Lets Talk Distributions

[ygolo]

I didn't post this in the science section because I wanted to find out more about how they relate to the Big Five, MBTI Step II and MBTI Step III. I am a "lay person" when it comes to these things but quite statistically savvy. It may sound arrogant, but I believe I understand common factor analysis, principle component analysis, other factor models, and multivariate linear regression in general, better than most people--even many who (over)use it regularly.

This is what I do know (I'll be doing a lot of "explaining," not to be condescending, but simply to get people who may be interested up to speed).

There are two kinds of distributions that seem to come up in this forum:

• "bimodal" distributions. Bi-modal meaning "having two modes." Mathematically speaking the mode of a distribution is the most frequently occurring value in the distribution--the "peak" if you will. A bimodal distribution will show two peaks. Granted, one may be the official mode, mathematically speaking. But plotting the distribution visually will show to peaks.
  
  This kind of distribution, I believe, is popular in the Myers-Briggs and related typologies. I have no idea what particular bimodal distributions are used for each dichotomy, but I suspect the sum of two Gaussians of different means is popular.
  
• "Gaussian" distributions. Also, called "bell curves," or "normal" distributions. I dislike the use of the word "normal" because, in my training, that is reserved for the Gaussian of mean 0, and standard deviation of 1. Also, words like "normalize" are used for distributions of all sorts, so it can create confusion in the belief that when we "normalize" something we are trying to force fit something to a Gaussian (which may or may not be true).
  
  Gaussians are the kinds of distributions seen in the Five Factor Model typology, I believe.

Some facts that I believe everyone participating in the discussion should know

• The most important statistical fact (beyond the Law of Large numbers which people seem to know inherently) I believe people should know is the Central Limit Theorem.
  The Central limit theorem states that the sum of independent, identically distributed random variables of finite variance tends towards a Gaussian distribution. It should be clear to people that the same is true for averages of identically distributed random variables (simply scaled down by the number of variables added together).
  
  The relevance here is that if you have a big questionnaire in which all the questions have bimodal distributions in the answers, the sum or average will tend to be Gaussian, unless there is a strong correlation between the answers given on each of the questions. This seems to be an artifact of testing also. In a way, you can create "noise" in a test which when added together tends to be Gaussian (this is especially true if the noise is purely random).
  
• A psychological tendency know as the Central Tendency Bias. When given a range of selections to chose from, people tend to chose toward the middle, even if a more extremal value is more accurate. When it comes to answering questions describing our own personalities, this will also tend to create a more Gaussian distribution.
  
• The distribution of answers on a question with only two answers will necessarily be bimodal because there are only two possible values. That is Bivalent implies bimodal. This seems to be an artifact of how the question is asked, not necessarily anything real.
  

My questions in general concerning the "validity" of personality systems

• Why we believe that Step III will be more valid than the current MBTI?
• Why is the FFM more "academically blessed?"
• Why are MBTI, DiSC, Temperament (all Myers-Briggs like), etc. more popular in corporations still?
• Do you believe the use of either typologies leads to Self-fulfilling prophecies?
• Do you believe use of either typology will do more harm than good?
• Although, I understand the statistics behind various factor analysis, I find psychometric papers hard to read, because of assumed knowledge of what particular letter-denoted variables are, and general use of psychometric jargon. Is there a good way to find out what factor models are being used, and what the original data sets, correlation matrices, or covariance matrices were?

 

[ptgatsby]

This kind of distribution, I believe, is popular in the Myers-Briggs and related typologies. I have no idea what particular bimodal distributions are used for each dichotomy, but I suspect the sum of two Gaussians of different means is popular.

IIRC, it's not. The actual distribution is kurtotic and is still unimodal (I am assuming you are talking about the test scores, not preferences) Unfortunately, CAPT doesn't support much research into this, strangely enough, so there isn't much else I can say to it. It's been mentioned to me several times now, however, that test results from step II are decidedly not bimodal.

 

[ygolo]

IIRC, it's not. The actual distribution is kurtotic and is still unimodal (I am assuming you are talking about the test scores, not preferences) Unfortunately, CAPT doesn't support much research into this, strangely enough, so there isn't much else I can say to it. It's been mentioned to me several times now, however, that test results from step II are decidedly not bimodal.

Its funny, when I was introduced to the FFM, I remember reading that one of the differences is that the distributions are not bi-modal.

It is quite possible (IME likely) that non-zero kurtosis is the result of an underlying bimodal distribution added with Gaussian noise.

To bring onlookers up to speed:
kurtosis is the 4rth "moment" of a distribution.

The moments of a distribution is an analogy (a perfect mathematical one) to physical moments.

The first moment is the mean of the distribution.
The second is the variance.
The third skewness.
The fourth is kurtosis.

You can find all the moments of a distribution using a moment generating function assuming it exists.

I hope someone knows where to find further information.

 

[ptgatsby]

Its funny, when I was introduced to the FFM, I remember reading that one of the differences is that the distributions are not bi-modal.

That's what I thought at first. However, a while back I got PMed from a researcher using MBTI who corrected me. I remember looking into it and coming to the same conclusion. Then again later, elsewhere, I was talking to a psychologist who mentioned it to me when CAPT was talking about massaging their data. It was generally rejected to do any normalization - the reference was how it was unusual to not attempt to fit the data to any existing model, even though the data tended to resemble a normal model.

(I bring it up for those that want to look into it - I'm out of the psychometrics investigation department now )

 

[edcoaching]

The reason corporations still use MBTI etc. is because the instruments themselves have no magic--it's how individuals/teams/coaches/trainers APPLY knowledge about self and others that brings about change or efficiencies or better communication or cohesive teams or whatever the purpose of taking the instrument was.

So...corporations are often looking for trainers/consultants who have expertise in those applications. They often use the MBTI because it's pretty reasonable and very effective when interpreted by knowledgeable people who help people find their best-fit types as opposed to only using reported types.

For really good trainers...it doesn't really matter what instrument they use. The real work starts in the interpretation and application. Most of them don't need any instrument but instead can help people understand differences through reflection and exercises.

 

[edcoaching]

Step III

And Step III...it's a whole different animal.

It will only be available for purchase by people trained in counseling. The instrument is totally separate from Step I and Step II and looks for type development--how well a person uses Perception (through S and N) and Judgment (through T and F).

Here's a link to the most current information on it.

MBTI Step III - CAPT.org

 

[ygolo]

Maybe I've been brainwashed by working in a technical field, but if the tests themselves aren't useful indicators how do you go build a "body of knowledge?"

How do you know if your coaching is effective or good? do you use feedback surveys? or do you just have a great memory?

How does one transfer the knowledge of what is effective from one coach to another?

Do you find Myers-Briggs theory itself applicable?

Sorry if this feels like the third degree, I just have a lot of questions.

I am asking because, I have never been a "natural" at anything. I generally get better by learning and incorporating "Best known Methods" in particular fields into my thinking.

The reason I turned to personality theories is to learn something I could incorporate into my thinking.

I don't necessarily want to become a coach, but I do want to know how they go about doing things.

 

[edcoaching]

Maybe I've been brainwashed by working in a technical field, but if the tests themselves aren't useful indicators how do you go build a "body of knowledge?"

First off, you rely not on reported type [results from MBTI, Golden, PTI, etc.] but on best-fit type--the type a person self-identifies through multiple methods which may include an instrument. The best studies are based on best-fit, not reported type, because the instruments were never meant to be diagnostic tools. They're self-reporting so there's more error variance than, say, in the MMPI.

Second, a huge body of knowledge has been built up by professionals who have gathered information from confirmed people of the 16 types that show distinct patterns in all kinds of things--career choice, communication preferences, change needs, decision making, and so on.

Third, you see "what works" and capture that in studies. For example (and this won't surprise you) Extraverted and Sensing students catch onto math concepts faster when they use hands-on materials and are given time to experiment with them in order to make sense of the problem. They need to move, talk and ask questions to develop understanding. We filmed students doing the same tasks and there were clear differences (and yes, we used best-fit, not reported type, in the study).

How do you know if your coaching is effective or good? do you use feedback surveys? or do you just have a great memory?

I mostly coach teachers, so I'm looking for whether they change their teaching practices. Sometimes I'm looking at assignments, classroom management, differentiated activities, rigor...I might actually record class time spent in each learning style, or rate the rigor of assignments, or together we'd look at student work to see if any one group of students is not catching on. So my effectiveness is judged by whether the teacher is meeting the needs of more students.

For teams, sometimes I survey before and after. If I've been called into mediate in a huge conflict situation, I might do a blind survey a few weeks later to find out who thinks they've made progress toward resolution and who thinks more intervention is needed. The last time I did that, where there'd been huge problems, over 70% were ready to move ahead with teaming, 20% were ready but wanted a few more protocols to continue the progress, and just 10% felt things hadn't been resolved (100% had felt there was too much conflict to team effectively before the intervention...)

How does one transfer the knowledge of what is effective from one coach to another?

There are great books and resources on coaching, teambuilding, conflict resolution, etc. Type puts patterns to things we see in human nature and you can learn how to use those patterns to foster understanding.

There are workshops all over the place where you can experience things that work and learn how to use them with others.

I train coaches through "live" case studies, where they learn how to adjust their style to interview and create action plans with people of dissimilar types. They're a blast and people quickly grasp why changing up their style is so important.

Do you find Myers-Briggs theory itself applicable?

Absolutely. It's the theory, not the instruments, that does the work. Here are some examples.

• When I finally got teachers to grasp the different needs of Judging and Perceiving students at one school, the teachers worked to implement strategies that took the failure rate on science fair, ,history day, major reports, etc., from 30 % to 0-2%.
• In a team where over 60% of the employees were siding with the "old" president who still worked there, I used type theory to help them understand and appreciate the style of the new president. The intervention was so lasting that other department chiefs had me work with their staffs.
• One team's meetings had been ending in shouting matches. We did an afternoon workshop just on communication and at the end the biggest troublemaker looked at all the work posted around the room and said, "Can we always sit in our [ST, SF, NF, NT] groups so we remember that we actually speak foreign languages?" The employees asked to have me return for at least 4 other meetings, working on other issues with them.
• One student, responsible for 50% of the referrals to the principal's office, learned about his own type and his best approaches to learning and so did his teachers. He was NEVER in the principal's office again.

I could go on and on. Ethically used, type can help people understand each other's strengths in ways that can truly be constructive. Hope this doesn't sound like a lecture--it is true that it is often misused, so a lot of people have only had superficial experiences and have no idea how effective deep use of the theory can be...

 

[ygolo]

Thanks edcoaching. That was very edifying.

Since the original topic seems to be a boondoggle (unless you can speak to the distributions), I'd like to follow-up on your last post.

1) How does one go about finding the best-fit type of a person?
2) What are some principles to adjusting one's style to others?
3) How do you overcome skepticism regarding applying type theory in groups?
4) What sources would you recommend to understand Myers-Briggs theory like a coach?
5) What other knowledge is needed to put type theories in context?

 

[edcoaching]

Thanks edcoaching. That was very edifying.

Since the original topic seems to be a boondoggle (unless you can speak to the distributions), I'd like to follow-up on your last post.

Sorry about that...but you did ask about Step III

1) How does one go about finding the best-fit type of a person?

Think I'll make that a separate thread

2) What are some principles to adjusting one's style to others?

If they're the ones who have to do the changing, then you're the one who has to switch styles. So...if you want an employee to perform better, communicate in their style. If a student is struggling, meet their learning style needs.

Adjusting for E and I means thinking about wait time, time to process out loud, etc. Adjusting for J and P means thinking about the other person's closure style, not your own. Fairly simple yet rocket science in its effectiveness.

The heart of communication style, then is the function pairs. ST, SF, NF, NT. Quick tips:
ST: Be brief and cover the details in order
SF: Give me the details that affect me and those I work with or serve
NF: Relate to big ideas and listen to me as well
NT: Respect my intelligence and give me the options

3) How do you overcome skepticism regarding applying type theory in groups?

If I've been brought in as a trainer, within the first 10 minutes I get the group involved in an exercise where the type differences are clearly demonstrated. They sit down saying, "Okay, this is real. Now show us what we can do with it..."

If they're considering whether to use it at all, usually the skepticism arises from what they've heard about the instruments. I emphasize that it's application that counts and describe the very real results I've gotten.

If it's an individual within a group, usually by the end of the day they've seen enough to know that even if it's not their first choice of theories, there's something to it.

4) What sources would you recommend to understand Myers-Briggs theory like a coach?

Visit Differentiated Coaching for Educators - Home and take a look at the coaching style descriptions available on the first page, and the case studies. The book is great too. You'll see seminars on coaching through type offered around the country by different local type organizations. Check calendars at Welcome to APT International And, there's a coaching SIG that you can join free that is organized through the same organization.

5) What other knowledge is needed to put type theories in context?

The stock answer is that you need to have the expertise in whatever field you're going to use type. So...you'd study marriage counseling, spiritual direction, coaching, teambuilding/organizational development, counseling, career counseling, etc. and use type within those contexts.

For example I'd already been trained as a strategic planning facilitator and the way we ran those sessions made an easy bridge to building teams.

 

[edcoaching]

back to the original post

Why is the FFM more "academically blessed?"

There is such bias against a bimodal distribution in the psychological community for the reasons you listed that the FFM, coming from factor analysis, fits what they think they know as reality. There is still great prejudice against Myers as well because she wasn't a psychologist, even though she developed two statistical techniques that no one else used until they could use supercomputers...

They also think an instrument should measure. Type instruments don't measure, they sort. One group or the other. Bimodal.

Do you believe the use of either typologies leads to Self-fulfilling prophecies?

If people use it to excuse their behaviors, yes. If people use it for development and growth, individually or in teams, no. I see people learn to operate out of their preferences when appropriate all the time (and thus move toward maturity)

Although, I understand the statistics behind various factor analysis, I find psychometric papers hard to read, because of assumed knowledge of what particular letter-denoted variables are, and general use of psychometric jargon. Is there a good way to find out what factor models are being used, and what the original data sets, correlation matrices, or covariance matrices were?

You'd have to find the manuals for the NEO-PI, Sloan (I think that's a separate one) etc.

I'm not that big of an instrument buff--I can do what I do with or without an instrument and sometimes it's better to use nothing at all than to risk people feeling like an instrument is labeling them...

 

[Kora]

Now there's even a Step III? Oh wow.

 

[edcoaching]

Now there's even a Step III? Oh wow.

It's TOTALLY different. Not about finding 4 letters but about finding your best paths to development...

 

[INTJMom]

...
My questions in general concerning the "validity" of personality systems
Why are MBTI, DiSC, Temperament (all Myers-Briggs like), etc. more popular in corporations still?

I'm not sure, but I suspect that they may be more heavily marketed, and that for various reasons.
It takes a long time for new ideas to catch on.

Do you believe the use of either typologies leads to Self-fulfilling prophecies?

I have witnessed it a little bit of that on forums.
I assume it happens with a very small percentage of the people.

Do you believe use of either typology will do more harm than good?

As in everything else, it depends what it is used for. I have heard of people suffering negative consequences in the workplace by being pigeon-holed by their superiors. That is definitely a danger. I think Type Theory should be used as a guide for understanding, not as hard and fast ruler for pre-judging. I believe Type Theory does much more good than harm. It fosters understanding and acceptance among people. In my own experience, understanding my childrens' types may be the single most helpful thing I have ever learned as a mother.

 

[INTJMom]

...
Absolutely. It's the theory, not the instruments, that does the work. Here are some examples.

• When I finally got teachers to grasp the different needs of Judging and Perceiving students at one school, the teachers worked to implement strategies that took the failure rate on science fair, ,history day, major reports, etc., from 30 % to 0-2%.
• In a team where over 60% of the employees were siding with the "old" president who still worked there, I used type theory to help them understand and appreciate the style of the new president. The intervention was so lasting that other department chiefs had me work with their staffs.
• One team's meetings had been ending in shouting matches. We did an afternoon workshop just on communication and at the end the biggest troublemaker looked at all the work posted around the room and said, "Can we always sit in our [ST, SF, NF, NT] groups so we remember that we actually speak foreign languages?" The employees asked to have me return for at least 4 other meetings, working on other issues with them.
• One student, responsible for 50% of the referrals to the principal's office, learned about his own type and his best approaches to learning and so did his teachers. He was NEVER in the principal's office again.

I could go on and on. Ethically used, type can help people understand each other's strengths in ways that can truly be constructive. Hope this doesn't sound like a lecture--it is true that it is often misused, so a lot of people have only had superficial experiences and have no idea how effective deep use of the theory can be...

Thank you for sharing your experience with us.
This part of your post reflects the very reason why I am so excited about MBTT!
It has been a tremendous help in my life, and I wouldn't have half the success I have in my relationships if it wasn't for MBTT! and namely, Barron and Tieger's work especially.

 

[edcoaching]

This part of your post reflects the very reason why I am so excited about MBTT!
It has been a tremendous help in my life, and I wouldn't have half the success I have in my relationships if it wasn't for MBTT! and namely, Barron and Tieger's work especially.

Yeah, Tieger's stuff is great...I've talked to lots of INTJ moms who were "saved" by type as they learned why the preschool years weren't quite as enchanting for them as they were for a lot of moms. One told me, "Crafts? Pouring juice? There aren't any goals in my day. I want to discuss the book I just read, learn something, explore something!" They so appreciated when their kids hit grade school...

 

[ptgatsby]

They also think an instrument should measure. Type instruments don't measure, they sort. One group or the other. Bimodal.

That should be binary, not bimodal... unless they introduced strength as a component, anyway, which would require it to measure, not sort. If they have, I actually have to reject the premise of sorting into two groups rather than comparative to population, since the distribution of the sorters do not indicate any preference of one dimension over the other in a bimodal fashion.

 

[ygolo]

That should be binary, not bimodal... unless they introduced strength as a component, anyway, which would require it to measure, not sort. If they have, I actually have to reject the premise of sorting into two groups rather than comparative to population, since the distribution of the sorters do not indicate any preference of one dimension over the other in a bimodal fashion.

You get a spread because of noise and randomness in the environment. It is quite common in classification problems. Granted, I am coming from an an engineering background but the principles ought to be the same.

For instance, when making a decision of whether or not there is an object in front of you based on the intensity of a reflected signal coming back.

This is a statistical phenomenon. You will get a bimodal distribution of the signal coming back if you run experiments with a portion of the time with object there, and a portion without it there(proportions chosen according to prior likely hood of object being there). The reason is that the medium carrying the signal introduces noise.

The less noise there is the more cleanly bi-valent the distribution will be. But a bi-valent (binary) distribution is a kind of bimodal distribution.

 

[ptgatsby]

You get a spread because of noise and randomness in the environment. It is quite common in classification problems. Granted, I am coming from an an engineering background but the principles ought to be the same.

For instance, when making a decision of whether or not there is an object in front of you based on the intensity of a reflected signal coming back.

This is a statistical phenomenon. You will get a bimodal distribution of the signal coming back if you run experiments with a portion of the time with object there, and a portion without it there(proportions chosen according to prior likely hood of object being there). The reason is that the medium carrying the signal introduces noise.

The less noise there is the more cleanly bi-valent the distribution will be. But a bi-valent (binary) distribution is a kind of bimodal distribution.

Good points, but I was only referring to the "model" being chosen to fit the data into.

The question I ask you - why do you accept a binary/bimodal distribution as the model of choice? Do you see "sorting" as different than "measuring"? Are the traits fairly reduced to a 0/1 state?

If you know that it should be bi-modal, then it works. Do you?

 

[ygolo]

Good points, but I was only referring to the "model" being chosen to fit the data into.

The question I ask you - why do you accept a binary/bimodal distribution as the model of choice? Do you see "sorting" as different than "measuring"? Are the traits fairly reduced to a 0/1 state?

If you know that it should be bi-modal, then it works. Do you?

I see sorting as one form of measurement. It has to do with what possible values the actual situation would create. Probability theory, plus some basic assumptions followed with mathematical reasoning yields which model we use.

In the case of detecting an object, I know it will be bimodal. The object is either there or not, and there will be noise. This follows from the understanding of the situation at hand.

In the case of a coin-flip, we also know it will be bimodal (a Bernoulli distribution to be more precise.)

In the case of defects in a part, or random events in a continuum, the distribution would be a Poisson distribution.

One expects Gaussians when averaging or summing large number of quantities.

One expects when multiplying random variable the the log of the resulting random variable will Gaussian.

Gaussians also come up in linear regression. In fact, this is when Gauss introduced the distribution, when he created linear regression.

An understanding of the problem at hand determines the distribution to use based on probability theory and plausible "first principles". It will often also give a-priori conditions. There is no getting around this problem. One always has to have assumptions about distribution based on some logical understanding before modeling. Believing that you don't have assumptions only means you don't understand your assumptions.

If your intention is to sort. Your are likely going to sort to a finite number of categories. The "measure" in this case is discrete. But you have to have a way to make the measurement also. The measuring apparatus needs to be calibrated, and once you do, you will know what sort of distortion or noise the instrument will introduce. The laws of probability will then give you an expected kind of distribution and a-priori values for the parameters of the distribution. The data then modifies the distribution to give a "posterior" distribution.

This actually a very interesting topic in itself. But I am probably belaboring something you knew, since this is introductory inferential statistics.