A Q Methodological Tutorial

The following text consists of eight postings in late 1991/early 1992 to
QUALRS-L@UGA, a qualitative methods list out of the University of Georgia.
A revised version was published as AA Primer on Q Methodology,@ Operant
 Subjectivity, 1993, 16, 91-138, by Steven R. Brown.
 
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Date:         Sun, 24 Nov 91 23:58:23 EST
From:         "Steven R. Brown" 
Subject:      Q METHODOLOGY:  1. BACKGROUND
To:           Qualitative Research for the Human Sciences 


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|                            Q METHODOLOGY                             |
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                              Introduction

In the latter half of September, as the Qualitative Research for the Hu-
man Sciences list (QUALRS-L) was just beginning, mention was made of Q
methodology and its connection to qualitative research methods.  (The
first mention was on September 22, by Michael Foley, who was responding
to someone's inquiry concerning the use of correlation in discourse
analysis.)  The discussion quickly died, but was renewed in late October
when Robert Mrtek recommended Q to a quantitative analyst (as the person
characterized himself) who was interested in combining qualitative and
quantitative methods.  Jean Latting then asked if there was any step-by-
step information about Q technique, to which Mrtek then responded with a
list of references and with brief mention of the use of SPSS for data
analysis.  The discussion was then joined by Arthur Kendall, Rich Hof-
mann, and myself, and in some instances theoretical and conceptual disa-
greements were apparent.  Subsequently, exchanges on the list were
supplemented by private correspondence, one of which came to me as fol-
lows:

    ... maybe for the rest of the list you could explain, in simple
    terms, exactly what Q methods are good for -- in other words,
    what are they going to tell me about a phenomenon that I cannot
    learn some other way?

    This I propose to do in a series of short notes -- the first of
which is appended -- designed to provide a basic understanding of the
main features of the methodology.  Due largely to its mathematical sub-
structure, Q is fairly well known in quantitative circles, but it is
hoped that the following introduction will alert subscribers to this
list of its significance for qualitative research as well, including
what it might "tell me about a phenomenon that I cannot learn some other
way."


                             1. Background

What is currently referred to as "Q methodology" was introduced by
psychologist/physicist William Stephenson (1902-1989) in a letter to

_Nature_ in 1935, and spelled out in more detail in "Correlating Persons
Instead of Tests" (1935), "Foundations of Psychometry: Four Factor Sys-
tems" (1936), and in a celebrated paper with Sir Cyril Burt ("Alterna-
tive Views on Correlations Between Persons," 1939) in which the two laid
out their contrasting views.  His major statement is _The Study of Be-
havior: Q-technique and Its Methodology_ (1953).

    In large measure, the differences of opinion which have recently ap-
peared on QUALRS-L can be traced to the theoretical divergences of the
1930s.  Burt's viewpoint, bolstered by such notable factor analysts as
R.B. Cattell, Hans Eysenck, and L.L. Thurstone, has generally carried
the day and has been ensconced in research methods texts in a variety of
fields, not to mention users' manuals for SPSS and other statistical
packages, which helps explain why Stephenson's views often sound so out
of step despite the fact that Q methodology was his innovation.

    Recently, however, Stephenson's ideas have gained in prominence out-
side psychology.  Spurred initially by his own _The Play Theory of Mass
Communication_ (1967/1988), a number of other books and articles have
appeared which have served to clarify Q's presuppositions and to demon-
strate its applicability in virtually every corner of human endeavor.
In 1977, publication began of _Operant Subjectivity: the Q Methodology
Newsletter_ (now in volume 14), which was recently adopted as the offi-
cial journal of the newly created International Society for the Scien-
tific Study of Subjectivity.  The Society has met annually since 1985
and has generally pursued the implications and applicability of
Stephenson's ideas in psychology, communication, political science,
health, environmental, and related areas.  On-going exchanges are also
to be found on QTemp, a Bitnet list accessible via ListServ@KentVM.

    Fundamentally, Q methodology provides a foundation for the system-
atic study of subjectivity, and it is this central feature which recom-
mends it to persons interested in qualitative aspects of human behavior.
Most typically, a person is presented with a set of statements about
some topic, and is asked to rank-order them (usually from "agree" to
"disagree"), an operation referred to as "Q sorting."  The statements
are matters of opinion only (not fact), and the fact that the Q sorter
is ranking the statements from his or her own point of view is what
brings subjectivity into the picture.  There is obviously no right or
wrong way to provide "my point of view" about anything -- health care,
the Clarence Thomas nomination, the reasons why people commit suicide,
why Cleveland can't field a decent baseball team, or anything else.  Yet
the rankings are subject to factor analysis, and the resulting factors,
inasmuch as they have arisen from individual subjectivities, indicate
segments of subjectivity which exist.  And since the interest of Q meth-
odology is in the nature of the segments and the extent to which they
are similar or dissimilar, the issue of large numbers, so fundamental to
most social research, is rendered relatively unimportant.  In principle
as well as practice, single cases can be the focus of significant re-
search.

    In short, the focus is all on quality rather than quantity, and yet
some of the most powerful statistical mechanics are in the background,
but sufficiently so as to go relatively unnoticed by those users of Q
who are disinterested in its mathematical substructure.  What this might
mean for the student of qualitative methods is illustrated in a single
study, which will be serialized in the days to follow.


************************************************************************ 


Date:         Thu, 28 Nov 91 23:20:19 EST
From:         "Steven R. Brown" 
Subject:      Q METHODOLOGY:  2. CONCOURSE THEORY
To:           Qualitative Research for the Human Sciences 


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|                            Q METHODOLOGY                             |
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                          2. Concourse Theory

As noted in Part 1 (Background), Q methodology is comprised of proce-
dures and a conceptual framework that provide the basis for a science of
subjectivity, and its phenomena consist of the ordinary conversation,
commentary, and discourse of everyday life -- of the kind that prolifer-
ates, for example, when discussion turns to such things as the Gulf War,
the care of geraniums, whether we can trust Boris Yeltsin, pornography,
literary and popular impressions about the movie _The Silence of the
Lambs_, psychotherapeutic strategy, the meaning of life, what to do
about the current recession, and so forth.

    In Q, the flow of communicability surrounding any topic is referred
to as a "concourse" (from the Latin "concursus," meaning "a running to-
gether," as when ideas run together in thought), and it is from this
concourse that a sample of statements is subsequently drawn for adminis-
tration in a Q sort.  The best references on concourse theory are
William Stephenson's "Concourse Theory of Communication" (1978),
"Consciring: A General Theory for Subjective Communicability" (1980),
and "Protoconcursus: The Concourse Theory of Communication" (1986).

    Concourse is the very stuff of life, from the playful banter of
lovers or chums to the heady discussions of philosophers and scientists
to the private thoughts found in dreams and diaries.  From concourse,
new meanings arise, bright ideas are hatched, and discoveries are made:
it is the wellspring of creativity and identity formation in individ-
uals, groups, organizations, and nations, and it is Q methodology's task
to reveal the inherent structure of a concourse -- the vectors of
thought that sustain it and which, in turn, are sustained by it.

    By the same token, concourses are not restricted to words, but might
include collections of paintings, pieces of art, photographs, and even
musical selections.  In his dissertation on "The Shifting Sensorium"
(1990), for example, Paul Grosswiler has created a multimedia Q sort
comprised of writings, snippets from videos and records, and pictures;
and in his recent paper on "Humor Communicability" (1991), Dennis Kinsey
employs as "statements" a selection of Gary Larson cartoons.  The idea
of concourse incorporates virtually all manifestations of human life, as
expressed in the lingua franca of shared culture.

    A concourse can be gotten in a number of ways.  The most typical is
by interviewing people and jotting down or recording what they say, but
commentaries from newspapers, talk shows, and essays have also been
used.  The level of discourse dictates the sophistication of the
concourse: hence, factors which should be taken into account in deci-
sions about who should receive a liver transplant at a particular hospi-
tal would likely involve the medical personnel, the potential recipients
(and perhaps the donor), and possibly even a philosopher specializing in
medical ethics (or sociologist with expertise in medical sociology) who
might be called in as a consultant.  A study of public opinion, on the
other hand, would necessitate interviewing representatives of those seg-
ments of the society apt to have something to say about the issue in
question.

    An illustration might be useful at this point to give substance to
the above generalities, and for convenience we can take the commentary

that was generated on QUALRS-L about Q methodology itself -- from about
September 22nd until early this month.  Readers unfamiliar with Q meth-
odology will not be surprised to find that much of the commentary to
follow is of a specialized nature, hence comprehendable in detail by a
relatively small audience; the same could be said, however, of a qual-
itative analysis of clients in therapy or members of a delinquent gang:
a subculture has specific issues which are central to it, and often a
specialized language evolves for expressing ideas that may appear ob-
scure to the outsider (who nevertheless may see things more clearly by
virtue of being outside).  What follows are just a few of the elements
from the small concourse which was generated.  The names of authors of
the comments follow in parentheses, along with the date of the QUALRS-L
transmission:

o   It allows us to sort patterns of speech among speakers. (Michael
    Foley, 9/22)

o   It uses an ipsative technique of sorting a representative set of
    subjective statements drawn from a concourse of possible
    feelings or reactions about a subjective condition. (Robert
    Mrtek, 10/27)

o   In Q-factor techniques, a case by case matrix of some sort of
    similarity measure (usually an ipsatized correlation) is ana-
    lyzed. (Arthur Kendall, 10/28)

o   Q factor analysis is a simple variation of factor analysis, ac-
    tually component analysis. (Rich Hofmann, 10/28)

o   Q methodology is a set of procedures, theory, and philosophy
    supporting the study of the same kind of subjectivity that is
    the focal point of much qualitative research. (Brown 11/4)

(The original commentary from which the above were abstracted was na-
turally more detailed.  A copy of the original can be gotten by sending
a private request for the file QUAL CONCOURSE to SBrown@KentVM.)

    As is apparent, the statements in the concourse are subjective as
opposed, say, to the statement that "correlation is a statistical
method," which is uncontroversial and ostensibly true.  Concourses such
as the above comprise the raw material of a human science in its subjec-
tive respects, and it is frequently at this point that a qualitative
analysis breaks down.  Once "texts" (in the widest sense) have been
gathered -- from interviews, diaries, participant observation, etc. --
the task becomes one of organization, analysis, and presentation, and in
most instances the observer is forced to fall back (as in content analy-
sis) on categories which are superimposed on the data.  As will be seen
in the sequel, Q methodology likewise involves the artificial categoriz-
ing of statements, but ultimately this artificiality is replaced by cat-
egories that are operant, i.e., that represent functional as opposed to
merely logical distinctions.


************************************************************************ 

Date:         Sun, 01 Dec 91 23:01:14 EST
From:         "Steven R. Brown" 
Subject:      Q METHODOLOGY:  3. Q SAMPLES
To:           Qualitative Research for the Human Sciences 



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|                            Q METHODOLOGY                             |
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                              3. Q Samples

In Part 2, it was noted that concourse comprises the raw materials for Q
methodology, and for the human sciences generally insofar as they are
concerned with life as it is lived, i.e., from the vantagepoint of the
person involved.  The example rendered consisted of the brief commentary
that had accrued on QUALRS-L concerning the nature and scope of Q meth-
odology itself.  Diversity in viewpoint was abundant, from the techni-
calities of factor analysis to the abstractions of quantum theory, from
the simplicity of Q sorting to more complex philosophical considerations
about subjectivity.  The concourse is far from complete and could, if
desired, be supplemented with comment and controversy dating from the
mid-1930s, when Q was born.  Still, what has appeared on QUALRS-L is
sufficiently comprehensive to demonstrate a range of opinion, and to in-
troduce the problem of what to do with all the assertions that have been
entered into the discursive arena.

    For experimental purposes, a subset of statements, called a "Q sam-
ple," is drawn from the larger concourse, and it is this set of state-
ments which is eventually presented to participants in the form of a Q
sort.  The statements selected for this particular study are as follows:


                 Q SAMPLE FOR QUALRS-L PERSPECTIVES ON Q

    -----------------------------------------------------------------

    (1)  It  permits  the a priori     (2) Q methodology is a set  of
    structuring of  hypotheses  in     procedures,  theory,  and phi-
    the  design of the Q set to be     losophy supporting  the  study
    sorted.                            of    the    same    kind   of
                                       subjectivity that is the focal
                                       point of much qualitative  re-
                                       search.

    -----------------------------------------------------------------

    (3)  The method can be coupled     (4) The interpretation of fac-
    with analysis of  variance  to     tors  is more difficult if the
    test hypotheses.                   Q sorts are internally  incon-
                                       sistent  than  when  they  are
                                       based on structured Q sets re-
                                       presenting testable scientific
                                       hypotheses.

    -----------------------------------------------------------------

    (5) Centroid  factor  analysis     (6)  "Ipsative"  generally ap-
    is recommended since its inde-     plies to patterns of objective
    terminacy  is  compatible with     scores for  persons,  and  has
    quantum theory and, at the ro-     little    to   do   with   the
    tational stage, with  interbe-     subjectivity  intrinsic  to  Q
    havioral principles.               methodology.


    -----------------------------------------------------------------

    (7)  Cluster analysis may bear     (8) The history of Q methodol-
    some statistical similarity to     ogy attests to the largely ar-
    Q factor analysis, but in most     bitrary    division    between
    respects it is quite different     qualitative and quantitative.
    from  the  version  of  factor
    analysis  used  in Q methodol-
    ogy.

    -----------------------------------------------------------------

    (9) Cluster analysis is really     (10) Variance designs are only
    something  quite different and     used   to   represent  theory.
    has  no  commitment  to   that     Testing is in terms of depend-
    subjectivity  which is central     ency factor analysis.
    to Q methodology.

    -----------------------------------------------------------------

    (11) The idea is  to  come  up     (12) Q can give some fascinat-
    with  a  set  of  traits  that     ing  insight  into  underlying
    characterize individuals, then     philosophic  structures  which
    compare  individuals  for  the     comprise subjective phenomena.
    distribution of these sets.

    -----------------------------------------------------------------

    (13)  It is intended to get at     (14) It allows for the  inter-
    patterning within  individuals     pretive  study  of  subjective
    (case-wise) rather than simply     behaviors without imposing the
    across   individuals  (factor-     usual  biases  of   structured
    wise sorting).                     survey questionnaires.

    -----------------------------------------------------------------

    (15) Q-factor is an early form     (16)   Factor  scores  can  be
    of cluster analysis.               tough to come by  because  the
                                       correlations  are  of  reduced
                                       rank.

    -----------------------------------------------------------------

    (17)  There  is  more  to  the     (18)  Q has never involved the
    method than just the technique     correlation and factor  analy-
    of Q sorting.                      sis by rows of the same matrix
                                       of  data  that  is analyzed by
                                       columns in R methodology.

    -----------------------------------------------------------------

    (19) The  frequencies  in  the     (20) It uses an ipsative tech-
    piles  must  be  restricted to     nique  of  sorting a represen-
    the frequencies that would  be     tative   set   of   subjective
    expected  if  you had a normal     statements    drawn   from   a
    curve, with each  pile  corre-     concourse of possible feelings
    sponding   to  an  area  of  a     or reactions about  a  subjec-
    normal curve.                      tive condition.

    -----------------------------------------------------------------


    As with sampling persons in survey research, the main goal in se-
lecting a Q sample is to provide a miniature which, in major respects,
contains the comprehensiveness of the larger process being modeled.  The
problem, of course, is how to select from the concourse so as to provide
representativeness in the Q sample, and the main device relied upon to
achieve this is Fisher's experimental design principles (see Brown, "On
the Use of Variance Designs in Q Methodology" (1970)).

    In this particular case, the simplest of designs was employed.
While perusing the concourse, it was noted that some of the statements
were of a technical nature, viz.:

       The method can be coupled with analysis of variance to test
    hypotheses.

On the other hand, there were comments of a more abstract and
methodological nature (methodological, that is, in its wider and more
philosophical sense):

       Q can give some fascinating insight into underlying philo-
    sophic structures which comprise subjective phenomena.

As a preliminary matter, therefore, all statements in the concourse were
categorized as either (a) methodological or (b) technical, depending on
their main thrust, all the time recognizing that few statements are ever
one or the other exclusively.

    It is often the case that more than one dimension (e.g., methodolog-
ical/technical) is at issue, and so at this point we could have subdi-
vided the (a) and (b) statements above -- e.g., into (c) Stephenson, (d)
Burt, and (e) Neither, to take into account the intellectual heritage of
the points of view at issue.  This would have provided the following de-
sign, with 2x3=6 cells:


                          (a) methodological  (b) technical
          ---------------------------------------------------
           (c) Stephenson        (ac)              (bc)
           (d) Burt              (ad)              (bd)
           (e) Neither           (ae)              (be)
          ---------------------------------------------------


Equal numbers of statements would then be selected from each of the
cells (e.g., 8 of type ac statements, 8 of type ad, etc.)  for a Q-
sample size of N=(6)(8)=48 statements for Q sorting by respondents.

    To keep matters simple, only N=20 statements were chosen for this
illustration, 10 from category (a) methodological and 10 from (b) tech-
nical.  The statements in each category are as follows (numbers are as-
sociated with the above statements):

    (a) Methodological:  2  5  6  8  9 12 14 17 18 20

    (b) Technical:       1  3  4  7 10 11 13 15 16 19

As can be seen, the statements are numbered randomly.  They are then
typed one to a card, much as appears above.  The result is a pack of
cards (numbering 20) ready for Q sorting.

    Before concluding this section, it is important to note that, unlike

scaling theory, no assumption is made that the 20 statements above in
any sense measure a "methodological" or "technical" position or stance
or understanding per se.  In _The Study of Behavior_ (1953, chap. 2),
Stephenson distinguishes among general, singular, and induced prop-
ositions, and the a priori placing of statements into this or that cate-
gory is exemplary of the former: a statement can be considered primarily
methodological or technical on an ad hoc and mainly logical basis ("all
things being equal," as we say) -- as if it has generalized meaning --
but in concrete (singular) situations, words and phrases can mean wholly
different things to different people.

    This matter is raised at this point since one of the most influen-
tial chapters on Q methodology, in Kerlinger's _The Foundations of Be-
havioral Research_ (1986), places great importance on the proper
categorization of Q statements -- as if, as in scaling, they could have
only one meaning -- and also because Robert Mrtek, in his contributions
to QUALRS-L on this issue, cited Kerlinger's work approvingly.
Kerlinger's work is indeed important, but he attached too much weight to
variance designs and their analysis, and overlooked Stephenson's admoni-
tion (in _The Study of Behavior_) that "it is a mistake to regard a sam-
ple as a standardized set or _test_ of statements, any more than one can
hope to regard a particular set of children as a standard sample..." (p.
77).  There are many features to this subtle matter, but the bottom line
is that meanings are not to be found solely in the categorical cogi-
tations of the observer, but as well (and even more importantly) in the
reflections of the individual as he or she sorts the statements in the
context of a singular situation.

************************************************************************

Date:         Wed, 04 Dec 91 09:30:56 EST
From:         "Steven R. Brown" 
Subject:      Q METHODOLOGY: 4. Q SORTING
To:           Qualitative Research for the Human Sciences 


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|                            Q METHODOLOGY                             |
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                              4. Q Sorting

In Part 3 (Q Samples), a set of N=20 statements was displayed -- ab-
stracted from the concourse presented in Part 2 -- and it is this Q sam-
ple which is administered to participants (subjects, respondents) in the
form of a Q sort.  The statements are administered in the form of a pack
of randomly numbered cards (one statement to a card) with which the per-
son is instructed to operate according to some rule (called a "condition
of instruction").  Typically we are interested in the person's own point
of view, and so we would instruct the Q sorter to rank the statements
along a continuum from "most agree" at one end to "most disagree" at the
other.  To assist in the Q sorting task, the person is provided with a
scale and a suggested distribution.  More detailed descriptions of Q
sorting are to be found in Brown's _Political Subjectivity_ (1980) and
in McKeown and Thomas' _Q Methodology_ (1988).

    An example may help clarify what is involved, and for this purpose
is shown the Q sort which I performed in rendering my own point of view

using those statements presented in Part 3:


                          Brown's Position
                     -3  -2  -1   0  +1  +2  +3
                    ----------------------------
                     16   3   1   7   6   5   2
                     19  13   4   8  17   9  12
                         15  11  10  18  14
                                 20


Generally, the person is given the Q sample and instructed to read
through them all first so as to get an impression of the range of opin-
ion at issue and to permit the mind to settle into the situation.  At
the same time, the person is also instructed to begin the sorting proc-
ess by initially dividing the statements into three piles: those state-
ments experienced as agreeable in one pile, those disagreeable in a
second pile, and the remainder in a third pile.  The rating scale is
spread across the top of a flat area (like a kitchen table), and may
range from +3 to -3, or +4 to -4, or +5 to -5, depending on the number
of statements.  The distribution is symmetrical about the middle, but
usually flatter than a normal distribution.  Both the range and the dis-
tribution shape are arbitrary and have no effect on the subsequent sta-
tistical analysis, and can therefore be altered for the convenience of
the Q sorter; there are, however, good reasons for encouraging the per-
son to adhere to whatever distribution shape is adopted for the study.

    The above figure shows that strongest agreement is with statements 2
and 12, which read as follows:

    (2)  Q methodology is a set of procedures, theory, and philoso-
         phy supporting the study of the same kind of subjectivity
         that is the focal point of much qualitative research.

    (12) Q can give some fascinating insight into underlying philo-
         sophic structures which comprise subjective phenomena.

It is clear, therefore, that my primary concern while peforming the Q
sort was with the issue of subjectivity, and this is reinforced at +2 by
statements 9 and 14:

    (9)  Cluster analysis is really something quite different and
         has no commitment to that subjectivity which is central to
         Q methodology.

    (14) It allows for the interpretive study of subjective behav-
         iors without imposing the usual biases of structured survey
         questionnaires.

One of the continuing frustrations that Q methodology has had to face
for the more than 50 years of its existence has been the restriction of
its theoretical and methodological thrust through the partial incorpo-
ration of its technical procedures -- as if all physics had to offer
were its cyclotrons and behavior analysis its Skinner boxes.  Hence aca-
demic psychology quite easily adopted Q sorting as a data-gathering
technique, and even certain aspects of Q factor analysis, but ignored
the idea of a natural science of subjectivity, and it is this protest
that dominates the positive end of the above Q sort performed by one of
Stephenson's students.  Statement 17 punctuates the protest, like a
parting remark:

    (17) There is more to the method than just the technique of Q
         sorting.  (+1)

    A significant characteristic of each and every Q sort on any and all
topics is its schematic nature, or what Stephenson, in his "Consciring"
paper (1980), referred to as Peirce's Law (in re Charles Peirce's "Law
of Mind").  There is therefore a consistency in sentiment throughout the
Q sort.  Under -3, for example, we see a denial of the antithesis of
what is found under +3:

    (16) Factor scores can be tough to come by because the corre-
         lations are of reduced rank.

    (19) The frequencies in the piles must be restricted to the fre-
         quencies that would be expected if you had a normal curve,
         with each pile corresponding to an area of a normal curve.

Individuals unfamiliar with Q methodology are reminded that the
concourse of communicability surrounding it (i.e., as expressed previ-
ously over QUALRS-L) can be highly specialized; even so, it should be
easily recognized that what characterizes the positive end of the above
Q sort distribution has to do with subjectivity, whereas the above
statements, both scored -3, concern themselves with technicalities.
This is not to say that statements 16 and 19 were found unacceptable
_because_ they dealt with technicalities: there are good technical rea-
sons for rejecting them, but the technicalities are rooted in an appre-
ciation of the subjectivity enbraced under +3 and +2.

    Most Q technique studies involve administration of the Q sort to se-
veral respondents, but to far fewer than is the case, say, in survey re-
search: even in studies of public opinion, samples of persons (P sets)
rarely exceed 50 for reasons which will be discussed subsequently.  In
this particular study, we would naturally be interested in including the
views of those individuals who originally contributed to the concourse
-- i.e., Professors Foley, Mrtek, Kendall, et al.  For the sake of time
and for purposes of demonstration, I provided simulations of these indi-
viduals' views, based on their contributions to QUALRS-L.  "Professor
Foley's Views," for example, is as follows:


                    Foley's Position (simulated)
                     -3  -2  -1   0  +1  +2  +3
                    ----------------------------
                      7   5   6   2   1   3  11
                     18   9   8  10   4  15  13
                         14  12  17  20  16
                                 19


Without going into great detail, let us simply note that the Foley Q
sort asserts that "The idea is to come up with a set of traits that
characterize individuals, then compare individuals for the distribution
of these sets" (no. 11, +3), and that "It is intended to get at pattern-
ing within individuals (case-wise) rather than simply across individuals
(factor-wise sorting)" (no. 13, +3).  Both of these were points of view
which Foley espoused in his contributions to QUALRS-L (on September
23rd), and his primary concern with technical and statistical features
characterizes his Q sort at the negative end as well where it is denied
that cluster analysis and Q factor analysis are fundamentally different
(no. 7, -3), and that "Q has never involved the correlation and factor
analysis by rows of the same matrix of data that is analyzed by columns

in R methodology" (no. 18, -3).

    At different times over the space of three or four days, Q sorts
were constructed as well to represent the views of other contributors to
QUALRS-L:  Professors Mrtek, Kendall, and Hofmann.  For obvious reasons,
a Q sort representing William Stephenson's viewpoint was also con-
structed for purposes of comparison with other views; and a Q sort for
Fred Kerlinger, whose work on Q had been mentioned (Kerlinger, 1986);
and also one representing a composite of the views of Sir Cyril Burt and
R.B. Cattell, prominent exponents of factor analysis (R method) in its
formative days.  Also for theoretical purposes, a Q sort was constructed
to represent the kind of conventional view about Q technique that one
might get from a typical textbook on research methods.  And finally, for
reasons to which we will return, a Q sort rendition was given of what a
"quantum theoretical" viewpoint about Q might be.  There were therefore
10 Q sorts in all -- my own plus nine hypothetical standpoints.

    As noted previously, it is unnecessary to claim that any of the
above Q sorts is in any sense a "true" reflection of Foley's or Mrtek's
or Burt's or anyone else's view, although I would be somewhat surprised
were I to learn that I had missed the mark entirely.  These Q sorts are
formal models of my understanding of the points of view at issue, ren-
dered ostensible through technique.  The next installment in this series
will show how these perspectives can be systematically compared.  Mean-
while, in light of the discussion which has recently appeared on
QUALRS-L concerning interviewing, it is important to note that a com-
pleted Q sort should be followed where possible with an interview so
that the Q sorter can elaborate his or her point of view.  The Q sort
provides focus to the interview by indicating which of various topics in
the Q sample are most worth talking about: obviously those statements
scored +3 and -3 should be addressed first since they are demonstrably
the most salient, but those scored 0 can be revelatory by virtue of
their lack of salience.

    Before concluding this section, it is well to take brief stock of
what has been achieved.  (1) The Q sample is comprised solely of things
which people have said, and it is therefore indigenous to their under-
standings and forms of life.  (2) The Q sorting operation is wholly sub-
jective in the sense that it represents "my point of view" (whether the
"me" at issue is Brown, Foley, Mrtek, or someone else): issues of valid-
ity consequently fade since there is no external criterion by which to
appraise a person's own perspective.  (3) As a corollary, the factors
which subsequently emerge -- factors, that is, in the factor-analytic
sense -- must represent functional categories of the subjectivities at
issue, i.e., categories of "operant subjectivity."  All of this applies
to any Q sort on any topic administered to any person in any land under
any condition of instruction at any time.  Subjectivity is ubiquitous,
and Q methodology provides for its systematic measure.


************************************************************************ 

Date:         Wed, 11 Dec 91 23:58:34 EST
From:         "Steven R. Brown" 
Subject:      Q METHODOLOGY: 5. CORRELATION
To:           Qualitative Research for the Human Sciences 


+----------------------------------------------------------------------+
|                                                                      |
|                            Q METHODOLOGY                             |

|                                                                      |
+----------------------------------------------------------------------+


                             5. Correlation

In their book on _Basics of Qualitative Research_ (1990), Anselm Strauss
and Juliet Corbin are quite explicit in distinguishing qualitative from
quantitative research:  "By the term _qualitative research_ we mean any
kind of research that produces findings not arrived at by means of sta-
tistical procedures or other means of quantification" (p. 17).  One of
the advantages of qualitative research, of course, is that it permits
the systematic gathering of data which are not always amenable to
quantification, but to appraise data on the basis of whether or not they
have been subjected to statistical analysis is surely a case of mis-
placed emphasis.  It is important to be able to assay the subjectivity
at issue in a situation, which Q does: the fact that the resulting data
are also amenable to numerical treatment opens the door to the possibil-
ity of clarity in understanding through the detection of connections
which unaided perception might pass over.  In Q, the role of mathematics
is quite subdued and serves primarily to prepare the data to reveal
their structure.

    In the prior posting (Part 4), the Q sorts for my own view and that
of Michael Foley (simulated) were pictured, and so it is convenient to
draw on these two again to demonstrate the simplicity and subsumptive
power of correlation (with apologies beforehand to those already au faix
with statistics).  In tabular form, the two sets of scores are as fol-
lows (where D=F-B is the difference between Foley's and Brown's scores,
and D**2 is the difference squared):


                item  Foley  Brown   D=F-B   D**2
               -----------------------------------
                  1.    1      -1      2       4
                  2.    0       3     -3       9
                  3.    2      -2      4      16
                  4.    1      -1      2       4
                  5.   -2       2     -4      16
                  6.   -1       1     -2       4
                  7.   -3       0     -3       9
                  8.   -1       0     -1       1
                  9.   -2       2     -4      16
                 10.    0       0      0       0
                 11.    3      -1      4      16
                 12.   -1       3     -4      16
                 13.    3      -2      5      25
                 14.   -2       2     -4      16
                 15.    2      -2      4      16
                 16.    2      -3      5      25
                 17.    0       1     -1       1
                 18.   -3       1     -4      16
                 19.    0      -3      3       9
                 20.    1       0      1       1
               -----------------------------------
                 Sum    0       0      0     220


We note, in column D, the discrepancy between the score for each item in
the Foley Q sort compared to that in the Brown Q sort, and for statis-
tical reasons that number is squared (column D**2).  Hence, for example,

Foley gives statement no. 1 a score of +1 whereas Brown scores it -1, a
difference of D=2, the square of which is of course 4.  The squared dif-
ferences are then summed, which, as the above table shows, produces
Sum=220.  Note that if the two Q sorts had been identical, each D would
have been 0, each D**2 would have been 0, and Sum would have been 0:
when this occurs, the correlation is perfect (an extremely rare event)
and is registered as r = +1.00, r being the symbol for correlation.

    The specific calculation in this case is achieved first by squaring
all of the scores in the Foley and Brown Q sorts and summing those
squared numbers, which produces a sum of 66 for each, or 132 for the two
combined.  The correlation is calculated by forming the ratio of the sum
of squares for Foley and Brown combined to the sum of the squared dif-
ferences, and then subtracting this from 1.00.  Or, in this case:

    r = 1 - (Sum D**2/132)
      = 1 - (220/132)
      = -0.67

Just as a perfect positive correlation is registered as +1.00, a perfect
negative correlation is -1.00, and so the correlation between Foley and
Brown of r = -0.67 indicates a quite high level of disagreement, the
statements which the one embraces tending to be the ones which the other
rejects, and vice versa.

    Foley's and Brown's are but two of the ten Q sorts at issue, and
when each of the ten is compared with the others, the result is a 10x10
correlation matrix, as follows:


            Mrtek      Hofmann   Burt-Cattell  textbook    Brown
      Foley      Kendall    Stephenson  Kerlinger    quantum
  SORT  1     2     3     4     5     6     7     8     9    10
  ----------------------------------------------------------------
   1   1.00  0.17  0.79  0.76 -0.70  0.86  0.48  0.85 -0.71 -0.67
   2   0.17  1.00  0.14 -0.05  0.06  0.12  0.74  0.20 -0.08  0.24
   3   0.79  0.14  1.00  0.73 -0.70  0.70  0.27  0.82 -0.53 -0.57
   4   0.76 -0.05  0.73  1.00 -0.85  0.80  0.23  0.82 -0.77 -0.81
   5  -0.70  0.06 -0.70 -0.85  1.00 -0.82 -0.17 -0.76  0.73  0.76
   6   0.86  0.12  0.70  0.80 -0.82  1.00  0.39  0.82 -0.65 -0.66
   7   0.48  0.74  0.27  0.23 -0.17  0.39  1.00  0.44 -0.48 -0.28
   8   0.85  0.20  0.82  0.82 -0.76  0.82  0.44  1.00 -0.74 -0.67
   9  -0.71 -0.08 -0.53 -0.77  0.73 -0.65 -0.48 -0.74  1.00  0.85
  10  -0.67  0.24 -0.56 -0.82  0.76 -0.65 -0.27 -0.67  0.85  1.00
  ----------------------------------------------------------------
   See Part 4 (Q Sorting) for the definitions of the 10 Q sorts.


As indicated, Brown (no. 10) correlates with Foley (no. 1) in the amount
-0.67, and a quick perusal down column 10 shows that Brown correlates
substantially and positively only with Q sort no. 5 (Stephenson, his
mentor) and no. 9 (quantum theory); otherwise, he correlates negatively
with virtually everyone else save for Mrtek, although the positive cor-
relation in that case (r = 0.24) is insubstantial.  Foley on the other
hand correlates quite highly with Kendall and Hofmann.

    To determine how large a correlation must be before it is considered
substantial, we calculate the standard error, a rough and ready estimate
of which is given by the expression 1/(SQRT(N)), where N is the number
of statements (N=20 in this case) and SQRT is the square root: the value
is therefore 1/(SQRT(20)) = 1/(4.47) = 0.22.  As a rule of thumb, corre-

lations are generally considered to be statistically significant if they
are approximately 2 to 2.5 times the standard error -- i.e., somewhere
between 2(0.22) = 0.44 and 2.5(0.22) = 0.56 (irrespective of sign).
Hence in the above correlation matrix, Brown's positive correlation with
Stephenson is substantial (i.e., in excess of 0.56) as is his negative
correlation with Foley (i.e., in excess of -0.56), whereas his corre-
lation with Kerlinger is insignificant (i.e., is less than 0.44).

    But it is rarely the case that the correlation matrix is of much in-
terest since attention is usually on the factors to which the corre-
lations lead: the correlation matrix is simply a necessary way station
and a condition through which the data must pass on the way to revealing
their factor structure.  What this involves is the subject of the next
chapter.

    In the meantime, it is worth stressing that the statistics associ-
ated with Q are not intended as a substitute for the obvious fact that
the correlation matrix above is suffused with subjectivity, each Q sort
being a transformation of a person's own vantagepoint, and with the co-
efficients merely registering the degree of similarity or dissimilarity
in perspective.  Moreover, although Q emerged from psychometric dis-
cussions in the 1930s, it is less and less the case that users of Q
technique have need for much more than a minimal grasp of statistics.
Software packages for personal computers, such as Stricklin's (1990)
PCQ, or the new QMethod mainframe program nearing completion at Kent
(Atkinson, 1992), convert into joy what before was drudgery, and thereby
redirect attention back to the phenomenon and away from the means of its
measurement.

************************************************************************ 

Date:         Tue, 31 Dec 91 10:11:13 EST
From:         "Steven R. Brown" 
Subject:      Q METHODOLOGY: 6. FACTOR ANALYSIS
To:           Qualitative Research for the Human Sciences 


+----------------------------------------------------------------------+
|                                                                      |
|                            Q METHODOLOGY                             |
|                                                                      |
+----------------------------------------------------------------------+


                           6. Factor Analysis

Few statistical procedures can be more daunting than factor analysis,
but in Q methodology there is little more reason to understand the math-
ematics involved than there is to understand mechanics in order to drive
a car.  A certain minimal knowledge is required, of course -- such as
when (but not necessarily why) to change the oil -- but available and
forthcoming software packages are lessening the need to understand fac-
tor analysis in detail, thereby freeing intellectual sojourners to re-
main focused on the road ahead while taking for granted the mathematics
purring under the hood.  Those interested in further details, presented
with as much simplicity as the subject matter allows, are referred to
Adcock's (1954) out-of-print classic _Factorial Analysis for Non-
Mathematicians_, Brown's (1980) _Political Subjectivity_ (pp. 208-224),
and Stephenson's (1980) "Factor Analysis."

    Fundamentally, factor analysis examines a correlation matrix such as

that reported in Part 5 (Correlation), and, in the case of Q methodol-
ogy, determines how many basically different Q sorts are in evidence: Q
sorts which are highly correlated with one another may be considered to
have a family resemblance, those belonging to one family being highly
correlated with one another but uncorrelated with members of other fami-
lies.  Factor analysis tells us how many different families (factors)
there are.  The number of factors is therefore purely empirical and
wholly dependent on how the Q sorters actually performed.  In this exam-
ple, the factors will indicate different conceptions about Q methodol-
ogy, with those persons sharing a common conception defining the same
factor.

    The following table contains the initial set of "factor loadings"
(as they are referred to) for each of the 10 Q sorts in our illus-
tration.  The table was created by QMethod (Atkinson, 1992), which auto-
matically extracts seven centroid factors:


                                   Unrotated Factors
         Q Sorts         A     B     C     D     E     F     G
     ----------------------------------------------------------
       1 Foley          92    08    07    05    11   -06   -13
       2 Mrtek          15    78   -14    34   -10    13    12
       3 Kendall        78    04    31    20    01   -24    07
       4 Hofmann        87   -31    05    11   -19   -06    08
       5 Stephenson    -82    35   -10   -14    26   -13    02
       6 Burt-Cattell   89   -02    16    13   -01    11   -25
       7 Kerlinger      50    47   -66    46    20    17    07
       8 textbook       94    07    09    03   -01   -08    10
       9 quantum       -84    17    40    01    29    19    15
      10 Brown         -75    46    13   -03    03    17    05
     ----------------------------------------------------------
      Decimals to two places omitted.


The loadings express the extent to which each Q sort is associated with
each factor: hence the Foley Q sort is correlated with factor A to the
extent of 0.92, whereas Brown's is correlated -0.75; on factor B, their
respective loadings are 0.08 and 0.46.  As indicated in Part 5 (Corre-
lation), factor loadings in excess of 0.50 (plus or minus) can be con-
sidered significant; therefore, only the first two or three factors
contain significant loadings.

    However, the original set of factors is usually of little immediate
interest and only provides the raw materials for probing these subjec-
tive relationships from vantagepoints that might interest us.  One point
of interest, it will be recalled, was that Mrtek cited Kerlinger's work
with approval (see Part 3, Q Samples); for another, it was striking how
different Foley, Hofmann, and Kendall's views were from Stephenson's.
Factor rotation enables us to take advantage of these impressions and
any other bits of information at our disposal, as well as any guesses,
hunches, and notions that might come to mind.  It is at this point --
during factor rotation -- that Peirce's theory of abduction enters Q
most saliently, a matter to which we will return.

    With the above impressions in mind, we note, in examining the previ-
ous table, that any Mrtek-Kerlinger connection that might exist is not
"in focus": Mrtek is significantly associated with factor B (in the
amount 0.78) but not A (0.15); Kerlinger, on the other hand, is signif-
icant on A (0.50) and almost so on B (0.47).  All of the relationships
encompassed by factors A and B can be represented visually, as shown in

the following graph.  In this instance, the numbers in the graph are as-
sociated with the Q sorts in the previous table (e.g., Mrtek is no. 2,
Kerlinger no. 7), and their spatial locations are a function of the fac-
tor loadings: hence Mrtek is at 0.15 on A and 0.78 on B, and the same
for all the other Q sorts, with spatial proximity being indicative of
the degree of conceptual similarity:


                                (A)
                           4     6 81
                                 |3
                                 |
                                 |
                                 |          7
                                 |
                                 |
                                 |
                                 |                 2
          -----------------------+----------------------(B)
                                 |
                                 |
                                 |
                                 |
                                 |
                                 |         10
                                 |   9   5
                                 |
                                 |
                                 |


    The factors can be repositioned so as to highlight the connection
between the views of Mrtek and Kerlinger by rotating the factors such
that one of them extends through the center of gravity between Q sorts 2
and 7.  This is accomplished, in this case, by rotating the factors ap-
proximately 70-degrees clockwise.  (In earlier days, this task was ac-
complished with graph paper, a T-square, and a protractor, but QMethod
reduces to one or two seconds what before would have required several
minutes.)  The rotation produces the following result:


                                (A)
                                 |
                                 |  2
                                 |
                           7     |
                                 |
              81                 |
               6 3               |
                                 |                  10
                                 |                   5
          ---4-------------------+------------------9---(B)
                                 |
                                 |
                                 |
                                 |
                                 |
                                 |
                                 |
                                 |
                                 |

                                 |


The consequence of this rotation serves not only to focus Mrtek and
Kerlinger on factor A, but also Stephenson (no. 5) and Brown (no. 10) on
factor B (and Hofmann, no. 4, at the opposite pole of the same factor).
This rotation changes the factor A and B loadings for all the Q sorts,
and these are registered in the following table.  Note, in comparing
this with the prior table, that the loadings for factors C through G re-
main the same; only the loadings for factors A and B (now relabeled A2
and B2) have been altered to take into account the rotation above.


         Q Sorts        A2    B2     C     D     E     F     G
     ----------------------------------------------------------
       1 Foley          39   -83*   07    05    11   -06   -13
       2 Mrtek          79*   13   -14    34   -10    13    12
       3 Kendall        30   -72*   31    20    01   -24    07
       4 Hofmann        01   -92*   05    11   -19   -06    08
       5 Stephenson     05    89*  -10   -14    26   -13    02
       6 Burt-Cattell   29   -84*   16    13   -01    11   -25
       7 Kerlinger      62*  -31   -66*   46    20    17    07
       8 textbook       39   -86*   09    03   -01   -08    10
       9 quantum       -13    85*   40    01    29    19    15
      10 Brown          18    86*   13   -03    03    17    05
     ----------------------------------------------------------
       * Significant loadings.


    As noted previously, the Q factors in this case represent different
perspectives or conceptualizations concerning the nature of Q methodol-
ogy itself, and although we only have one rotation behind us at this
point, already the main outlines of what is at issue are beginning to
emerge: factor B is the manifestation of a strong bipolarity between
Stephenson and Brown on the one hand and Foley, Kendall, Hofmann, and
Burt and Cattell on the other; whereas factor A represents that under-
standing about Q methodology held by Kerlinger and Mrtek.

    Even so, another look at the previous table indicates that factor A2
can be strengthened somewhat by rotating it as before against those fac-
tors which contain some variability (albeit statistically insignificant)
held in common by Mrtek and Kerlinger.  On factor D, for example, Mrtek
is saturated 0.34 and Kerlinger 0.46, and on C they have loadings of
-0.14 and -0.66, respectively.  When A2 is graphed against D, for exam-
ple, the following configuration results, and a 35-degree clockwise ro-
tation adds to factor A (which now becomes A3) that portion of
variability for Q sorts 2 and 7 that was formerly associated with factor
D (now D2).


                                (A2)
                                 |
                                 |       2
                                 |
                                 |         7
                                 |
                                 |81
                                 |  6 3
                                10
                               5 |
          -----------------------+-4--------------------(D)

                                 |
                                 |
                                 |
                                 |
                                 |
                                 |
                                 |
                                 |
                                 |
                                 |


    What has been presented to this point is little more than a sketch,
but enough has perhaps been said to provide a basic grasp of what is in-
volved in factor analysis and rotation.  The initial factor loadings can
now be gotten at the press of a button at a computer terminal, hence re-
quire no knowledge of statistics.  What is important is to know what to
do with the factors once they have been obtained.  In most conventional
factor analyses, rotation proceeds according to statistical principles
of one kind or another (e.g., varimax rotation, which remains an option
in the QMethod package), but in Q methodology rotation may be guided by
the "abductory principles" of the investigator (Stephenson, 1961): it is
at this point that the researcher utilizes factor analysis, not as a
passive finder of Nature's truths, but as a probe into Nature's possi-
bilities.  There is an infinite number of ways in which the factors can
be rotated (the varimax solution is but one of these), and the investi-
gator probes this space in terms of preconceived ideas, vague notions,
and prior knowledge about the subject matter, but with due regard also
for any obvious contours in the data themselves.  As it turns out in
this instance, a more conventional factor analysis (e.g., principal axis
extraction and varimax rotation of factors with eigenvalues greater than
1.00) would have produced essentially the same solution, but theoretical
rotation often leads to results which are quite at variance with those
produced by conventional means.

    The final result of the original factoring and all of the subsequent
rotation described above is the following table of rotated loadings:


                                    Rotated Loadings
                   Q Sorts            I         II
               -------------------------------------
                 1 Foley            (82)        32
                 2 Mrtek            -14        (86)
                 3 Kendall          (72)        26
                 4 Hofmann          (93)        05
                 5 Stephenson      (-90)       -04
                 6 Burt-Cattell     (83)        29
                 7 Kerlinger         31        (89)
                 8 textbook         (84)        30
                 9 quantum         (-83)       -14
                10 Brown           (-87)        13
               -------------------------------------
                Significant loadings in parentheses.


As can be seen, the factor analysis indicates two broad classes of Q
sorts, factors I and II.  The first is bipolar, however, and this indi-
cates three different understandings about Q methodology: factor Ia (the
positive pole of the first factor) contains the views of Foley, Kendall,
Hofmann, Burt and Cattell, and also that version of Q found in conven-

tional research methods textbooks.  In contrast to this, factor Ib (the
negative pole of the same factor) contains the views of Stephenson and
Brown, and also a quantum-theoretical perspective (to be discussed in
the sequel).  Factor II represents yet a third vantagepoint, as found in
Mrtek and Kerlinger.  The _contents_ of these viewpoints -- their simi-
larities and differences -- will be the subject of the next installment
in this series.

    At the risk of redundancy, we conclude by again pressing the point
that Q methodology is fundamentally about subjectivity -- its meaning
and measure, which, as quantum theory has shown, are inextricably tied.
One can imagine Professors Brown, Foley, Hofmann, Kendall and Mrtek
seated in a faculty lounge somewhere and professing to one another with
respect to their views about Q methodology -- although we could move
from the ridiculous to the sublime by replacing Q with any other suit-
able topic.  As discussion proceeds, contributions are made to the ex-
panding pool of communicability.  In the background is intellectual
heritage -- of Cyril Burt, William Stephenson, and Fred Kerlinger, and
including textbooks in which "the proper way to conduct a Q study" is
described.

    In the rapid give and take of discussion, the casual observer and
even the participants themselves may be unaware of the intellectual vec-
tors at issue, which are nevertheless rendered ostensible through the
application of suitable measuring procedures.  The result is "factors as
operant subjectivity" (Stephenson, 1977), the x-ray plates of subjective
communicability, i.e., as expressed from "my point of view," yet as ob-
jective as a physiological response or a pigeon pecking a key.  It is a
remarkable achievement.

************************************************************************ 

Date:         Mon, 06 Jan 92 00:50:54 EST
From:         "Steven R. Brown" 
Subject:      Q METHODOLOGY: 7. INTERPRETATION
To:           Qualitative Research for the Human Sciences 


+----------------------------------------------------------------------+
|                                                                      |
|                            Q METHODOLOGY                             |
|                                                                      |
+----------------------------------------------------------------------+


                           7. Interpretation

The interpretation of factors in Q methodology proceeds primarily in
terms of factor scores rather than (as is typical in R methodology) in
terms of factor loadings.  A factor score is the score for a statement
as a kind of average of the scores given that statement by all of the Q
sorts associated with the factor.  As an illustration, consider from the
previous section (Part 6, Factor Analysis) those Q sorts which defined
factor Ia:


                     Factor Ia    Loadings  Weights
                     Q Sorts         f         w
                 -----------------------------------
                   1 Foley          .82      2.50
                   3 Kendall        .72      1.50

                   4 Hofmann        .93      6.88
                   6 Burt-Cattell   .83      2.67
                   8 textbook       .84      2.85
                 -----------------------------------
                   w = f / (1 - f**2)


Hence the Q sorts representing the views of Foley, Kendall, and others
were all interrelated (to the extent of the factor loadings shown), and
what we seek is a kind of composite Q sort for this group.  We could
simply merge the separate Q sorts by taking the average score for each
statement, but for the sake of precision the Q sorts are weighted to
take into account that some are closer approximations of the factor than
others.

    As indicated in the table, the weights are gotten by dividing each
factor loading (f) by the expression 1 minus the square of the factor
loading: the weight for the Foley Q sort, for instance, is w = 0.82 / (1
- 0.82**2) = 2.50.  Hofmann's Q sort has the highest loading (0.93),
hence is given the most weight (6.88).  The weighting procedure can be
illustrated in terms of the following three statements which received
the scores indicated in the respective Q sorts (e.g., Foley gave a +3
score to statement no. 11, Kendall scored the same statement +2, etc.):

     Statement 11:  +3  +2  +2  +3  +3
     2.50(3) + 1.50(2) + 6.88(2) + 2.67(3) + 2.85(3)      =  40.83

     Statement 10:   0   0   0  -1   0
     2.50(0) + 1.50(0) + 6.88(0) + 2.67(-1) + 2.85(0)     = - 2.67

     Statement  5:  -2  -2  -2  -3  -2
     2.50(-2) + 1.50(-2) + 6.88(-2) + 2.67(-3) + 2.85(-2) = -35.47

Foley's score for statement 11 is weighted 2.50, Kendall's 1.50, and so
forth, the total being 40.83; and the respective totals for statements
10 and 5 are -2.67 and -35.47: statement no. 11 therefore has high posi-
tive salience for factor Ia, no. 5 high negative salience, and no. 10
somewhere in the middle.  Weighted composites are calculated for all 20
statements.  For convenience, the statements are returned to the ori-
ginal Q sort format, the two statements with the highest weighted com-
posites being assigned +3, the three next highest being scored +2, and
so forth, as shown in the tables below.  The same procedure is also
undertaken for factors Ib and II.  (Recall that Ib is merely the nega-
tive pole of Ia, but in this case the Q sorts defining that pole of the
factor were separately merged and are reported as a separate group: as
might be expected, Ia and Ib are highly negatively correlated, r =
-0.88.)


              Factor Ia                      Factor Ib
     -3  -2  -1   0   1   2   3     -3  -2  -1   0   1   2   3
     --------------------------     --------------------------
      5   2   6   4   1  16  11     16   3   4   1   8   2   5
     18   7   8  10   3  19  13     19  13  11   6  14   9  18
          9  12  14  15  20             15  20   7  17  12
                 17                             10

                             Factor II
                    -3  -2  -1   0   1   2   3
                    --------------------------
                     5   6   7   2  11   4   1

                    10  16   9   8  13  12   3
                        19  14  15  17  20
                                18


The numbers in the above displays are associated with the statements
shown in Part 3 (Q Samples): hence, Q sorts comprising factor Ia collec-
tively demonstrate the highest agreement (+3) with statements 11 and 13,
and disagree most with nos. 5 and 18.

    Before turning to factor interpretation, it is useful to pause and
take stock of what has been achieved to this point.  Ten separate per-
spectives on Q methodology have been rendered, based on statements drawn
from a naturally occurring discourse, yet these 10 have been shown to
condense around three operant types (factors Ia, Ib, and II), the intel-
lectual structures of which are shown in the tables above.  There has
been minimal intrusion by the observer: the words belong to the partic-
ipants, and the factors have emerged from them as genuine operational
definitions of their subjective points of view.  (That the Q sorts in
this example are mainly theoretical in no way obviates the principles
involved.)  The factors are qualitative categories of thought in the
sense that additional participants would have virtually no impact on the
factor scores: Quality is operationally distinct from quantity.  Conse-
quently, although we do not know the proportions of factor Ia, Ib, or II
types which exist in the general population (a matter of nose-counting
best left to surveys) -- and although we lack evidence of any other
points of view that might also exist -- we can neverthelss proceed to
compare and contrast the three distinctive ways of thinking which we
have located with full confidence that they really do exist (demonstra-
bly so) in a form similar to that shown above.

    Quick access into what is distinctive about the three perspectives
can be gotten by examining statements which distinguish them.  (Differ-
ences of 2 between factor scores can be considered significant.)  For
illustrative purposes, consider the following three statements (scores
are for factors Ia, Ib, and II, respectively, and are taken from the
preceding tables):

 3 -2  1  (13) It is intended to get at patterning within individuals
          (case-wise) rather than simply across individuals (factor-wise
          sorting).

Factor Ia, as we know, is comprised of the views of Foley, Kendall, Hof-
mann, and Burt and Cattell, and is also the view most often encountered
in research design and psychometrics texts.  Statement 13, originally
expressed by Foley, gains the greatest support in factor Ia (+3), is
strongly disfavored in Ib (-2) and is relatively unimportant in II (+1).
Implicit in the casewise-vs.-factorwise view expressed in this statement
is the idea of ipsative vs. normative measurement, and also the "reci-
procity principle" which Stephenson dismissed but which Burt clung to
until his dying day (Burt, 1972).  The term "patterning" in item 13 is
reminiscent of profile analysis: based on intraindividual (ipsative)
patterns, profiles bear only superficial resemblance to Q and are other-
wise lacking in implications for subjectivity (Stephenson, 1953, p.
164); Stephenson therefore associated them with R methodology, which
helps account for statement 13's -2 score in factor Ib.

-3  3 -3  (5)  Centroid factor analysis is recommended since its inde-
          terminacy is compatible with quantum theory and, at the rota-
          tional stage, with interbehavioral principles.


    Statement 5 is highly differentiating for factor Ib (Stephenson,
Brown, quantum theory).  The mathematical similarities between factor
analysis and quantum mathematics have been known since the mid-1930s;
moreover, centroid factor analysis has an additional feature in common
with quantum mechanics by virtue of its indeterminacy, which is why most
statisticians prefer principal components and other more determinant
forms of analysis.  And theoretical rotation provides the opportunity
for the observer to play an active role in the analysis, which is in
line with the interbehavioral psychology of J.R. Kantor.  Much of this
is spelled out in Stephenson's "Q-methodology, Interbehavioral Psychol-
ogy, and Quantum Theory" (1982) and in his five-part series on "William
James, Niels Bohr, and Complementarity" (1986-1988).

 1  0  3  (1)  It permits the a priori structuring of hypotheses in the
          design of the Q set to be sorted.

    Factor II embraces the views of Kerlinger and Mrtek, and statement
no. 1, originally issued by Mrtek, succinctly expresses one of the main
points highlighted by Kerlinger (1986).  The idea of structuring state-
ments in some hypothetical way is certainly included in Q (see Part 3, Q
Samples), but not for hypothesis testing in the way Kerlinger proposes.
For Stephenson, much more importance was to be attached to the meanings
of the Q sorter (which were contained in the factor analysis) than to
the a priori meanings of the investigator as structured into the Q sam-
ple.

    It is doubtful that the topic of structured Q samples is one about
which factor Ia is concerned, but it is a salient matter for Ib, and in
this regard some inkling of what is at issue between Ib and II can be
gotten by examining factor II in more detail.  Consider the following
statements, which further distinguish this factor (scores for Ia, Ib,
and II):

 1 -2  3  (3)  The method can be coupled with analysis of variance to
          test hypotheses.

 0 -1  2  (4)  The interpretation of factors is more difficult if the Q
          sorts are internally inconsistent than when they are based on
          structured Q sets representing testable scientific hypotheses.

 0  0 -3  (10) Variance designs are only used to represent theory.
          Testing is in terms of dependency factor analysis.

Statements 3 and 4 were expressed by Mrtek, and, combined with no. 1
(supra), advance the idea that samples of Q statements should be struc-
tured so as to be internally consistent and to permit hypothesis testing
via variance analysis.  An alternative view, expressed in statement 10
and found in Stephenson (1953, chap. 2) -- that "testing" should be car-
ried out in terms of the operantcy of factor analysis rather than the
categories of variance designs -- is rejected by factor II.  The scores
associated with these statements, as well as those presented previously,
reveal a consistent point of view.

    Ironically, the consistency of factor II's point of view might have
been overlooked had we followed factor II's own advice.  Recall that the
20-statement Q sample was structured (Part 3, Q Samples), half of the
statements dealing with technical matters, half with broader methodolog-
ical issues.  The following table records the outcomes when variance
analysis was applied to the three sets of factor scores reported previ-
ously:


        Source of       ----------- F-ratios ------------
        Variance    df  Factor Ia   Factor Ib   Factor II
       ---------------------------------------------------
        Meth/Tech    1    10.42*      26.33*       0.22
        Error       18
        Total       19
       - - - - - - - - - - - - - - - - - - - - - - - - - -
        Cell Means (n=10)
         Methodological   -1.10        1.40       -0.20
         Technical         1.10       -1.40        0.20
       ---------------------------------------------------
        *p<.01


Hence, factors Ia and Ib diverged in a statistically significant way in
their reactions to the statements -- Ia favoring the technical items, Ib
the methodological ones -- but factor II made no such differentiation.
Had we been restricted to the results of variance analysis, therefore,
we might have been puzzled as to the meaning of factor II, which, how-
ever, stands revealed in terms of factor analysis.

    I once heard a statistician characterize factor analysis as that
branch of multivariate analysis in which the researcher grasps the data
by the throat and screams "Speak to me!" and in Q methodology this is
not all that far-fetched.  Just as each Q sort portrays a version of the
world "as I see it," so does each factor represent a version of the
world that is commonly held and which speaks to us through the unison of
the factor scores, and factor interpretations (at the risk of a tautol-
ogy) cannot stray far from the factors of which they are interpretations
if they aspire to descriptive accuracy.

    Thorough descriptions of Q factors go into far greater detail than
is possible here, and often involve the interlacing of factor results
and depth interviews; the interested reader is therefore referred to il-
lustrations in the literature.  Perhaps the best source on interpreta-
tion in Q methodology is Stephenson's (1983) "Against Interpretation"
(cf. Brown, 1980, pp. 247-258).  A worked example is Brown and
Mathieson's "The Operantcy of Practical Criticism" (1990), a study of
poetic interpretation which is available in electronic form and can be
accessed by sending the message "Send Brown V1N190" to Comserve@RPIECS.
A running bibliography on applications appears in _Operant Subjectivity:
the Q Methodology Newsletter_.

    In addition to being a psychologist, William Stephenson also held a
doctorate in physics; it is therefore not surprising that he saw paral-
lels between Q methodology and quantum theory, and also relativity the-
ory.  In this connection, it is instructive to conclude this section by
noting how Q renders explicit the location of the observer relative to
the field of observation: in this case, the observer is obviously situ-
ated in factor Ib, and it is from this perspective that interpretations
of Ia and II have been rendered.  It should also be obvious that observ-
ers from other coordinate systems could (if they were so inclined) ren-
der their own perspectives on the same matters via the same procedures,
and that connections between and among the relative vantagepoints and
interpretations could be rendered ostensible for purposes of inspection.
The importance of Q methodology is that it brings any and all such sub-
jective communicability into the same observational field, hence trans-
forms the '70s phrase "This is where I'm coming from" from an imprecise
affectation to a scientific principle.



************************************************************************ 

Date:         Sun, 19 Jan 92 00:23:33 EST
From:         "Steven R. Brown" 
Subject:      Q METHODOLOGY: 8. BIBLIOGRAPHIC CONCLUSION
To:           Qualitative Research for the Human Sciences 


+----------------------------------------------------------------------+
|                                                                      |
|                            Q METHODOLOGY                             |
|                                                                      |
+----------------------------------------------------------------------+


                      8. Bibliographic Conclusion

                              ...  maybe  for  the  rest of the list you
                              could explain, in  simple  terms,  exactly
                              what  Q  methods  are good for -- in other
                              words, what are  they  going  to  tell  me
                              about  a  phenomenon  that  I cannot learn
                              some other way?

It was this comment from a subscriber to QUALRS-L that led to this seri-
alized summary of Q methodology, and I leave it to the reader whether
what has been said is in simple terms.  As to whether Q reveals what
cannot be learned in other ways: that is a demanding challenge that can-
not be successfully risen to in each and every study, but it does occur
often enough.  Even in single-case studies such as the above -- e.g.,
studies in which all Q sorts have emanated from the same person -- it is
quite often the case that the results are surprising to the person or
persons who did the Q sorting.  In reference to the above illustration,
for instance, I was of course aware prior to measurement that there were
differences (in my own mind at least) between my views and what I under-
stood to be the views of others -- but two factors? three? bipolar?
orthogonal?  I really had no idea what form the segmentation and its
structure would take, or precisely which issues would distinguish the
factors; the results nonetheless made perfect sense _in retrospect_.

    In part, it is this indeterminant aspect of subjectivity that paral-
lels the indeterminacy of quantum theory, for we know in advance neither
how many factors there will be nor what structure they will reveal.
Moreover, at the level of the single case in particular, the factors
display complementarity: my own point of view in this study was in fac-
tor Ib, but on occasions I have expressed views compatible with factors
Ia and II, and in a sense Q is all of these.  It does measure patterns
within individuals (factor Ia) and it also permits the a priori struc-
turing of hypotheses (factor II), but it is also something more -- a
comprehensive approach to the study of subjectivity (factor Ib).  To say
that Q is all three of these is not equivocation or inconsistency or
contradiction, but a matter of probabilism, paradox, and the fluidity of
meaning and salience within concrete fields of activity.

    The serialized illustration presented above adds one more entry in a
2200+ Q bibliography which was one-fourth this size only 25 years ago
(Brown, 1968).  Persons interested in reading further can obtain a
lengthy course syllabus/bibliography that was current as of 1988 (by is-
suing the email command "Send QMethod Syllabus" to Comserve@RPIECS).  A
running bibliography is carried in _Operant Subjectivity_, the journal
of the International Society for the Scientific Study of Subjectivity.

A sampling of recent literature on Q methodology (since 1985) would in-
clude the following:

o   The history of Q is tied closely to the career of its inventor, Wil-
    liam Stephenson (1902-1989), and particulars of his life are con-
    tained in sketches by Barchak (1991) and Brown (1991), and in the
    memorial issue of _Operant Subjectivity_ (January 1990).  Logan
    (1991) provides an overview of Stephenson's major ideas.

o   A significant feature of Q methodology is its capacity to deal in a
    systematic way with single cases, and further examples are Stephen-
    son's (1990) study of himself from the standpoint of Lasch's theory
    of narcissism, which can be compared with Goldman's (1991) single-
    case analysis from the same theoretical vantagepoint.  In this con-
    nection, the use of Q in psychoanalytic case studies has been
    discussed by Edelson (1989).

o   Short introductions to Q are often valuable to persons requiring
    quick exposure to the main ideas.  In this regard, a chapter-length
    introduction to Q is provided by Brown (1986).  Stephen (1985) pro-
    vides an introduction for the communication field; Dennis (1986)
    does likewise for nursing.  Cottle (1991) has recently given ex-
    tended consideration of various aspects of Q methodology.  The only
    explicit reference to qualitative research is of slightly older vin-
    tage (Sell & Brown, 1984).

o   Mention was made of the tie between Q methodology and Kantor's
    interbehavioral psychology.  Further remarks are to be found in Ste-
    phenson (1987) and Lichtenstein (1988).

o   Reference was also earlier made to Stephenson's (1986-1988) five-
    part series on "William James, Niels Bohr, and Complementarity,"
    which spells out the connection between Q and quantum theory.  Ste-
    phenson (1988) provided a summary statement which appeared in
    _Integrative Psychiatry_, which included observations by four com-
    mentators.  A two-part paper on "exclusionary psychometrics" (Ste-
    phenson, 1990) criticizes the Newtonian bias of the journal
    _Psychometrika_, including its exclusion of Q.  The distinction be-
    tween substantive and transitive thought, introduced by William
    James and critical to quantum theory, is explored in companion pa-
    pers comparing Joyce's _Ulysses_ and _Finnegans Wake_ (Stephenson,
    1991).

o   Oral histories and person-centered interviews are important tools in
    qualitative research, and Sharpless (1986) has explored the con-
    nection between oral history and Q.  Sanders and Morris (1990) have
    provided a more recent example.  (The latter paper can be obtained
    by sending the email command "Send Sanders V1N190" to Comserve@-
    RPIECS.)

o   Deconstruction, social construction, identity theory, and discourse
    analysis are important contemporary approaches which Q methodology
    has subserved.  Kitzinger's (1986, 1987) studies on lesbianism are
    illustrative, as is Marshall's (1991) study of women lawyers.
    Stainton Rogers and Stainton Rogers (1989, 1990) have used Q to de-
    construct the child abuse controversy and alcoholism.  The previous
    authors are British.  In the U.S., McKeown (1990) has discussed Q in
    terms of textual interpretation more generally, and Dryzek (1990)
    has tied Q to discourse analysis.

o   Q has been applied to a wide variety of substantive matters, as can

    be inferred from the above.  Other illustrative examples would in-
    clude Cottle et al.'s (1989) and Senn's (1991) studies of
    pornography, Gopoian and Brown (1989) on political campaign strat-
    egy, Peritore's (1990) series of studies on religion and politics in
    Brazil, and Steuernagel and Poole's (1989) examination of an aspect
    of Rawls' theory of justice.

    Finally, mention should be made of recent and on-going research
which will doubtless appear in print in the not-too-distant future.

o   The July 1991 issue of _Operant Subjectivity_ lists a dozen or so
    new dissertations on topics such as global citizenship and identity
    theory, by Mary Margaret Pignone (1992); medical decisionmaking
    among the chronically ill, by Jean Bartels (1990); parents' and
    teachers' conceptions of giftedness versus talent, by Susan Dobbs
    (1991); environmental values, by Ann Hooker (1992); practical know-
    ledge among nursing home care-givers, by Dolores Nelson (1991); cri-
    teria used in selecting projects for development in the pharma-
    ceutical industry, by Sybil Seoka (1992); the development of public
    administrative knowledge among scholars and practitioners, by Tung-
    Wen Sun (1992); and the integration and enculturation of Vietnamese
    refugees, by Sharon Sykora (1991).

o   Projects in the in-progress phase of development include those of
    John Dryzek (University of Oregon), who is currently examining theo-
    ries of democracy from the standpoint of citizens, under a grant
    from the National Science Foundation; Joanne Gallivan (University
    College of Cape Breton, Nova Scotia), who is examining gender and
    humor, under a grant from the Canadian Social Sciences and Humani-
    ties Research Council; Leonard J. Barchak (McNeese State Univer-
    sity), who is researching market segments on behalf of the Lake
    Charles Symphony Orchestra, under a grant from the Humanities Coun-
    cil of Louisiana; and Jean Kantambu Latting (University of Houston)
    who is exploring organizational cultures, under a grant from the Na-
    tional Science Foundation.  Robert M. Lipgar (University of Chicago)
    is exploring aspects of group and organizational psychology.

o   Current work by Jack Gargan (Kent State University) in the area of
    strategic planning will be of general interest: members of small
    decision-making groups (e.g., corporate boards, fund-raising groups,
    etc.) use free-association procedures such as nominal group tech-
    nique to generate ideas about "what steps might we take in order to
    achieve our goals?"  ("What goals ought we to pursue?" can also be
    the focal question.)  Once generated, the various alternative rec-
    ommendations are placed in a Q sample for priority sorting.  The
    factors point to alternative agendas within the organization; the
    consensus items point to projects for which, despite group divi-
    sions, cooperation is possible.  The value of Gargan's work relates
    to cognitive limitations on rationality posed by the volume and com-
    plexity of information: Q factors reduce the complexity to a manage-
    able number of dimensions which can be examined at leisure; the
    factor scores point the group in the potentially most profitable di-
    rections, thereby ameliorating a major barrier to rationality in
    decision-making.

                        ________________________


The above listing bears witness to the fruitfulness of an interesting
methodological idea that was put forth almost 60 years ago, and which
has since shown itself to be applicable in a most general way: Around

any topic whatever there bushes-out a concourse of subjective communic-
ability, a sampling of which can be subjected to experimental treatment
to determine its structure.  All else flows from this simple beginning.

    Qualitative research was born of a disappointment with the capacity
of so-called objective methods to capture significant features of human
experience.  The revolution provided a necessary corrective, but the en-
thusiasm that was generated in the process often led to an overshooting
of the mark and to excesses in the opposite direction.  An extreme re-
action has been to reject any procedure bearing the slightest resem-
blance to number, but the consequence has been to deprive the student of
behavior of devices which can extend perception beyond unassisted lim-
its, and can secure those fresh and intellectually nutritious observa-
tions which a growth in knowledge requires.  Q methodology is a useful
addition to the qualitative researcher's arsenal: it is simple to the
point of elegance, well fortified with mathematics (which needn't be un-
derstood), increasingly supported by computer software programs, and
grounded in modern philosophical and scientific principles.  And it has
a wealth of exemplary applications to help show the way.  The qualita-
tive analyst would be hard pressed to find a more adequate methodologi-
cal ally.


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   Maryland.


+----------------------------------------------------------------------+
|                                                                      |
|     This eight-part series on Q methodology is in the public domain  |
|  and may be freely reproduced.  Users are requested to keep the      |
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|                                                                      |
+----------------------------------------------------------------------+


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:: Steven R. Brown        ::::::::::::::      ::::::::::       :::::::::
:: Department of Political Science  ::::::::::::::::::::::::::::::::::::
:: Kent State University      ::::::::::::::::::::::          ::::::::::
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