Automatic Modeling of Personality Types

Transcription

1 Automatic Modeling of Personality Types BA Thesis Afstudeerscriptie written by Douwe Oosterhout born June 30th, 1985 in Ramotswa, Botswana under the supervision of Dr. Reinhard Blutner, submitted in partial fulfillment of the requirements for the degree of BA Kunstmatige Intelligentie at the Universiteit van Amsterdam.

2 Abstract A model using two qubits to represent Jung s personality types is compared to an extension of Jung s theory, the Myers-Briggs Type Indicator. The -qubit model can generate artificial personalities, which in turn can be compared to real world data. This data is gathered by a questionnaire. Conceptual advantages are the use of less variables and the better fitting of Jung s theories by use of the shadow personality. An attempt is made to find empirical differences. However, these are hard to find due to principal reasons of the models.

3 Contents 1 Introduction Personality types according to C.G. Jung.1 Thinking vs Feeling Sensation vs Intuition Introversion vs Extroversion The Shadow The MBTI 4 4 Singer-Loomis TDI 5 5 Two qubit approach The Qubit Using two qubits to represent Jung s personality types Conceptual advantages of the qubit model Questionnaire 1 7 Fitting the data to MBTI and the two Qubit model 1 8 Generating artificial personalities 13 9 Cronbach s alpha and cluster analysis Conclusion and further research References 17 1 Appendix A : the questions used in German, English and Dutch Instructions Questions Appendix B : The personalities 5 1

4 1 Introduction For centuries psychologists and philosophers have tried to crack the code of human personality. The complexities of covering human personality has started a lot of debates what should and should not be covered by a personality model, be it explanations about our behavior, or our psyche. This in turn ensured that many models spawned from brains of these psychologists and philosophers. Two such widely used models are Jung s personality type model by Carl Gustav Jung 191 and the Big Five model. Where Jung s model has four psychological functions and two attitudes to express personality, the Five Factor Model, as the Big Five is also named, uses five personality traits or factors are used. The Big Five model is more empirically driven than the MBTI or Jung s model, although correlations have been found which suggests that the models each models scales can be related to one another. McCrae & Costa, It is Jung s personality type theories we shall be using in this paper. An adaptation to Jung s model, the Myers-Briggs Type Indicator MBTI is one the most used personality models in western civilization. It is used in many applications such as relationship counseling, career planning and many more. Its widespread use makes it an important comparator when introducing a new model. In this paper a two-qubit approach, to which Jung s model fits very intuitively, is compared to the MBTI. Jung himself never formalized his own model and introduced it purely from a psychological point of view. However using two qubits to express Jung s theories lends itself perfectly for formalization. It encompasses ideas of Jung that the MBTI does not, such as the shadow personality. Ambiguity however shadows over both models as both can reach certain states where multiple personalities can be detected. The two qubit model allows us to calculate expected values for the psychological functions and attitudes, which in turn allows us to generate artificial personalities. The artificial personalities need to be compared to real world personalities. To obtain these a questionnaire was made which was filled in by 5 subjects. From this questionnaire the MBTI score was calculated which could then be compared. Besides a conceptual analysis of the two models, some empirical analysis is also performed. This is done in the form of analyzing the reliability of the questions by using Cronbach s alpha. Furthermore a cluster analysis is performed to see if each question clusters with it s counterparts of the same type. A further task is to generate artificial personalities using the two qubit model s three parameters. These personalities can then be used to automatically fill in the questionnaire. The simulation results can then be principally compared with the empirical ones. This is done by use of Cronbach s alpha and a cluster analysis of the questions. First off Jungian psychology will briefly be explained, together with some adaptations such as the MBTI. After that the qubit will be explained, which uses formulas and theories from quantum physics. After this the connection between Jung s personality models and qubits will be brought to light and the differences will be discussed. Personality types according to C.G. Jung Jung 191 theorized that four psychological functions were needed to classify one s personality, namely sensation S, thinking T, feeling F and intuition N. Also two kinds of psychological attitudes were needed to specify one s personality, introvert I and extrovert E. Although everybody initially has access to the four psychological functions, what makes everyone different is the various preferences people have to certain functions and there attitude toward their preference. According to Jung, on the one hand we have thinking and feeling as

5 rational functions and on the other hand we have sensing and intuition as non-rational functions. People rarely develop both rational or non-rational functions in their personalities, which leaves us to believe thinking and feeling and sensing and intuition should be opposites. Figure 1 gives us an intuitive look at the psychological functions. The result of having two axes, each with two psychological functions, combined with the two attitudes leaves us with eight different personality types one can have. Each personality has a primary psychological function and an auxiliary function, which have the same attitude, and are expressed the strongest. We experience these functions consciously. The two left over functions are the tertiary and inferior functions and are experienced unconsciously. Jung also specified that everyone also has a shadow personality which sits on the other side of the spectrum and can sometimes be triggered to take over. Naturally no personality type is better than another and no one fits perfectly into one of the types. Jung suggested his model be used as a compass rather than a hard determination of personality. Personality types are determined with questionnaires, where one could choose from fixed answers. Figure 1: Compass view of Jung s psychological functions, taken from Jung et al. 1968, p. 60 I will now tell more about the different psychological functions and attitudes, as well as the shadow..1 Thinking vs Feeling As mentioned earlier, the thinking and feeling functions are the rational functions. Thinking is intuitively a rational function as it creates rational judgments of the perceived world, but feeling might not be. Jung did not see the feeling function as a function for affection and emotion, but a function that performs value judgments. This requires thought and deduction and can thus be seen as a rational function. When seeing another war on the news a person with a strong feeling function would feel deeply sorrowful for the people suffering in that war, people losing their houses etc. Thinkers would feel less compassion and be more interested in hard facts, such as number of casualties, or the reasons of why the war started in the first place. 3

6 . Sensation vs Intuition The sensation and intuition functions are the non-rational functions as they do not have anything to do with rationality. They are the perceptive functions and determine what one does with information that one gets from the world. Sensation creates a world view based on one s senses, so for example a person with a strong sensing function often perceives the colors of the flowers in the garden. This is in strong contrast with people with a stronger intuitive function, which perceives the relationships and possibilities of the information one receives. Flowers that are all situated with equal distance to each other would cause an intuitionist to infer that they were planted there rather than sprouted by natural reproduction. Of course a sensationalist could also perceive this, as no function binds exclusively to a person, but as one function runs stronger than the other, it will initially create a different perception of the world..3 Introversion vs Extroversion The four psychological functions introduced by Jung can all manifest in two attitudes, namely introvert and extrovert. This represents the orientation of one s primary psychological function. If someone is extrovert, that person would reflect on the outer world, whereas an introvert would reflect on his inner self. The result of this is for example that extroverts eagerly attach to others around them and don t mind talking to strangers. This in great contrast to introverts whom prefer to keep to themselves and would rather be left alone or be with people they really trust..4 The Shadow As mentioned earlier every person contains every psychological function and attitude. It is only someone s preference to use one, but not the other that makes every person unique. However, every person also contains a shadow personality. This shadow sits unconsciously in every person and its personality is the exact opposite of someone s personality. So say, if someone is an extroverted thinker, his shadow will be an introverted feeler. A shadow there to counterbalance our personality, in other words it is in superposition with our personality. A persons personality is thus not wholly determined by their main personality, but in conjunction with their shadow. Jung finds that it is important for someone to understand their shadow, not only for personal development, but also for social harmony. Stevens, In the next three sections three extensions to Jung s personality model will be discussed, namely the Myers-Briggs Type Indicator which introduces a new dimension, the Singer-Loomis Type Deployment Instrument which is able to differentiate someone s personality from his or her shadow and an approach which implements two qubits to describe Jung s personality model. 3 The MBTI MBTI stands for the Myers-Briggs Type Indicator and uses Jung s theory of personality types, but adds an extra dimension. Myers and Briggs 196,1980 theorized that a lifestyle function was needed to better capture the different personalities of the world. This lifestyle function indicated which psychological axis one preferred, be it the judging function, which relates to the thinking-feeling axis, or the perceiving function which relates to the sensing-intuition axis. To be more concrete, people who have a stronger preference for the judging function tend 4

7 to plan their life more, whereas perceivers rather live their life unplanned. With this added dimension we can now construct 16 different personality types. The MBTI has now become one of the most used personality type models in the world. If we look at the MBTI from a statistical point of view, we can describe it with four parameters. These are of course the four dimensions they use to describe someone s personality: extrovert/introvert, sensing/intuition, thinking/feeling and judging/perceiving. These parameters can be seen as Boolean random variables, named E, S, T and J respectively. They map each side of their dimension to { 1, 1}. For example, the random variable E maps the extrovert side to 1 and the introvert side to 1. We define µe = 1 = e, µs = 1 = s, µt = 1 = t and µj = 1 = j. This gives us the following expectation values: E = e 1 1 S = s 1 T = t 1 3 J = j 1 4 Here are some example personalities, with their appropriate values: Name Personality type E e S s T t J j Daan INFP Tim ISTP Ruben ISFP Sanne ENTP In Daan s case, using the MBTI description, being an INFP, shortly put, means that he is idealistic and loyal to his values and to people who are important to him. Sanne however, being an ENTP, is in short a quick, ingenious, stimulating, alert, and outspoken person. In stead of seeing an opposite complementary personality as a shadow, such as Jung described, Myers-Briggs see the inferior, least developed function as the shadow. A problem with the MBTI is that it can sometimes be in an ambiguous state where a person can have two personalities. Say e = 1 and t = 1 and s equals some small ɛ. This gives us E = 0 and T = 0. Is this person then an extroverted thinker with an introverted feeling function or an introverted thinker with an extroverted feeling function? It is this type of ambiguity that can wrongly give someone a opposite personality. 4 Singer-Loomis TDI The Singer-Loomis model Singer & Loomis, 1984 is another adaptation to Jung s. TDI stands for Type Deployment Instrument. The SL-TDI changed the way subjects could respond to questions by implementing a one-to-five scale. This way a subject can indicate how often he or she would give a certain response, resulting in more dynamic results. Also, in stead of asking questions about a psychological function they ask questions about psychological functions in a certain attitude. This is because they think that the attitudes are inseparable from the functions, because they are always used in a introverted or extroverted way. Dugan & Wilson, 00 They also assume that the functions do not cancel each other out. In other words, one can have a strong thinking function, but this does not mean that you have a weak feeling function. Asking questions in the Singer-Loomis TDI way takes care of the ambiguity problem the MBTI has, as it is now clear which attitude each function works with. However by asking questions in a 5

8 certain attitude and thus relieving people from giving answers to bipolar questions, Singer and Loomis have created a way where a single dimension can emerge as the primary and secondary function. This is in disagreement with Jung s ideas where the inferior function is always the opposite of the primary function. When formalizing the Singer-Loomis TDI we can use the same random variables as defined in the MBTI case, excluding the random variable J of coarse, because it is not used by the model. Now because they assume that every psychological function is used in an introverted or extroverted manner the probabilities are calculated as combined probabilities, e.g. µe = 1, T = 1. These dependencies do however enlarge the number of parameters needed to express the model formally. The three random variables and eight dependency relations sum up to 11 parameters and this is only in the simpler bipolar case. Of course, the chosen random variable can be connected to form a Bayesian network as a formal expression of the full model. However, because of the high number of free parameters this can form a descriptive model only without any explanatory value. 5 Two qubit approach A -qubit model to Jung s methodology has recently been introduced Blutner & Hochnadel, 009. This model makes use of certain formulas and ideas from quantum theory such as qubits, Pauli s spin matrices. It is this model I will be researching in this paper. It will primarily be compared to the MBTI. It will be introduced formally in the next section. To formally introduce the -qubit model, we must first introduce some formalisms from quantum physics which are necessary to understand the approach. 5.1 The Qubit A qubit is in a sense similar to a computer bit in that they both have two states, 0 and 1. The biggest difference however is that a qubit has the possibility to be in a superposition of the two states, whereas a bit can be only one or the other. A qubit can be represented by a Bloch sphere. This allows us to represent a qubit with the two parameters θ and ϕ. Here θ is the superposition parameter and ϕ indicates the phase factor of the qubit. An example can be found in figure. Figure : Bloch sphere, taken from sphere.svg under the Creative Commons Attribution ShareAlike 3.0 licence. 6

9 In the two qubit model the phase factor is ignored, leaving us with one parameter to represent our psychological functions. Without parameter ϕ we are left with a circle, namely the circle of figure 3. Figure 3: A Bloch sphere representation where the phase factor is 0 A qubit state is called pure when the superposition is linear. This means that the qubit can be represented with the following formula, using the bra-ket notation: Ψ = α 0 + β 1 5 where 0 and 1 are orthogonal unit vectors representing state 0 and 1 mentioned above and α + β = 1. It is intuitive to view a qubit as polarized light. If light is polarized in one direction, polarizing it again in a direction which is perpendicular to the previous polarization will block any light of coming through. Thus the polarizations are mutually exclusive. Similarly it could be viewed as a photon, as photons can also be polarized. This is visualized in figure 4. All intermediate lines from the x-axis to the z-axis are possible states the photon can be in. As this picture can also be seen as two vectors spanning a two-dimensional space it is in agreement with formula 5. Figure 4: Visualization of possible photon states As Bloch spheres operate on the Hilbert space it is useful to define states on such a space. Here we use Pauli s spin matrices, because these together with the identity matrix I form an orthogonal basis for the Hilbert space. They are defined as follows: 7

10 0 1 σ x = i σ y = i σ z = 0 1 Looking back at figure 4 we see that given a certain vector, the angle θ can be attained. This gives us the means to determine the state our photon is in: ψ = cos θ sin θ Formula 9 relates directly to our Bloch sphere representation, only there our pure states oppose each other 180 in stead of the 90 here, so the angles have to be multiplied by. Now the cosine gives us our location on the z-axis and the sinus function gives us our location on the x-axis. Because they both use only one and the same variable, formula 9 gives us the possibility to represent two photons with one variable as seen in figure 3. The state of the first photon can thus be calculated with the formula cos θ. The state of the second photon can be calculated with sin θ, giving us: ψ = cos θ sin θ We can now easily determine the expected value of a function by using the standard formula for expected values in quantum physics: σ z = ψ T σ z ψ 11 this gives us σ z = cos θ sin θ cos θ sin θ = cos θ 1 Similarly we find σ x = sin θ 13 σ y has been omitted because we will not be using it further on. So if we take θ = π 4 we get σ z = 0 and σ x = 1, or if θ = π 8 we find σ z = 1 and σ x = 1 This is to give us an intuition to what is possible when using this representation. We will now implement these theories to model Jungs personality types by using two qubits. 5. Using two qubits to represent Jung s personality types As mentioned we will be using two qubits to represent Jungs personality model. We can quickly see the analogy between Jungs personality functions and a qubit when we look at figures 1 and 3. The compass like structure makes for a perfect analogy. This allows us to use the previously introduced formulas for the calculation of expected values to determine someones personality. As our Thinking-Feeling function T is situated on the z-axis on the Bloch sphere it is σ z 8

11 formula 8 that is the observable for this function. As the thinking function T = σ z, the opposite function, feeling, can be represented by F = σ z. The Sensing-Intuition S function sits on the x-axis and is thus represented by σ x formula 6. When using the formulas for calculation the expected values formulas 1 and 13 and filling in θ for values between π and π we find figure 5. Figure 5: The eight Jungian personality types represented by their expected values In figure 5, if one would draw a vertical line at each of the numbers, the eight Jungian personality types emerge. So at number 1 we find a dominant Feeling function, a secondary intuition function, a tertiary sensing function and an inferior thinking function. The second qubit expresses the attitudes. Here we choose for the z-axis to represent the Extroversion-Introversion attitudes. This is also represented by σ z. However, because we are in another qubit we do not use θ as our variable, but α. The x-axis is not used in the two qubit model and is simply an intermediate state, which has no effect on the personality types. In stead of using the angle θ from our Bloch sphere representation in the two qubit model, we will be using θ = θ. This way our representation looks like figure 6. Figure 6: Alternate representation of our qubit. Two such qubit are now combined using the tensor product. As we will be using the model as described by equation 9, where opposite functions are perpendicular, we can describe a state or personality type as the following: cos α sin α cos θ sin θ Here the left vector describes a persons attitude and the right vector a persons psychological functions. We also wish to include the shadow of one s personality type in its state vector. For this reason we superpose the state vector 14 with a state vector perpendicular to it. This is: 14 9

12 sin α cos α sin θ cos θ In the two qubit model, the shadow is entangled with someones personality. In the present case, this means that a psychological function is inseparably connected with a certain attitude. Since more than one attitude is possible for each personality, the superposition of attitudepsychological function pairs accounts for the description of the full personality. This gives us the the general state representation of the two qubit model: 15 ψ = τ cos α sin α cos θ sin θ sin 1 τ α cos α sin θ cos θ 16 Where τ is the entanglement factor and 1 τ is needed for normalization. We now define the basic observables in this -qubit model, which are our two opposing personality types and opposing attitudes. However, because a personality type is now represented by a qubit with personality types and the attitude qubit we get the following formulas: 1 0 E = I T = I S = I Where I is the identity matrix. Now once again, with the states and observables we can calculate the expected values. For complexity purposes all parts of the equation where a matrix multiplication results to 1 have cos θ been omitted i.e. sin θ I = 1. 1 τ E = ψ T Eψ = τ cos θ sin θ sin α cos α τ cos θ sin θ 1 τ In the same way we find sin α cos α τ 1 τ cos θ τ sin θ sin α cos α sin α cos α τ cos θ sin θ = 3 τ 1 cos α τ 1 τ sinα 4 T = τ 1 cos θ τ 1 τ sinθ 5 S = τ 1 sin θ τ 1 τ cos θ 6 10

13 In a similar fashion we can calculate µe = 1, represented further on as E +. µe = 1 is the chance that a personality will answer the extrovert answer when given a question about 1 0 the extrovert-introvert attitude. Here the observable is I. We find: 0 0 ψ T E + ψ = sin α + τ cos α τ 1 τ sin α 7 And similarly: ψ T T + ψ = sin θ + τ cos θ τ 1 τ sin θ 8 ψ T S + ψ = 1 1 sin θ + τ sin θ τ 1 τ cos θ 9 With these expectations in place we can use these formulas to create our own personalities. These can then be compared to some self obtained personalities. The outcome will be discussed further on. However, we must be cautious. Some values of our parameters can lead to ambiguous results, just like in the MBTI. Figure 7 shows us formula 5 for different fixed τ and a variable θ from π to π. If we look at the central curve with value 1 at θ = 0 here τ = 0, we see that the value 0.5 for example can be achieved by multiple θ. Figure 7: Function T as a function of theta for different tau. 5.3 Conceptual advantages of the qubit model The MBTI is formally defined by four random variables, so it thus takes four variables to produce result. It can get even worse if there are dependencies between these random variables, which in the case of the EI and TF can be determined by seeing if the following holds. P E T P E 30 If this would be the case another variable would need to be added to capture this dependency. This means that the MBTI hold at least four variables. The -qubit approach however uses three variables only, namely τ, θ and α to describe all personalities. The three parameters describe the full distribution without the need for additional parameters. This provides us with a more elegant solution than say the Singer-Loomis TDI which uses at least 11 parameters. The incorporation of the shadow and the entanglement of the shadow with a personality makes the -qubit model fit better to Jung s theories, as opposed to the MBTI which does not use a shadow. Also the notion of superposition result in far more dynamic personality types than the 11

14 generic 16 types of the MBTI. Jung s theories tell us that opposing functions should be used, so thinking should oppose feeling, however the Singer-Loomis TDI ignores this, allowing opposing functions to become the primary and auxiliary functions. This part of Jung s theory is followed in the -qubit model. 6 Questionnaire The self obtained personalities were obtained by asking subjects 4 questions. There were four categories of six questions each. Each category was one of the MBTI dimensions. The questions were given in random order. After each question the subject was asked to indicate how certain he or she was of their answer. This was done on a scale from 1 to 5, where 1 was completely uncertain and 5 was completely certain. All the questions where taken from the Myers Briggs test. The MBTI uses far more questions, but most had to be removed to keep within the time frame of this thesis. An example question, which was part of determining the Thinking-Feeling value, is: Are you swayed more by : 1 convincing evidence a touching appeal After receiving an answer the following was asked: How certain are you about your answer? 1 to 5 Say someone would answer here with certainty 3, this would then result in an answer value of -3, because the feeling function to which the answer refers sits on the opposite side of the thinking function. After the test the answers were stored in a file. 5 people were asked to voluntarily participate in the questionnaire. 7 Fitting the data to MBTI and the two Qubit model For each person a Myers-Briggs type could then be determined. This was simply done by scaling all answers to the interval [ 1, 1]. Now for each group of questions, each representing a function or attitude, the mean value could be determined. In the thinking-feeling case this meant that if the value was bigger than 0 the thinking function was appointed to the personality. Obviously, if the value was smaller than zero the feeling function was appointed. To get the parameters τ, α and θ for the -qubit model a χ -fit was used. As mentioned earlier, and as depicted in figure 7, sometimes multiple solutions are possible. The χ -fit however only finds one solution, when appointing personality types. Due to time constrictions, looking for the other solutions was not possible and could be subject for further research. To incorporate the Myers-Briggs lifestyle function J, we simply looked at the dominant personality function. If the sensing or intuition function was dominant, the lifestyle function would become the perceiving function P. Otherwise we would use the judgment function J. All personalities, both MBTI and -qubit, can be found in the appendix. In the MBTI case the psychological functions and attitudes are represented reasonably equal. However the thinking function was represented significantly within the first ten subjects. 1

15 This could be because these subjects were Artificial Intelligence students. This study asks for a lot of logical and causal reasoning skills, which in turn makes this outcome logical. In the -qubit case we also see the dominance of the thinking function in the first ten subjects. Furthermore we find a change of primary function in 5% of the time. Dugan and Wilson found a 46% change when comparing the Singer-Loomis model to the MBTI. 00, p. 3 To what extent these changes are the same is yet to be determined. In the -qubit case there were three subjects with a τ value of over 0.95, which indicates that they have a weak shadow. In these cases we find what we would expect, a near match with the MBTI case, as the MBTI does not incorporate a shadow function. If we look at a subject with a lower τ, such as subject 16, we find MBTI personality INTJ. In the -qubit case we find the ESTJ personality which is entangled with it s shadow INFJ. The strength of the entanglement, as stated by the variable τ, is 6%. This means that the shadow takes up 38% of the personality. If the shadow were to intervene in some of the questions asked in the questionnaire, approximately 38% of the time in this case, it could be the reason why the MBTI personality differs from the -qubit personality. In the MBTI case there is no explanation to why someone who is an introvert according to the MBTI would give extrovert answers to some of the questions, as the MBTI does not use any shadows or forms of superposition. The - qubit model does do this which, if you believe in Jung s theories, makes it the richer, more explanatory model of the two. 8 Generating artificial personalities Simulations give people an easy way of testing hypotheses. A car simulator gives people the chance to learn to drive without having to worry about making mistakes and simulations of models give scientists the possibility to gather data that might be time consuming or difficult to gather in the real world. In this case personalities many can be generated to be tested upon, for example by psychologists or people with a background in Artificial Intelligence. Also robots could later be given random personalities, which makes having a model for accurately generating them useful. Using a formalized model to Jung s psychology has this advantage, we can now generate artificial personalities. Given some random value for the parameters τ, α and θ we can create a personality. This is done by filling in the variables into formulas 4, 5 and 6. Now this personality can fill in the questionnaire. Again, using the variables we can determine the chance that a personality will answer the extrovert answer by using formula 7. Using a random number generator artificial answers could be generated, returning 1 if the answer was extrovert and -1 if the answer was introvert with the chance given by the parameters. The same can be done for the psychological functions T and S using formulas 8 and 9 respectively. To fully simulate the questionnaire, where answers can be given with a certainty level scaling from 1 to 5, for each question the random answer generator ran 5 times where after the returned values were summed up. 9 Cronbach s alpha and cluster analysis A fairly common way to evaluate the reliability and consistency of a questionnaire is the use of Cronbach s Alpha. It measures the internal consistency reliability, in other words how well a set of questions or items measure the same concept. In our case we can measure how well each set of questions measure the same set of psychological functions or attitudes e.g. the questions 13

16 for the Feeling vs the Thinking function. The definition of Cronbach s Alpha Cronbach, 1951, p. 31 is as follows: α = N Ni=1 σ Y 1 i N 1 σx 31 Where N is the number of components, σ X is the variance of the total test scores and σ Y i is the variance of component i. As an example, we can use Cronbach s alpha to get an impression of how good the Introvert/Extrovert questions relate to one another. If they all genuinely measure the same concept we will get a alpha score of around 1. A score of 0.7 and above is generally accepted as reliable and means that the questions are related to each other and measure the same concept. However the threshold of 0.7 is only a guideline as Cronbach s alpha can be influenced by multiple factors Spiliotopoulou, 009, such as the distribution of the data, the sample size and the width of the scale. In our case we have a uniform distribution in our data which causes an underestimate of the alpha value. A low alpha value would prevent us from being able to make any valid assessments about the outcome of our data. Values of Cronbach s alpha can also be negative. This happens when the average covariance between the variables is negative Nichols, According to Nichols the most probable cause of finding a negative alpha with a small sample size is that while the true population covariances among items are positive, sampling error has produced a negative average covariance in a given sample of cases For our questionnaire we find the following results: Type α E T -4,4 S -1,5 When filling in the questionnaire with generated personalities we can also calculate Cronbach s alpha. We find: Type α E -1,3 T -13, S 0 In both cases we find very bad alpha values, even when we take the influencing factors into account no decent score is achieved. This could be related to the small sample size of 5 people. Another reason could be that there is something wrong with the questions and that they indeed don t measure the same concept. However, we also find bad values in the artificially generated case. Here we know we are measuring the same concept, but we still get low and even negative scores. Therefore there must be a principal reason that the alpha values are so bad. A reason for this may be found in figure 5. Here we see that if a personality has a strong primary function, the auxiliary and tertiary functions will always be situated very close to each other and thus have approximately the same chance of answering a question. This generates a lot of variance in the data which in turn lowers the alpha value. Additionally to calculating Cronbach s alpha a cluster analysis was performed. One would expect that questions that measure the same thing would cluster together. When performing this on the answers of the questionnaire, we find figure 8. Here we only used the first 18 14

17 questions because the -qubit model cannot fill in the final six questions about the judgment and perception axis the MBTI contains. The three groups of six have been colored in to get a quick intuitive look of how the data is clustered. Figure 8: Cluster analysis performed on the results of the questionnaire When we perform the same cluster analysis on the data we get from the artificially filled in questionnaire, we find figure 9. Figure 9: Cluster analysis performed on the results of the questionnaire with artificial personalities In both cases we see that no true clusters are found. The three sets of questions overlap each other and each question is almost evenly divided over the space. As we find no clustering and as the origin of the questions are from the MBTI and were carefully selected that they do measure the same concept, we again must conclude that there must be principal reason for these results. Using Cronbach s alpha and cluster analysis can therefor at this time not be used 15

18 to determine empirical differences between the MBTI and the -qubit case. This could be a subject for further research. 10 Conclusion and further research A first step has been made in the comparison between the -qubit model and the MBTI. Although only 5 subjects were compared to a Myers-Briggs test with only 4 questions, the full MBTI has about 73 questions, some conclusions can be made. Conceptually the -qubit model seems better because of the use of less variables than the MBTI. Also it follows Jung s theories more accurately by implementing a shadow which is entangled with someones personality. In the results found, people with a weak shadow showed a near perfect match with the MBTI, indicating some correlation. Although the use of the shadow makes the -qubit model more divers and descriptive. Also the first attempts to find some empirical evidence of which models might perform better need further research. Cronbach s alpha and the cluster analysis showed us some bad results, but this is however probably to some innate properties of the models. In the future more subjects should be used to ensure that a small sample size is not the problem with Cronbach s alpha. Also using the full MBTI questionnaire should lead to better MBTI results for comparison. Further research could also make a comparison with the Singer-Loomis TDI. The model can partly mimic the Singer-Loomis TDI, which always uses psychological functions in combination with a attitude, by defining some new operators. If we would want to combine the thinking-feeling function with the extroversion-introversion attitudes we simply take E T as the new operator. The curse of ambiguity that resides in this model is a big problem for the model. The ambiguity makes it difficult to conclude anything concretely when you know that the fitted personalities could have another solution. The the full extent of it s effect needs further research. The future should however be met with some optimism. The use of few variables to describe personalities and the ability generate more accurate personalities gives it the upper hand, for now. 16

19 11 References Blutner, R & Hochnadel, E. Yet unpublished Two Qubits for C.G. Jung s Theory of Personality. Cronbach, L. J Coefficient alpha and the internal structure of tests. Psychometrika, 163, Dugan, S., & Wilson, K. 00. Singer-Loomis TDI: The next generation of psychological type instrument: University of Calgary, Haskayne School of Business, Working Paper Jung, C. G Psychologische Typen. Zürich: Rascher. McCrae, R R & Costa, P T Reinterpreting the Myers-Briggs Type Indicator From the Perspective of the Five-Factor Model of Personality. Journal of Personality 57: Myers, I. B The Myers-Briggs Type Indicator. Palo Alto, Cal.: Consulting Psychologists Press. Myers-Briggs, I., & Myers, P. B Gifts Differing: Understanding Personality Type. Palo Alto, Cal.: Davies-Black Publishing. Singer, J., & Loomis, M. E The Singer-Loomis Inventory of Personality. Palo Alto, Cal.: Consulting Psychologists Press. Spiliotopoulou. 009 Reliability reconsidered: Cronbach s alpha and paediatric assessment in occupational therapy. Australian Occupational Therapy Journal Nichols, D. P My Coefficient a is Negative!. SPSS Keywords, Number Stevens, A Jung - A very short Introduction. Oxford: Oxford University Press. 17

20 1 Appendix A : the questions used in German, English and Dutch 1.1 Instructions Instruction Mark the answers which you think most valid. Next, indicate for how certain you take this answer: 1. completely uncertain. uncertain but with a week preference for the given answer 3. moderately uncertain with a clear preference fort he given answer 4. moderately certain 5. absolutely certain Instruktion Whlen Sie die jenige Antwort, die Sie fr zutreffend halten. Nachdem Sie die Antwort gewhlt haben, geben Sie an, wie sicher Sie sich bei der Entscheidung waren: 1. völlig unentschieden. unsicher mit nur leichter Prferenz fr die angekreuzte Antwort 3. relativ unsicher mit deutlicher Prferenz fr die angekreuzte Antwort 4. einigermaen sicher 5. sehr sicher Instructies Geef het antwoord dat het meest bij jou past. Geef vervolgens aan hoe zeker je bent van je antwoord: 1. volledig onzeker. onzeker, maar je hebt een zwakke voorkeur voor het gegeven antwoord 3. gematigd onzeker, maar wel met een duidelijke voorkeur voor het gegeven antwoord 4. gematigd zeker 5. absoluut zeker EXAMPLE Common sense is o usually reliable o frequently questionable BEISPIEL 18

21 Gesunder Menschenverstand ist o oft vertrauenswrdig o oft fragwrdig VOORBEELD Gezond verstand is o over het algemeen betrouwbaar o regelmatig twijfelachtig 1. Questions E/I 1. Verhalten Sie sich in Gesellschaft so, dass Sie o den ersten Schritt tun, die Unterhaltung in Gang zu bringen o warten, bis Sie angesprochen werden At a party, o do you take the first step in order to start a conversation o do you wait until somebody else starts talking to you Op een feestje, o neem jij de eerst stap om een gesprek te beginnen o wacht je af totdat iemand met jou gaat praten. Wie verhalten Sie sich beim Luten des Telefons: o Sie beeilen sich, um als erster den Hrer abzunehmen o Sie hoffen, dass ein anderer den Hrer abnehmen wird When the phone rings, do you: o hurry to get to it first o hope someone else will answer it Als de telefoon gaat o neem je hem meteen als eerste op o hoop je dat iemand anders opneemt 3. Haben Sie lieber o viele Freunde mit kurzzeitigem Kontakt o einige Freunde mit lnger andauerndem Kontakt Do you prefer to have o many friends with short-living contacts o only a few friends with long-standing contact Heb je liever o veel vrienden waar je kortdurend contact mee hebt o alleen een paar vrienden waar je langdurig contact mee hebt 4. Ist es so, da 19

22 o es Ihnen leichtfllt, sich eingehend mit Fremden zu unterhalten o Sie Fremden gegenber wenig zu sagen wissen Is it the case that o it is simple for you to speak with people you don t know o you have less to say to people you don t know In het geval dat je een onbekende tegen komt o praat je er toch makkelijk mee o heb je eigenlijk niets te zeggen 5. Suchen Sie bei einer Party den Kontakt mit o mglichst vielen, einschlielich Fremden o nur wenigen, die Sie kennen At a party do you o interact with many people, even strangers o interact with a few friends Op een feestje o ga je om met veel mensen, ook onbekenden o ga je alleen om met een paar vrienden 6. Sind Sie meistens o leicht ansprechbar o etwas reserviert Do you consider yourself o rather talkative o somewhat reserved Zie jij jezelf als o praatgraag o ietwat teruggetrokken T/F 1. Treffen Sie Entscheidungen lieber auf der Grundlage von o Normen o Gefhlen Are you more comfortable in making your judgements based on o Norms o Feelings Waar baseer je liever je oordelen op? o Normen o Gevoelens. Fllt es Ihnen leichter, o Urteile auf logischer Basis zu treffen 0

23 o Werturteile zu treffen Are you more comfortable in making o Judgements on a logical basis o Value judgements Maak je liever o Oordelen op een logische basis o Waarde oordelen 3. Welches ist das grere Kompliment: o er ist ein sehr logischer Mensch o er ist ein sehr sentimentaler Mensch Which is more of a compliment o There s a logical person o There s a sentimental person Wat krijg je liever als compliment? o Jij een verstandig persoon o Jij bent een gevoelsmatig ingesteld persoon 4. Fhlen Sie sich mehr hingezogen zu dem, was Sie o berzeugt o berhrt Are you swayed attracted more by o convincing evidence o a touching appeal Wordt je meer aangetrokken door o overtuigend bewijs o een emotioneel pleidooi 5. Sind Sie mehr beeindruckt von o Prinzipien o Emotionen Are you more impressed by o principles o emotions Wordt je meer overtuigd door o principles o emoties 6. Was wnschen Sie sich selbst mehr: o einen klaren Verstand o starkes Mitgefhl What do you wish more for yourself 1

24 o a pretty clear brain o strong sympathy Wat heb je liever? o Gezond verstand o Veel symapahtie kunnen tonen S/N 1. Schriftsteller sollten sich o klar und unmissverstndlich ausdrcken o mehr unter Zuhilfenahme von Analogien ausdrcken Do you like writers who o say what they mean o use metaphors and symbolism Hou je meer van schrijvers die o zeggen wat ze bedoelen o metaforen en symbolismen gebruiken. Wodurch lassen Sie sich eher leiten: o durch Fakten o durch Prinzipien Are you more often lead o by facts o by principles Word je vaker geleid door o feiten o principes 3. Verlassen Sie sich eher auf Ihre o Erfahrungen o Ahnungen Do you prefer to trust o your experience o your intuition Vertrouw je liever op je o Ervaringen o Intutie 4. Was schtzen Sie an sich selbst mehr: o einen ausgeprgten Sinn fr Realitt o ein lebhaftes Vorstellungsvermgen Do you prize in yourself o a strong hold on reality

25 o a vivid imagination Beschrijf jij jezelf meer als iemand met o beide benen op de grond o een levendige fantasie 5. Welche Art von Geschichten bevorzugen Sie o Action- und Abenteuergeschichten o Phantasie- und Heldengeschichten In stories do you prefer o action and adventure o fantasy and heroism Wat prefereer je in verhalen? o actie en avondtuur o fantasie en heldhaftigheid 6. Nehmen Sie sprachliche uerungen eher o wrtlich o bertragen/metaphorisch Are you inclined to take what is said o more literally o more figuratively Neem je gesproken uitlatingen eerder o figuurlijk o letterlijk J/P 1. Treffen Sie eine Wahl o eher berlegt o eher impulsiv Do you tend to make your choices o well thought out o rather spontaneous Maak je je keuzes o goed doordacht o nogal spontaan. Welche Situation sagt Ihnen mehr zu: o die strukturierte und planmige o die unstrukturierte und unplanmige What situation do you prefer o structured and planned o unstructured and unplanned 3

26 Welke situatie staat je meer aan: o een geplande gestructureerde o een ongeplande en ongestructureerde 3. Was zieht Sie mehr an: o vernnftige Menschen o einfallsreiche Menschen Are you more attracted to o reasonable people o creative and unconventional people Voel je je meer aangetrokken tot o verstandige mensen o creatieve en onconventionele mensen 4. Neigen Sie mehr dazu, o eher vorstzlich als spontan zu handeln o eher spontan als vorstzlich zu handeln Do you have a tendency o to act planned rather than spontaneous o to act spontaneous rather than planned Heb je de neiging om o gepland te handelen o spontaan te handelen 5. Neigen Sie mehr dazu, o eher rasch zu entscheiden o grndlich und eher langsam zu entscheiden Is it your way to o make up your mind quickly o pick and choose at some length Neem je je beslissingen o snel o doordacht en langzaam 6. Neigen Sie dazu, Ihre Arbeitsaufgaben, o gut geplant zu erledigen o eher spontan und ungeplant zu erledigen On the job, do you want your activities o scheduled o unscheduled Wil je op je werk dat al je activiteiten o gepland zijn o ongepland zijn 4

27 13 Appendix B : The personalities # MBTI -qubit 1 ISTJ 60% ESFP ISTP 66% ISFP 3 INTJ 76% INTP 4 ESTP 75% ESTP 5 ENFP 73% ENTP 6 ESTJ 6% ESFP 7 ESTP 94% ESTJ 8 ISTJ 53% ENTP 9 INTP 70% ESTP 10 ENTJ 74% ESTJ 11 ESFJ 58% ESFP 1 INFP 6% ENFP 13 ESFP 90% ESFP 14 INTJ 69% ESTP 15 ISTJ 66% ISFJ 16 INTJ 6% ESTJ 17 ESTJ 94% ESTJ 18 ESTP 75% ESFP 19 ESFJ 55% ESTP 0 INFJ 55% ENTJ 1 ESTJ 75% ISTP ENTJ 75% INTJ 3 ESFJ 83% ESFP 4 ESFP 7% ESTP 5 ENFP 59% INTP 5