Abstract:

This paper is a request for comments on an analysis system to be used with
enneagram personality profile test results for helping to interpret the
results of the test.

Introduction:

Personality profile tests are useful tools for analizing and determining a
person's type in the Enneagram system.  These tests usually result in a set of
scores, one score for each of the enneagram Types, where the highest score is
supposed to be the test taker's core Type.  Scores in other Types are used to
determine the dominant Wing and whether the person is in a stress or security
point.  Other analysis based on the results of such tests can be made, and
theories about attributes, such as Harmonics, have resulted from such analysis.

The RHETI is one such test, and is perhaps the definitive enneagram scoring
system.  There are 288 total statements in the test, each of which corresponds
to one of the types.  Each enneagram Type, then, has 32 statements.  Each
statement is paired with a statement from another Type, resulting in each Type
being "compared" to each other Type a total of 4 times each.  This results in a
total of 144 forced-choice questions, in each of which the user must choose
between two statements.

A program:

Being a computer programmer, when I was introduced to the Enneagram my first
response was to build a computer program to administer an enneagram
personality profile test and perform some rudimentary analysis on the results.
The RHETI, for example, contains 144 questions which makes it relatively
accurate, but also rather tedious to take and total the results from.  I
wanted to provide a system which would ease the test-taking process, in
addition to providing various charts and diagrams about the results;
essentially, convenience items. While in the process of building this system, I
encountered some questions about the fundamental nature of the enneagram.  How
important is the highest score in determining the core Type?  How important
are the scores in attributes such as Wings, stress/security points, and
Harmonics?  In essence, how best do we determine our core types based on the
results of a personality test?

I've tried numerous models for interpreting the results of a test, and the one
I've settled on is described below.  I would like to emphasize that I do not
believe that automatic, computerized analysis of enneagram tests can replace
human analysis.  In particular, the program is a *tool* which can be used
to *aid* human analysis, not replace it.  The program merely does that
which computers do best: tracking and charting numbers, and presenting the
data in various forms.  This program is practically useless without additional
sources of information.  At it's best, this program is used in conjunction
with a number of enneagram books and the results of this program may provide a
compact form for taking to a qualified enneagram teacher for consulting.

The program consists of three parts, one of which is hidden.  The first part
is the test administrator, which allows a person to take an enneagram
personality profile test.  Since there is no such test that I know of that is
in the public domain, and since at this point I do not have permission from
any person holding a copyright on such a test to distribute their test, the
data files on which this part of the program relies have been ommitted from
distribution.  Consequently this feature of the program is unavailable.  The
second part of the program is a graphical chart of test results.  If the user
has the results from a test, such as the RHETI, they can enter the data into
the program and see the results charted.  The third part of the program is an
analysis of the results; this is partially hidden from the user, only visible
through the charting of the results.

This program will be distributed entirely free, and with source code.  The
only restriction on distribution will be that the program can not be sold. 

The analysis:

The analysis of the results is what concerns us in this paper.  The computer
requires a formula for determining which Types are dominant.  The equations
are below, and are simple to perform with a calculator.

In all cases, the "score" is the current Type being evaluated; the dominant
Wing is the Type on either side of the current Type with the highest score;
the dominant s/s point is the Type on the enneagram graph with the highest
score; and the dominant harmonic is the Type 2 away from the current Type to
either side with the highest score.  Here are some examples; it helps to have
an enneagram graph to look at while reading the examples:

     Type      : 5
     Wings     : 4, 6
     S/S Points: 7, 8
     Harmonics : 7, 3

     Type      : 9
     Wings     : 8, 1
     S/S Points: 3, 6
     Harmonics : 7, 2

The equations:

The first equation shown is for the RHETI, or any other test where the
maximum possible score in any type is 32, and the minimum is 0.  This is the
simple version of the equation, but only works for tests like the RHETI, where
the maximum score in a type is 32.

f(n) =  0  <= n < 9    ->  0
        9  <= n < 14   ->  1
        14 <= n < 19   ->  2
        19 <= n < 24   ->  3
        24 <= n < 33   ->  4

d(type t) = f( t's dominant wing score ) + 
           f( t's dominant s/s point score ) +
           f( t's dominant harmonic score ) 

g(type t) =  t's score - ( 12 - d( t ) )

total(type t) = t's score + d( t )

Start with the type with the highest score and calculate 'd' of the type, and
'total' of the type.  Then calculate 'g' of the type.  The number you get from
'g' is the minimum score; you can ignore all Types with scores below this
number as being potential core types.  Then get the type with the next highest
score and repeat.  Stop when there are no types left with a score at least
equal to the highest 'g' value.

Nothing beats an example.

Type : 1    2    3    4    5    6    7    8    9
Score: 10   13   12   19   25   12   21   6    26

The highest score is in Type 9.  9's dominant wing is 1, the dominant S/S
point is either 3 or 6 (they have the same score), and the dominant harmonic
is 7.
d( type 9 ) is then:
  f(9's dom. wing score)+f(9's dom. s/s point score)+f(9's dom. harmonic score) =
  f( 10 ) + f( 12 ) + f( 21 ) =
  1 + 1 + 3 =
  5
total( type 9 ) is:
  9's score + d( type 9 ) =
  26 + 5 =
  31
g( type 9 ) is:
  9's score - ( 12 - d( type 9 ) ) =
  26 - ( 12 - 5 ) =
  19

Since 'g' is 19, we can ignore all types with a score less than 19 as
potential core types, which rules out 1, 2, 3, 6, and 8, and leaves 4, 5, and
7 as potentials.  

The next highest score is 5, and we repeat.  5's dominant wing is 4,
its dominant s/s point is 7, and its dominant harmonic is also 7.

d( type 5 ) is:
   f( 19 ) + f( 21 ) + f( 21 ) =
   3 + 3 + 3 = 9
total( type 5 ) is:
   25 + 9 = 34
g( type 5 ) is:
   25 - ( 12 - 9 ) = 25 - 3 = 22

and we can rule out any type with a score less than 22, which eliminates all
other Types as potential core types.

In the end, we have:

   Type :   9    5
   Total:   31   34

So the odds are good that, while 9 has a higher score than 5, 5 is really the
dominant type.  This is because 5 has relatively strong scores in its wing,
s/s points, and harmonics, while 9 has relatively weak scores in these areas.

The complicated version:

If you are using a test which does not have a maximum type score of 32, you
must use the more complicated version.  The basic rules are the same, but all
values are normalized to 32:

n_max is the maximum possible score in any Type; RHETI n_max is 32
n_min is the minimum possible score in any Type; RHETI n_max is 0
h(m) = 32/(n_max-n_min) * (m-n_min)	# from value to normalized value
i(m) = (m * ((n_max-n_min)/32)) + n_min
f(n) =  0  <= h(n) < 9   ->  0
        9  <= h(n) < 14  ->  1
        14 <= h(n) < 19  ->  2
        19 <= h(n) < 24  ->  3
        24 <= h(n) < 33  ->  4
d(type t) = f( t's dominant wing score ) + 
           f( t's dominant s/s point score ) +
           f( t's dominant harmonic score ) 
g( type t ) = i((h( t's score ) - ( 12 - d( t ) )))
total(type t) = t's score + i(d( t ))

This is much easier to do with a program, but all it does is modify the
algorithm to work with a different scoring system.

Theory:

The high score is heavily weighted in this system.  For example, a high score
in a wing only counts for 1/8th of the total score, and together all secondary
attributes (wing, s/s point, harmonic) together can count for a maximum of 1/2
the total score.

There are many variables in such a system; how much *do* secondary
characteristics count for, and which are important?  For example, wings and
s/s points are well-established enneagram attributes, but harmonics are
somewhat more obscure.  Some secondary attributes may not be represented at
all, and it may be that dominant types tend to have *low* scores in wings,
rather than high scores as this algorithm assumes.

An offshoot of this research will be whether it is possible to apply this
algorithm recursively to the wing, s/s, and harmonic types to resolve
ambiguous scores in those attributes as well.

The request:

I ask that people who have test results, especially the RHETI, calculate their
results with this system and email me with comments about the system.  Please
answer the following questions; any of the information is, of course,
voluntary, although please avoid emailing me only your RHETI scores without
comments.  I'm trying to gather data as to the accuracy of the system, and
RHETI scores alone will not help.  The whole purpose is to determine if such
an analysis *helps* determine the core type and secondary characteristics. 

1) What do *you* think your core type is?  Your dominant wing?  Your currently
   dominant s/s point?  Your dominant harmonic?
2) Does it seem to accurately reflect your type?
3) If you have been to a trained enneagram teacher, does it reflect what s/he
   told you about your type?
4) If you have ambiguous test results, such as identical high scores
   in two or more types, does the system help you determine your type?
5) Finally, please include your RHETI scores

I will email you with notification that I received your email.  Unless you
request a response, I will not answer with a long email, and I will delete
your email after extracting the information; specifically, I will not record
your name or email address, to ensure anonymity.

Thank you for your help!
