview there is asked if the member in
a certain mood can create ideas of can devise solutions. The
subjects were also asked if they could determine the variety
and the quantity of ideas that was created during a moment of
Research: a dual pathway to creativity, a contradiction — 2/5
creativity. The outcomes of this results were not completely
that was expected. The positive activating mood was the best
mood to create ideas. In contrast with the hypothesis the
positive deactivating moods also showed an increase of creativity. The negative activating moods did not clearly lead to
an increase in creativity of in the number of ideas. And the
negative deactivating moods did very clear lead to an decrease
of creativity.
The conclusion of the research is that according to the
theory the positive activating moods lead to an increase in
creativity and negative deactivating moods lead to a decrease
of creativity. In contrast to the theory the positive deactivating
moods also lead to an increase in creativity and the negative deactivating moods did not clearly lead to an increase in
creativity.
1. Theoretical Background
De Dreu et al. (2008) Hedonic Tone and Activation Level
in the Mood–Creativity Link: Toward a Dual Pathway to
Creativity Model. [1]
Our theoretical framework is defined by the Dual Pathway
to Creativity Model which is set out in De Dreu et al. (2008).
De Dreu et al argue that mood states can be conceptualized
in two dimensions, namely their negative or positive tone as
well as their activating or deactivating nature (De Dreu et al.,
p. 740). The examples given by the authors are categorized
in the table below. In studying the effect of mood on creativity De Dreu et al. conclude that the activating nature of the
mood is the necessary prerequisite in generating creativity.
The outcome of this study refutes the common intuition that
negative moods can only have a negative effect on creativity.
The endresult of both paths is creative fluency and originality. The authors use this concept as the measure of creative
production, it consists in the number of nonredundant ideas,
insights, problem solutions or products generated. [1]
Table 1. Table of moods
Activating mood
Deactivating mood
Positive tone
Happy, elated
Calm, relaxed
Negative tone
Angry, fearful
Sad, depressed
Although negative mood states are thus equally able to
cause creativity, they do so in a different way compared to
mood states which have a positive tone. These differences
define the dual pathway-aspect of the mood-creativity link.
When a subject is in a positive mood state, he will realize a
creative result by means of cognitive flexibility and inclusiveness. Flexibility is a qualitative measure of creativity which
consists in the use of different cognitive categories. De Dreu
et al remark that flexibility can also be seen as a cognitive
process. They put forward this suggestion based on research
which state that in order to be creative, one must be flexible,
meaning to ability to break sets and to associate freely. [1]
When the mood state is negative the creative result can
still be realized with ‘hard work’. De Dreu et al. describe
this process as an in-depth exploration of few categories or
perspectives. This does not mean that a negative mood state
in combination with perseverance lead to fewer ideas. The
contrary is true, de dreu et al. report that all else being equal
generating many ideas in few categories even leads to more
ideas overall. Because there are only a few conventional or
unoriginal ideas per category, perseverance also yields a larger
number of original ideas. [1]
We will use the dual pathway to creativity model to study
Project Duurzaam Balinge. This initiative is aimed at enhancing sustainability in everyday situations. Duurzaam Balinge
consists in different workgroups in which citizens sit down
to generate sustainable ideas together. Although the subjects
cooperate in working groups we will be studying their creative performance on an individual level. Duurzaam Balinge
is the right team for this task because the working groups
are aimed at generating ideas. This enables us to study the
relation between mood and creativity of the subjects. [1]
2. Methods
2.1 Method 1
Method one consists of 2 parts, part 1 and part 2.
2.1.1 Part 1
In the first part we try to find the mood, the subjects felt during
a very creative meeting and the mood the subject felt during
a non creative meeting. Questions of this category tests, the
relationship between the creative result and the activating or
deactivating nature of the emotion experienced, see table 1 for
the different moods.
2.1.2 Part 2
In the second part we asked the subjects to remember a meeting where the subject felt a activating emotion. and asked
about the nature of the ideas and the amount of ideas, in other
words we asked if the ideas came from one categorie or from
many categories to check if there was cognitive flexibility
or cognitive persistence. After this we asked the subjects to
remember a meeting with a negative emotion, because the people from Duurzaam Balinge enjoy the meetings this negative
moods are felt less often, so we ask this specific.
2.2 Method 2
Because Method 1 was not succesfull we used a second
method to test the hypotheses of the relation of creativity
and the activating or deactivating nature of the emotion experienced. we made a new method. where the subjects where
asked about there experience with emotions and the experienced creativity. In other words we asked questions which
asked the amount of creativity they experienced with that specific emotion. we asked two questions per type of mood in
table 1, this was used to add a reliability to the data in the
analysis. This was done as follows, we looked at every taken
Research: a dual pathway to creativity, a contradiction — 3/5
Figure 1. An illustration of the dual-pathway to creativity model (De Dreu et al, p. 742)
question of the subjects and compared the same mood categories with each other of the same subjects question answers,
and used this to gain more accurate data.
2.3 Duurzaam Balinge
We approached the chairman of Duurzaam Balinge and asked
if Duurzaam Balinge wanted to participate in the research.
They wanted to participate in our research after which one of
use asked the interview questions to a member of Duurzaam
Balinge.
Duurzaam Balinge consists of men aged 40 to 70 years,
with various educations.
3. Analysis of the data
Our analysis of the data consists of 2 parts, in the first part we
analysed the data using non-weighted calculations, In other
words we didn’t used the multiple questions about the same
type of mood, to calculate a weight factor. In the second
part we calculated a weight factor to gain more precission.
Moreover in part 1 we calculated the statistical properties per
question and in part 2 we calculated the statistical properties
more general for all types of moods. We note that in method 1
part 1 we got a consistent answers of positve active emotions,
and the data obtained in method 2 part 2 had failed in gaining
data. Also we note that the analysis in part 2 is more accurate
then part 1.
To analyse the data we wrote a computer program in the
high-level programming language Python, which is often used
for analysing large amount of data in astronomy and physics.
as addition to python we used NumPy a extension of Python
which offers high-level mathematical functions for analysing
our data.
3.1 Creativity coefficient
In our data analysis we use values from 0 to 3 to indicate the
amount of creativity associated with a given mood, we call
this the creativity coefficients. creativity coefficient ranging
from 0 till 1.0 means no creativity associated with this mood.
Creativity coefficients ranging from 1.0 till 2.0 means there
is little creativity associated. this is kind of the neutral value
of the Creativity coefficient which says we can not say a lot
about the result. A creativity coefficient ranging from 2.0 till
3.0 indicate there is creativity associated with this mood.
3.2 part 1 of analysing
In part 1 of the data analysis we assumed that every subject had
filled in the interview questions properly. So in this part we
were able to use the arithmetic mean to calculate the average
or expectation value, in equation 1 is shown how to calculate
the arithmetic mean.
hxi =
1 N
∑ xi
N i=1
(1)
In our computer program we were able to use a so called
standard function of numpy to calculate the average of our
data. After calculating the average we wanted to calculate the
error of the data. before we are able to calculate the error, we
are going to calculate the standard deviation. For the standard
deviation we used a standard function in numpy to calculate it.
In equation 3 is shown how to calculate the standard deviation.
We also need to calculate the mean square to calculate the
standard deviation, the mean square is show in equation 2
hx2 i =
1 N 2
∑ xi
N i=1
(2)
When equation 2 is filled in left part of equation 3 we are
able to obtain the right part, which is the way we calculate the
standard deviation.
v
u
q
u1 N
2
2
σ = hx i − hxi = t ∑ xi2 −
N i=1
1 N
∑ xi
N i=1
!2
(3)
Using the standard error, which is generally the first part
of equation 4, we are able to calculate te precision of our
Research: a dual pathway to creativity, a contradiction — 4/5
measurement. using equation 3 we can derive the right part of
equation 4.
v
u
u 1 N
σ
1
Err = √ = t 2 ∑ xi2 − 3
N i=1
N
N
N
∑ xi
i=1
!2
(4)
using the equations given above we calculate the average
and error of our data to be able to say something about our
data. the data is shown in table 2
Activating mood
Deactivating mood
1
2n
1
2n
(6)
Using the calculated weight factors we are able to calculate the weighted average/mean of our data. using equation 7
we are able to calculate the weighted average. We note that
in our program we used some tricks from linear algebra to
calculate the average faster with less lines of code.
hxi =
∑Ni=1 xi wi
∑Ni=1 wi
(8)
We are able to calculate the standard deviation, using
equation 9.
s
N
2
∑Ni=1 xi2 wi
∑i=1 xi wi
(9)
−
∑Ni=1 wi
∑Ni=1 wi
v
2
u N
u ∑ x2 wi
σ
∑N xi wi
= t i=1 i 2 − i=1 3 (10)
Err = q
∑Ni=1 wi
∑Ni=1 wi
∑Ni=1 wi
Using the above equations we were able to extract the data
shown in table 3.
Table 3. Table of calculated creativity coefficients of 4
different mood categories
Activating mood
Deactivating mood
(5)
The consequence of this relation is that if the creativity coefficient of the 2 different questions has a difference of 1, the
1
weight of this data point is , and the when the creativity
2
coefficient of the questions has a difference of 2, the weight
1
of the data point becomes .
4
Because equation 5 is difficult to use in a program we use
the approximation given in equation 6. This approximation
excluded 0 difference between the creativity coefficients of
the 2 different questions, which means we added a loop in the
program to filter the 0, and change it by a weight factor of 1.
wi ∼
∑Ni=1 xi2 wi
∑Ni=1 wi
Also we calculated the error in our data using a similar
equation like equation 4, equation 10. We note that the term in
the root of equation 10 exist because of symmetry arguments.
Negative tone
0.8 ± 0.5
1.2 ± 0.5
1.0 ± 0.5
0.5 ± 0.3
3.3 part 2 of analysing
In part 2 of the data analysis we looked at the 8 questions
consisting of 2 questions in each mood category and compared
the questions of the same mood category. If the answer is
the same for both emotions from the same mood categorie
we gave the value from the datamatrix a weight of 1, if the
answers where a different by n point in the creativiy coefficient
the weight changed by n times multiplying 1 by a half, this
relation is mathematical shown in equation 5.
wi ∼
hx2 i =
q
σ = hx2 i − hxi2 =
Table 2. Table of calculated creativity coefficients of
different moods
Positive tone
2.8 ± 0.3
3.0 ± 0.0
2.5 ± 0.3
2.8 ± 0.3
Using a similar equation to calculate the weigted mean
square, equation 8.
(7)
Positive tone
2.9 ± 0.1
2.6 ± 0.2
Negative tone
1.8 ± 0.6
0.5 ± 0.4
4. Results
We got the following overall results, shown in table 4 (a1 and
a2 stands for analysis part 1 and 2).
Table 4. Table of calculated creativity coefficients of 4
different mood categories
Activating mood (a1)
Activating mood (a2)
Deactivating mood (a1)
Deactivating mood (a2)
Positive tone
2.8 ± 0.3, 3.0 ± 0.0
2.9 ± 0.1
2.5 ± 0.3, 2.8 ± 0.3
2.6 ± 0.2
Negative tone
0.8 ± 0.5, 1.2 ± 0.5
1.8 ± 0.6
1.0 ± 0.5, 0.5 ± 0.3
0.5 ± 0.4
5. Discussion and Conclusion
5.1 Hypothesis
According to De Dreu et al creativity is strongly influenced by
our mood. This theory is worked out under the heading theoretical background. This theory provided the foundation for
our hypothesis. Our main goal was to investigate the effects of
positive activating, positive deactivating, negative activating
Research: a dual pathway to creativity, a contradiction — 5/5
and negative deactivating moods on creativity. The hypothesis
is that both positive activating and negative activating moods
will grant the subjects increased levels of creativity whereas
both negative and positive deactivating moods will leave the
subjects without creativity.
Furthermore the theory suggests that there is a difference
between creativity resulting from positive activating mood
and creativity resulting from negative activating mood. Like
explained in the theoretical background a positive activating
mood is thought to result in cognitive flexibility, a greater
variety of ideas. Negative activating mood on the other hand
is thought to increase the persistence therefore increasing the
number of generated ideas.
5.2 Results
Unfortunately the subjects were not able to recall examples of
moments of creativity. It is therefore difficult to determine this
last part of the hypothesis since different generated ideas under
certain circumstances cannot be compared to one another in
order to determine the variety of ideas and the quantity of
ideas during moments of creativity can also not be analysed.
The results of the interviews did however show very clearly
that a positive activating mood was best at inducing creativity
with a value of 2, 9 ± 0, 1. This is exactly what we hypothesized since we expected that this activating mood leads to an
increase in creativity.
In contrast with our hypothesis the positive deactivating
moods also show an increase of creativity with a value of
2, 6 ± 0, 2. For this inconsistency with the theory several explanations can be given. First of all the group of subjects is
very limited so the margin of error is quite large, meaning
these results cannot be trusted fully. Furthermore the subjects might tend to answer the questions in accordance with
a positive bias. It is common believe that a positive mood
and relaxation are good for generating ideas and since the
subjects indicated they could not reproduce exact moments
of creativity it can be doubted how well their answers to the
questions can be trusted. Both of these arguments however
cannot be proven to be true that leaves one final possibility. It
is also possible that the theory used to generate our hypothesis
is incorrect. That would mean that a positive deactivating
mood does not necessarily undermine creativity.
The results of negative activating moods were also not
entirely in accordance with our hypothesis. The value of
1, 8 ± 0, 6 does not give inconclusive evidence that negative
activating moods lead to more creativity of the subjects. It
was expected that an increase in creativity would be visible in
an increase in the number of ideas generated with this type of
mood but since the subjects could not recall specific moments
of creativity this variable is not available.
Subjects did clearly indicate that negative deactivating
moods were highly unfavourable for creativity with the value
of 0, 5 ± 0, 4 meaning that creativity was low under these circumstances. This is in accordance with our hypothesis of the
negative deactivating moods which said that the deactivating
mood would limit creativity.
5.3 Conclusion
The hypothesis that positive activating moods increase creativity has been confirmed.
The hypothesis that positive deactivating moods decrease
creativity has been proven wrong.
The hypothesis that negative activating moods increase
creativity could not be confirmed, the results show that negative activating mood do not have an explicit positive or negative influence on creativity.
The hypothesis that negative deactivating moods decrease
creativity was confirmed.
It was not possible to analyse the different influences that
positive and negative moods can have on the type of creativity.
Acknowledgments
We thanks Onne Janssen for the review meetings about our
research model.
Appendix
After this page the appendix starts, the appendix exists of the
program code and the output of the program.
References
[1]
Baas M. De Dreu, C.K.W. and B.A. Nijstad. Hedonic tone
and activation level in the mood–creativity link: Toward a
dual pathway to creativity model. journał of Personality
and Social Psychology, 94:739–756, 2008.
Appendix: the used Code
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#! / u s r / b i n / env python
from
future
import d i v i s i o n
import numpy a s np
# d e f i n i t i o n o f d i s p l a y r e s u l t f u n c t i o n , makes d i s p l a y i n g c a l c u l a t i o n s e a s i e r .
def d i s p l a y r e s u l t ( n ) :
print ’ Mean , e x p e c t a t i o n v a l u e : %.1 f ’ % a v g l i s t [ n ]
print ’ Standard d e v i a t i o n : %.2 f ’ % s t d l i s t [ n ]
print ’ Median : %.1 f ’ % m e d i a n l i s t [ n ]
print ’ Standard e r r o r : %.2 f ’ % e r r o r l i s t [ n ]
print ’ Data ranged from ’ , m i n l i s t [ n ] , ’ t o ’ , m a x l i s t [ n ]
print ’ Root mean s q u a r e : %.1 f ’ % r m s l i s t [ n ]
# Import o f d a t a m a t r i c e s
# t h e v a r i a b l e s d a t a i s t h e d a t a m a t r i x t h e r e need t o be mentioned t h e d a t a i s
not y e t a
20 # m a t r i x i n t h i s p a r t o f t h e program
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22
23 data1 = np . l o a d t x t ( ” data . t x t ” )
24
25
26 # e x p l a i n a t i o n f o r t h e r e a d e r o f t h e d a t a
27
28
29 print ’ The output o f t h i s program c a l c u l a t e s some p r o p e r t i e s o f t h e data ’
30 print ’ ’
31 print ’ F i r s t t h e data ranged from 0 t o 3 , which means t h a t data between ’
32 print ’ 0 and 1 . 5 means t h e r e i s no c r e a t i v i t y a s s o c i a t e d with t h i s mood . ’
33 print ’ Data between 1 . 5 and 3 means t h e r e i s c r e a t i v i t y a s s o c i a t e d with t h i s
mood . ’
34 print ’ ’
35 print ’ ’
36 print ’ Important p r o p e r t i e s ’
37 print ’ For p r o v i n g our h y p o t h e s i s t h e r e a r e o n l y 2 s t a t i c a l p r o p e r t i e s which
are ’
38 print ’ i n t e r e s t i n g . These a r e t h e a r i t h m e t i c mean ( aka a v e r a g e ) and t h e
standard ’
39 print ’ e r r o r i n t h e measurement . ’
40 print ’ which means p e o p l e I am not , you can i g n o r e p r o p e r t i e s l i k e s t a n d a r d ’
41 print ’ d e v i a t i o n , median , data r a n g e , e t c ( aka o t h e r p r o p e r t i e s o f data ) ’
42 print ’ ’
43 print ’ About s i g n i f i c a n c e o f t h e numbers ’
44 print ’ Every number with more then one number a f t e r t h e comma need t o be
rounded up ’
6
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print
print
print
print
print
print
print
’ example 1 : 0 . 3 6 becomes 0 . 4 ’
’ example 2 : 0 . 4 1 becomes 0 . 5 ’
’ example 3 : But n o t e 0 . 5 0 becomes 0 . 5 ’
’ ’
’ ’
’PART 1 OF THE CALCULATIONS ’
’ ’
# d e f i n i t i o n o f t h e amount o f q u e s t i o n s
Q = 8
n = 4
# b e l o w we a r e making a m a t r i x o f t h e d a t a
data1 . shape = (Q, n )
# remove 1 from e v e r y e n t r y i n d a t a 1
data = data1 − np . o n e s ( (Q, n ) )
# A f t e r o b t a i n i n g t h e d a t a m a t r i x we t r a n s p o s e t h e m a t r i x t o make t h e
mathematics
74 # l e s s d i f f i c u l t .
75
76
77 dataT = data . T
78
79
80 # We know c a l c u l a t e e v e r y t h i n g from our d a t a m a t r i x .
81 # l i k e a r i t h m e t i c mean , median , a v e r a g e , min , max , RMS, s t a n d a r d d e v i a t i o n ,
standard error
82
83
84 s t d l i s t = [ ]
85 a v g l i s t = [ ]
86 m e d i a n l i s t = [ ]
87 e r r o r l i s t = [ ]
88 m a x l i s t = [ ]
89 m i n l i s t = [ ]
90 r m s l i s t = [ ]
91
92
93 f or n in r a n g e ( 0 , 8 ) :
7
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a v g l i s t . append ( np . mean ( data [ n ] ) )
s t d l i s t . append ( np . s t d ( data [ n ] ) )
m e d i a n l i s t . append ( np . median ( data [ n ] ) )
e r r o r l i s t . append ( np . s t d ( data [ n ] ) / ( np . s q r t ( 4 ) ) )
m a x l i s t . append ( np . max( data [ n ] ) )
m i n l i s t . append ( np . min ( data [ n ] ) )
r m s l i s t . append ( np . s q r t ( np . s t d ( data [ n ] ) ∗np . s t d ( data [ n ] ) + np . mean ( data [
n ] ) ∗np . mean ( data [ n ] ) ) )
101
102 # d i s p l a y i n g t h i s p a r t o f t h e c a l c u l a t i o n s , u s i n g t h e f u n c t i o n d i s p l a y r e s u l t
103
104
105 print ’ P o s i t i v e a c t i v e : ’
106 print ’ Measurement 1 : ’
107 d i s p l a y r e s u l t ( 2 )
108 print ’ Measurement 2 : ’
109 d i s p l a y r e s u l t ( 4 )
110 print ’ ’
111 print ’ P o s i t i v e d e a c t i v e : ’
112 print ’ Measurement 1 : ’
113 d i s p l a y r e s u l t ( 0 )
114 print ’ Measurement 2 : ’
115 d i s p l a y r e s u l t ( 5 )
116 print ’ ’
117 print ’ N e g a t i v e a c t i v e : ’
118 print ’ Measurement 1 : ’
119 d i s p l a y r e s u l t ( 1 )
120 print ’ Measurement 2 : ’
121 d i s p l a y r e s u l t ( 3 )
122 print ’ ’
123 print ’ N e g a t i v e d e a c t i v e : ’
124 print ’ Measurement 1 : ’
125 d i s p l a y r e s u l t ( 6 )
126 print ’ Measurement 2 : ’
127 d i s p l a y r e s u l t ( 7 )
128
129
130
131 # we now c a l c u l a t e e v e r y t h i n g w i t h w e i g h t e d a v e r a g e u s i n g t h e f a c t we d o u b l e
questioned the
132 # d a t a
133 # f i r s t we c a l c u l a t e t h e w e i g h t f a c t o r f o r e v e r y d a t a p o i n t
134 # c a l c u l a t e w e i g h t f a c t o r f o r t h e d i f f e r e n c t c a t e g o r i e s
135
136
137 v e c t o r p a = np . a b s o l u t e ( data [ 2 ] − data [ 4 ] )
138 v e c t o r p d = np . a b s o l u t e ( data [ 0 ] − data [ 5 ] )
139 v e c t o r n a = np . a b s o l u t e ( data [ 1 ] − data [ 3 ] )
140 v e c t o r n d = np . a b s o l u t e ( data [ 6 ] − data [ 7 ] )
141
142
8
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
# c a l c u l a t e inverse weight factor :
wpa
wpd
wna
wnd
=
=
=
=
2∗ v e c t o r p a
2∗ v e c t o r p d
2∗ v e c t o r n a
2∗ v e c t o r n d
# remove z e r o e n t r i e s and r e p l a c e t h e z e r o e n t r i e s w i t h ones
f or i in r a n g e ( 0 , 4 ) :
i f wpa [ i ] ==
wpa [ i
i f wpd [ i ] ==
wpd [ i
i f wna [ i ] ==
wna [ i
i f wnd [ i ] ==
wnd [ i
0:
] =
0:
] =
0:
] =
0:
] =
1
1
1
1
# c a l c u l a t e i n v e r s e o f i n v e r s e w e i g h t f a c t o r , aka w e i g h t f a c t o r / r e a l w e i g h t
factor :
167
168
169 rwpa = 1/wpa
170 rwpd = 1/wpd
171 rwna = 1/wna
172 rwnd = 1/wnd
173
174
175 # c a l c u l a t e t h e sum o f t h e v e c t o r s .
176
177
178 sumrwpa = np . sum ( rwpa )
179 sumrwpd = np . sum ( rwpd )
180 sumrwna = np . sum ( rwna )
181 sumrwnd = np . sum ( rwnd )
182
183
184 # c a l c u l a t e t h e w e i g h t e d sum o f t h e d a t a v e c t o r s
185
186
187 sumdatapa1 = np . sum ( rwpa∗ data [ 2 ] )
188 sumdatapa2 = np . sum ( rwpa∗ data [ 4 ] )
189 sumdatapd1 = np . sum ( rwpd∗ data [ 0 ] )
190 sumdatapd2 = np . sum ( rwpd∗ data [ 5 ] )
191 sumdatana1 = np . sum ( rwna∗ data [ 1 ] )
192 sumdatana2 = np . sum ( rwna∗ data [ 5 ] )
9
193 sumdatand1 = np . sum ( rwnd∗ data [ 6 ] )
194 sumdatand2 = np . sum ( rwnd∗ data [ 7 ] )
195
196
197 # c a l c u l a t e t h e w e i g h t e d mean/ e x p e c t a t i o n v a l u e o f t h e d a t a f o r a l l 4
categories
198
199
200 meanwpa = ( sumdatapa1 + sumdatapa2 ) / ( 2 ∗ sumrwpa )
201 meanwpd = ( sumdatapd1 + sumdatapd2 ) / ( 2 ∗ sumrwpd )
202 meanwna = ( sumdatana1 + sumdatana2 ) / ( 2 ∗ sumrwna )
203 meanwnd = ( sumdatand1 + sumdatand2 ) / ( 2 ∗ sumrwnd )
204
205
206 # c a l c u l a t e t h e w e i g h t e d sum o f t h e s q u a r e s o f t h e d a t a v e c t o r s
207
208
209 sum2datapa1 = np . sum ( rwpa ∗ ( data [ 2 ] ∗ data [ 2 ] ) )
210 sum2datapa2 = np . sum ( rwpa ∗ ( data [ 4 ] ∗ data [ 4 ] ) )
211 sum2datapd1 = np . sum ( rwpd ∗ ( data [ 0 ] ∗ data [ 0 ] ) )
212 sum2datapd2 = np . sum ( rwpd ∗ ( data [ 5 ] ∗ data [ 5 ] ) )
213 sum2datana1 = np . sum ( rwna ∗ ( data [ 1 ] ∗ data [ 1 ] ) )
214 sum2datana2 = np . sum ( rwna ∗ ( data [ 5 ] ∗ data [ 5 ] ) )
215 sum2datand1 = np . sum ( rwnd ∗ ( data [ 6 ] ∗ data [ 6 ] ) )
216 sum2datand2 = np . sum ( rwnd ∗ ( data [ 7 ] ∗ data [ 7 ] ) )
217
218
219 # c a l c u l a t e t h e w e i g h t e d mean s q u a r e o f t h e d a t a f o r a l l 4 c a t e g o r i e s
220
221 mean2wpa = ( sum2datapa1 + sum2datapa2 ) / ( 2 ∗ sumrwpa )
222 mean2wpd = ( sum2datapd1 + sum2datapd2 ) / ( 2 ∗ sumrwpd )
223 mean2wna = ( sum2datana1 + sum2datana2 ) / ( 2 ∗ sumrwna )
224 mean2wnd = ( sum2datand1 + sum2datand2 ) / ( 2 ∗ sumrwnd )
225
226
227 # c a l c u l a t e t h e s t a n d a r d d e v i a t i o n o f t h e w e i g h t e d d a t a
228
229
230 stdwpa = np . s q r t ( mean2wpa − meanwpa∗meanwpa )
231 stdwpd = np . s q r t ( mean2wpd − meanwpd∗meanwpd )
232 stdwna = np . s q r t ( mean2wna − meanwna∗meanwna )
233 stdwnd = np . s q r t ( mean2wnd − meanwnd∗meanwnd )
234
235
236 # c a l c u l a t e t h e r o o t mean s q u a r e o f t h e w e i g h t e d d a t a
237
238
239 rmswpa = np . s q r t ( mean2wpa )
240 rmswpd = np . s q r t ( mean2wpd )
241 rmswna = np . s q r t ( mean2wna )
242 rmswnd = np . s q r t ( mean2wnd )
10
243
244 # c a l c u l a t e t h e s t a n d a r d e r r o r i n t h e d a t a
245
246 e r r o r w p a = stdwpa / ( np . s q r t ( 2 ∗ sumrwpa ) )
247 errorwpd = stdwpd / ( np . s q r t ( 2 ∗ sumrwpd ) )
248 e r r o r w n a = stdwna / ( np . s q r t ( 2 ∗ sumrwna ) )
249 errorwnd = stdwnd / ( np . s q r t ( 2 ∗ sumrwnd ) )
250
251
252 # o u t p u t t h e d a t a
253
254 print ’ ’
255 print ’ ’
256 print ’PART 2 OF THE CALCULATIONS ’
257 print ’ ’
258 print ’ C a l c u l a t i o n s with w e i g h t e d means : ’
259 print ’ ’
260 print ’ P o s i t i v e a c t i v e : ’
261 print ’ Mean , e x p e c t a t i o n v a l u e : %.1 f ’ % meanwpa
262 print ’ Standard d e v i a t i o n : %.2 f ’ % stdwpa
263 print ’ Standard e r r o r : %.2 f ’ % e r r o r w p a
264 print ’ Root mean s q u a r e : %.1 f ’ % rmswpa
265 print ’ ’
266 print ’ P o s i t i v e d e a c t i v e : ’
267 print ’ Mean , e x p e c t a t i o n v a l u e : %.1 f ’ % meanwpd
268 print ’ Standard d e v i a t i o n : %.2 f ’ % stdwpd
269 print ’ Standard e r r o r : %.2 f ’ % errorwpd
270 print ’ Root mean s q u a r e : %.1 f ’ % rmswpd
271 print ’ ’
272 print ’ N e g a t i v e a c t i v e : ’
273 print ’ Mean , e x p e c t a t i o n v a l u e : %.1 f ’ % meanwna
274 print ’ Standard d e v i a t i o n : %.2 f ’ % stdwna
275 print ’ Standard e r r o r : %.2 f ’ % e r r o r w n a
276 print ’ Root mean s q u a r e : %.1 f ’ % rmswna
277 print ’ ’
278 print ’ N e g a t i v e d e a c t i v e : ’
279 print ’ Mean , e x p e c t a t i o n v a l u e : %.1 f ’ % meanwnd
280 print ’ Standard d e v i a t i o n : %.2 f ’ % stdwnd
281 print ’ Standard e r r o r : %.2 f ’ % errorwnd
282 print ’ Root mean s q u a r e : %.1 f ’ % rmswnd
11
1
Appendix: Output of the used code
The output o f t h i s program c a l c u l a t e s some p r o p e r t i e s o f t h e data
F i r s t t h e data ranged from 0 t o 3 , which means t h a t data between
0 and 1 . 5 means t h e r e i s no c r e a t i v i t y a s s o c i a t e d with t h i s mood .
Data between 1 . 5 and 3 means t h e r e i s c r e a t i v i t y a s s o c i a t e d with t h i s mood .
Important p r o p e r t i e s
For p r o v i n g our h y p o t h e s i s t h e r e a r e o n l y 2 s t a t i c a l p r o p e r t i e s which a r e
i n t e r e s t i n g . These a r e t h e a r i t h m e t i c mean ( aka a v e r a g e ) and t h e s t a n d a r d
e r r o r i n t h e measurement .
which means p e o p l e I am not , you can i g n o r e p r o p e r t i e s l i k e s t a n d a r d
d e v i a t i o n , median , data r a n g e , e t c ( aka o t h e r p r o p e r t i e s o f data )
About s i g n i f i c a n c e o f t h e numbers
Every number with more then one number a f t e r t h e comma need t o be rounded up
example 1 : 0 . 3 6 becomes 0 . 4
example 2 : 0 . 4 1 becomes 0 . 5
example 3 : But n o t e 0 . 5 0 becomes 0 . 5
PART 1 OF THE CALCULATIONS
Positive active :
Measurement 1 :
Mean , e x p e c t a t i o n v a l u e : 2 . 8
Standard d e v i a t i o n : 0 . 4 3
Median : 3 . 0
Standard e r r o r : 0 . 2 2
Data ranged from 2 . 0 t o 3 . 0
Root mean s q u a r e : 2 . 8
Measurement 2 :
Mean , e x p e c t a t i o n v a l u e : 3 . 0
Standard d e v i a t i o n : 0 . 0 0
Median : 3 . 0
Standard e r r o r : 0 . 0 0
Data ranged from 3 . 0 t o 3 . 0
Root mean s q u a r e : 3 . 0
Positive deactive :
Measurement 1 :
Mean , e x p e c t a t i o n v a l u e : 2 . 5
Standard d e v i a t i o n : 0 . 5 0
Median : 2 . 5
Standard e r r o r : 0 . 2 5
Data ranged from 2 . 0 t o 3 . 0
Root mean s q u a r e : 2 . 5
Measurement 2 :
Mean , e x p e c t a t i o n v a l u e : 2 . 8
12
Standard d e v i a t i o n : 0 . 4 3
Median : 3 . 0
Standard e r r o r : 0 . 2 2
Data ranged from 2 . 0 t o
Root mean s q u a r e : 2 . 8
3.0
Negative a c t i v e :
Measurement 1 :
Mean , e x p e c t a t i o n v a l u e : 0 . 8
Standard d e v i a t i o n : 0 . 8 3
Median : 0 . 5
Standard e r r o r : 0 . 4 1
Data ranged from 0 . 0 t o 2 . 0
Root mean s q u a r e : 1 . 1
Measurement 2 :
Mean , e x p e c t a t i o n v a l u e : 1 . 2
Standard d e v i a t i o n : 0 . 8 3
Median : 1 . 5
Standard e r r o r : 0 . 4 1
Data ranged from 0 . 0 t o 2 . 0
Root mean s q u a r e : 1 . 5
Negative deactive :
Measurement 1 :
Mean , e x p e c t a t i o n v a l u e : 1 . 0
Standard d e v i a t i o n : 1 . 0 0
Median : 1 . 0
Standard e r r o r : 0 . 5 0
Data ranged from 0 . 0 t o 2 . 0
Root mean s q u a r e : 1 . 4
Measurement 2 :
Mean , e x p e c t a t i o n v a l u e : 0 . 5
Standard d e v i a t i o n : 0 . 5 0
Median : 0 . 5
Standard e r r o r : 0 . 2 5
Data ranged from 0 . 0 t o 1 . 0
Root mean s q u a r e : 0 . 7
PART 2 OF THE CALCULATIONS
C a l c u l a t i o n s with w e i g h t e d means :
Positive active :
Mean , e x p e c t a t i o n v a l u e : 2 . 9
Standard d e v i a t i o n : 0 . 2 6
Standard e r r o r : 0 . 1 0
Root mean s q u a r e : 2 . 9
Positive deactive :
Mean , e x p e c t a t i o n v a l u e : 2 . 6
13
Standard d e v i a t i o n : 0 . 4 8
Standard e r r o r : 0 . 1 8
Root mean s q u a r e : 2 . 7
Negative a c t i v e :
Mean , e x p e c t a t i o n v a l u e : 1 . 8
Standard d e v i a t i o n : 1 . 2 7
Standard e r r o r : 0 . 6 0
Root mean s q u a r e : 2 . 2
Negative deactive :
Mean , e x p e c t a t i o n v a l u e : 0 . 5
Standard d e v i a t i o n : 0 . 7 6
Standard e r r o r : 0 . 3 1
Root mean s q u a r e : 0 . 9
14
Vragen
1
2
3
4
5
Als ik relaxed ben, ben ik creatief
Als ik boos ben, kan ik niet tot oplossingen komen.
Als ik blij ben, kan ik goed oplossingen bedenken.
Als ik gestrest ben, kan ik niet tot oplossingen komen.
Als ik opgetogen ben, ben ik in staat van het vinden van een
creatieve oplossing.
6 Als ik ontspannen ben, kan ik niet tot oplossingen komen.
7 Als ik lusteloos ben kan ik niet op ideeën komen.
8 Als ik verdrietig ben, voel ik mij belemmerd in het vinden
van oplossingen
W aar
Deels
waar
Niet
waar
O
O
O
O
O
Deels
niet
waar
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
Appendix: Question matrix
3
0
3
0
3
0
0
0
2
1
2
1
2
1
1
1
1
2
1
2
1
2
2
2
16
0
4
0
4
0
4
4
4
(1)