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Received:  by CIOS Mailer; Wednesday 24 Feb 2010 18:30:11
Date:         Wed, 24 Feb 2010 18:29:02 -0500
From:         "Robert Lipgar, PhD, ABPP" 
Subject: Re: Number of participants
To:           Q-METHOD@LISTSERV.KENT.EDU
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Re: Number of participantsYes, I feel that Steve Brown says it just =
right:=20

"With all due respect to Jos=E9 Quiles and the authors of the Webler et =
al. Primer, there is no recommended minimum or maximum number of =
respondents in a Q study and no items-to-persons formula that can be =
said to apply.  Abstract rules such as these almost invariably come from =
R factor analysis and from the logic of large numbers rather than from =
the logic of experimentation; they are then applied to Q simply because =
it is also factor-analytic, even though the reasoning for this may have =
been lost in translation.

"To specify a preferred number of participants in a Q study is to grasp =
the stick from the wrong end; i.e., a determination of P-set size =
typically comes after other decisions are made.  As a practical matter, =
a beginning is best made with a problem of some kind and with the kinds =
of persons who could be expected to have something relevant to say about =
the problem."  etc.=20

It is not just in Q research, I believe, but in so much of social =
science research at least, that "it all depends". . . depends on what =
questions we are asking and whether those questions are in a context of =
other particular findings, interests, reports, and research data. Just =
"keep on truckin'" and inquiring into issues that interest you and some =
relevant community.  We got some surprising and valuable results with a =
factor analysis of a matrix of 12 x 12, but of course there would always =
be much more to learn had we been able to get to study more populations =
engaged in the same kind of work and working with the same kinds of =
issues in "communties" beyond those at hand in Chicago and Evanston. So =
it goes, there is always more to do, but start with some =
questions/problems that you can articulate and that (some) others want =
to hear about.=20

Bob


From: BROWN, STEVEN=20  at 
Sent: Tuesday, February 23, 2010 11:10 PM
To: Q-METHOD@LISTSERV.KENT.EDU=20
Subject: Re: Number of participants



With all due respect to Jos=E9 Quiles and the authors of the Webler et =
al. Primer, there is no recommended minimum or maximum number of =
respondents in a Q study and no items-to-persons formula that can be =
said to apply.  Abstract rules such as these almost invariably come from =
R factor analysis and from the logic of large numbers rather than from =
the logic of experimentation; they are then applied to Q simply because =
it is also factor-analytic, even though the reasoning for this may have =
been lost in translation.

To specify a preferred number of participants in a Q study is to grasp =
the stick from the wrong end; i.e., a determination of P-set size =
typically comes after other decisions are made.  As a practical matter, =
a beginning is best made with a problem of some kind and with the kinds =
of persons who could be expected to have something relevant to say about =
the problem.  In the case of Newman's (2005) study of doctor-assisted =
suicide, for instance, reliance was placed on Thompson's theory of =
public opinion, which holds that with respect to any controversy there =
will be some individuals who are experts, some who speak authoritatively =
(but without expert knowledge), some who represent special interests =
(i.e., who have a material stake in the outcome of the controversy), and =
some who speak as a function of their class background; and, of course, =
there are always the unknowledgeable.  Also incorporating anticipated =
gender differences, this gives rise to the following factorial design:


  A. INTERESTS    (a) experts   (b) authorities  (c) special   (d) class =
  (e) unknowledgeable

  B. GENDER       (f) male   (g) female


Experts would include individuals such as medical ethicists, =
thanatologists, sociologists and psychologists of death and dying, etc.  =
Authorities would include priests, rabbis, and preachers, but also =
politicians and journalists, i.e., non-specialists who nevertheless =
render proclamations authoritatively due to their positions in society.  =
Special interests might include physicians (who might also fall in the =
authority category), grief counselors, hospice workers, the terminally =
ill and their relatives and close friends.  Class interests would =
include ordinary individuals from different social classes who lack any =
special interest in the outcome of the debate and who may be presumed to =
be responding from the value base that is characteristic of their class =
and social background.  Unknowledgeables might include children or young =
adults who have yet to face the loss of even a pet.

These theoretical considerations give rise to 5x2 =3D 10 combinations, =
and here is where numbers now begin to play a role.  Were we to select =
m=3D3 of each kind (i.e., 3 male experts, 3 male authorities, ..., and 3 =
female unknowledgeables), this would produce a P-set of size mAB =3D =
(3)(5)(2) =3D 30 individuals.  The mathematics would be altered were we =
to introduce a third effect, e.g.:


  C. AGE              (h) young   (i) middle   (j) elderly


Now there are ABC =3D (5)(2)(3) =3D 30 combinations, of which we might =
elect to take 1 or 2 of each, for a P set of 30-60.  We needn't be =
obsessive about complete balance.  We might find it difficult, for =
instance, to find any elderly or even middle-aged individuals who might =
be considered unknowledgeable, which would result in empty cells in the =
P structure, but this is of little concern since we expect the =
functionality of the Q factors to supersede the structural =
characteristics of the P set.  But the goal would be to make sure that =
no important group (e.g., authorities) is left unrepresented in the =
study.

The main purpose of the P-set structure is to provide diversity on the =
response side of the stimulus-response situation, comparable to the =
diversity provided by the the structure of the Q sample.  Between them, =
we expect these two structures, suitably replicated with items and =
persons, to reveal the main perspectives (i.e., Q factors) that are at =
issue.  Hence, it is not numbers as such, but diversity that is the =
goal.  There is, of course, the need to make sure where possible that =
the factors that emerge are suitably well defined, which usually means =
five or six pure cases with reasonably high factor loadings associated =
with each factor, but with any responses beyond the minimum being =
redundant.  However, we rarely know in advance how many factors there =
will be nor which respondents will be defining each, hence the need to =
over-sample.

As to the items : persons ratio, I have never heard anyone make clear =
what the consequences might be for violating these ratios.  Surely the =
world wouldn't come to an end.  Neither the PQMethod nor the PCQ =
programs would explode if more cases than items were included.  The =
factor analysis of the correlation matrix will still proceed (merrily =
so) without knowledge of the number of statements that produced the =
correlations.  Moreover, the character of the raw scores in a Q-method =
study (which arise from interactions) is quite different from the =
character of scores in R (which are independent and non-interactive), =
and this alone undermines consideration of item : person ratios in Q =
methodology.

Reference

Newman, T.D. (2005).  Physician assisted suicide and euthanasia: A Q =
study of the links between ethics and public policy.  Doctoral =
dissertation, Kent State University.

___________________________________________
*  _____  ______  ____  __ __  ____  ___ _  *  Steven R. Brown
| |  ___||_    _||  _ ||  |  ||  _ ||   | | |  Political Science
| |___  |  |  |  |  _| |  |  ||  _| |     | |  Kent State University
| |_____|  |__|  |____| \___/ |____||_|___| |  (sbrown@kent.edu)
*___________________________________________*_________________________
 Time paradoxes will have given me a headache.





On 2/23/10 2:51 AM, "Karen Roberts"  =
wrote:


  Apologies for the very basic question but I'm new to Q and trying to=20
  get my head around things.

  Is there a recommended minimum number of participants required for a=20
  Q-sort?  I have read that around 40-60 participants is typical (Watts=20
  & Stenner, 2005) but are there examples of studies using fewer=20
  participants?

  Should the number of participants at least equal the number of=20
  statements in the Q-sort?

  Any help would be most appreciated.
  Kind regards,
  Karen Roberts

  --
  Karen Roberts
  Subject Leader PGCE Modern Languages
  School of Education, Ellen Wilkinson Building (C2.20)
  The University of Manchester
  Oxford Road,Manchester,M13 9PL
  Direct line/voicemail: 0161 275 3416
  Fax: 0161 275 3528
  PGCE Office: 0161 275 8472
  Email: karen.roberts-2@manchester.ac.uk


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Yes, I feel that Steve Brown says it just =
right:=20

 
"With all due respect to Jos=E9 Quiles and the =
authors of=20
the Webler et al. Primer, there is no recommended minimum or =
maximum=20
number of respondents in a Q study and no items-to-persons formula that =
can be=20
said to apply.  Abstract rules such as these almost invariably come =
from R=20
factor analysis and from the logic of large numbers rather than from the =
logic=20
of experimentation; they are then applied to Q simply because it is also =

factor-analytic, even though the reasoning for this may have been lost =
in=20
translation.

"To specify a preferred number of participants in a =
Q study=20
is to grasp the stick from the wrong end; i.e., a determination of P-set =
size=20
typically comes after other decisions are made.  As a practical =
matter, a=20
beginning is best made with a problem of some kind and with the kinds of =
persons=20
who could be expected to have something relevant to say about the=20
problem."  etc. 
 
It is not just in Q research, I believe, but =
in so much=20
of social science research at least, that "it all depends". . . =
depends on=20
what questions we are asking and whether those questions are in a =
context of=20
other particular findings, interests, reports, and research data. Just =
"keep on=20
truckin'" and inquiring into issues that interest you and some relevant=20
community.  We got some surprising and valuable results with a =
factor=20
analysis of a matrix of 12 x 12, but of course there would always be =
much more=20
to learn had we been able to get to study more populations engaged in =
the same=20
kind of work and working with the same kinds of issues in "communties" =
beyond=20
those at hand in Chicago and Evanston. So it goes, there is always more =
to do,=20
but start with some questions/problems that you can articulate and that =
(some)=20
others want to hear about. 
 
Bob




From: BROWN, STEVEN 
Sent: Tuesday, February 23, 2010 11:10 PM
To: Q-METHOD@LISTSERV.KENT.EDU=
 
Subject: Re: Number of participants


With all due respect to Jos=E9 Quiles and =
the authors=20
of the Webler et al. Primer, there is no recommended minimum or =
maximum=20
number of respondents in a Q study and no items-to-persons formula that =
can be=20
said to apply.  Abstract rules such as these almost invariably come =
from R=20
factor analysis and from the logic of large numbers rather than from the =
logic=20
of experimentation; they are then applied to Q simply because it is also =

factor-analytic, even though the reasoning for this may have been lost =
in=20
translation.

To specify a preferred number of participants in a Q =
study=20
is to grasp the stick from the wrong end; i.e., a determination of P-set =
size=20
typically comes after other decisions are made.  As a practical =
matter, a=20
beginning is best made with a problem of some kind and with the kinds of =
persons=20
who could be expected to have something relevant to say about the =
problem.=20
 In the case of Newman=92s (2005) study of doctor-assisted suicide, =
for=20
instance, reliance was placed on Thompson=92s theory of public opinion, =
which=20
holds that with respect to any controversy there will be some =
individuals who=20
are experts, some who speak authoritatively (but without expert =
knowledge), some=20
who represent special interests (i.e., who have a material stake in the =
outcome=20
of the controversy), and some who speak as a function of their class =
background;=20
and, of course, there are always the unknowledgeable.  Also =
incorporating=20
anticipated gender differences, this gives rise to the following =
factorial=20
design:


A. INTERESTS    (a) experts=20
    (b) authorities  (c) special   (d) class=20
    (e) unknowledgeable

B. GENDER=20
        (f) male   (g)=20
  female

Experts would include individuals such as =
medical=20
ethicists, thanatologists, sociologists and psychologists of death and =
dying,=20
etc.  Authorities would include priests, rabbis, and preachers, but =
also=20
politicians and journalists, i.e., non-specialists who nevertheless =
render=20
proclamations authoritatively due to their positions in society. =
 Special=20
interests might include physicians (who might also fall in the authority =

category), grief counselors, hospice workers, the terminally ill and =
their=20
relatives and close friends.  Class interests would include =
ordinary=20
individuals from different social classes who lack any special interest =
in the=20
outcome of the debate and who may be presumed to be responding from the =
value=20
base that is characteristic of their class and social background.=20
 Unknowledgeables might include children or young adults who have =
yet to=20
face the loss of even a pet.

These theoretical considerations =
give rise=20
to 5x2 =3D 10 combinations, and here is where numbers now begin to play =
a role.=20
 Were we to select m=3D3 of each kind (i.e., 3 male experts, 3 male =

authorities, ..., and 3 female unknowledgeables), this would produce a =
P-set of=20
size mAB =3D (3)(5)(2) =3D 30 individuals.  The mathematics would =
be altered=20
were we to introduce a third effect, e.g.:


C. AGE=20
  =
            &=
nbsp;(h)=20
  young   (i) middle   (j)=20
elderly

Now=20
there are ABC =3D (5)(2)(3) =3D 30 combinations, of which we might elect =
to take 1=20
or 2 of each, for a P set of 30-60.  We needn=92t be obsessive =
about complete=20
balance.  We might find it difficult, for instance, to find any =
elderly or=20
even middle-aged individuals who might be considered unknowledgeable, =
which=20
would result in empty cells in the P structure, but this is of little =
concern=20
since we expect the functionality of the Q factors to supersede the =
structural=20
characteristics of the P set.  But the goal would be to make sure =
that no=20
important group (e.g., authorities) is left unrepresented in the=20
study.

The main purpose of the P-set structure is to provide =
diversity on=20
the response side of the stimulus-response situation, comparable to the=20
diversity provided by the the structure of the Q sample.  Between =
them, we=20
expect these two structures, suitably replicated with items and persons, =
to=20
reveal the main perspectives (i.e., Q factors) that are at issue. =
 Hence,=20
it is not numbers as such, but diversity that is the goal.  There =
is, of=20
course, the need to make sure where possible that the factors that =
emerge are=20
suitably well defined, which usually means five or six pure cases with=20
reasonably high factor loadings associated with each factor, but with =
any=20
responses beyond the minimum being redundant.  However, we rarely =
know in=20
advance how many factors there will be nor which respondents will be =
defining=20
each, hence the need to over-sample.

As to the items : persons =
ratio, I=20
have never heard anyone make clear what the consequences might be for =
violating=20
these ratios.  Surely the world wouldn=92t come to an end. =
 Neither the=20
PQMethod nor the PCQ programs would explode if more cases than items =
were=20
included.  The factor analysis of the correlation matrix will still =
proceed=20
(merrily so) without knowledge of the number of statements that produced =
the=20
correlations.  Moreover, the character of the raw scores in a =
Q-method=20
study (which arise from interactions) is quite different from the =
character of=20
scores in R (which are independent and non-interactive), and this alone=20
undermines consideration of item : person ratios in Q=20
methodology.

Reference

Newman, T.D. =
(2005).=20
 Physician assisted suicide and euthanasia: A Q study of the links =
between=20
ethics and public policy.  Doctoral dissertation, Kent State=20
University.

___________________________________________
* =20
_____  ______  ____  __ __  ____  ___ _  =
* =20
Steven R. Brown
|=20
|  ___||_    _||  _ ||  |  ||  _ =

||   | | |  Political=20
Science
| |___  |  | =
 | =20
|  _| |  |  ||  _| |     | =
| =20
Kent State University
| |_____|  |__|  |____| \___/ =
|____||_|___|=20
|  (sbrown@kent.edu)
*___________________________________________*_______________________=
__
 Time paradoxes will have given me a=20
headache.





On 2/23/10 2:51 AM, "Karen =
Roberts" <karen.roberts-2@MANCHESTER.AC.U=
K>=20
wrote:


Apologies for the very basic question but =
I'm new to Q=20
  and trying to 
get my head around things.

Is there a =
recommended=20
  minimum number of participants required for a 
Q-sort?  I have =
read=20
  that around 40-60 participants is typical (Watts 
& Stenner, =
2005) but=20
  are there examples of studies using fewer =

participants?

Should the=20
  number of participants at least equal the number of 
statements in =
the=20
  Q-sort?

Any help would be most appreciated.
Kind =
regards,
Karen=20
  Roberts

--
Karen Roberts
Subject Leader PGCE Modern=20
  Languages
School of Education, Ellen Wilkinson Building =
(C2.20)
The=20
  University of Manchester
Oxford Road,Manchester,M13 9PL
Direct=20
  line/voicemail: 0161 275 3416
Fax: 0161 275 3528
PGCE Office: =
0161 275=20
  8472
Email: karen.roberts-2@manchester.ac.u=
k



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