Your CIOS file request: Q-METHOD/06089030.805 hotline item

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Received:  by CIOS Mailer; Monday 8 Jun 2009 03:08:05
Date:         Mon, 8 Jun 2009 03:06:08 -0400
From:         "BROWN, STEVEN" 
Subject: Re: Analysis?
To:           Q-METHOD@LISTSERV.KENT.EDU
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There seems to be something definitely amiss about this situation.  It is i=
mpossible, as Peter Schmolck notes, to rotate the first four unrotated fact=
ors and end up explaining more variance (or even explaining less variance).=
  If only the first four unrotated factors are admitted into the varimax ph=
ase, then the rotated factors should explain exactly 72.55% of the variance=
, just as the unrotated factors did.  However, I do agree with Bob Braswell=
 that if (say) all eight principal components were allowed into the varimax=
 rotation, that it would then be possible that four of those rotated factor=
s could account for more variability than the first four unrotated factors =
by virtue of gaining some of the variance from those factors not retained i=
n the final four.  But Sam Hopper claims to have kept only four factors for=
 the varimax phase.  This doesn't add up and I would be inclined to re-run =
the analysis.

Even without this problem, however, Sam Hopper's rotated solution looks pro=
blematic.  Factors 3 and 4, for example, are only defined by a single Q sor=
t and should therefore probably not be retained unless there is something s=
pecial about those two individuals.  (The two sets of factor scores for the=
se two factors will be nothing more than the Q sorts for those two persons.=
)  Moreover, the defining Q sort for factor 4 carries a negative loading, s=
o that factor should probably be reflected.  In addition, it very much look=
s like factors 1 and 2 are highly correlated with one another.  This may be=
 one of those rare cases in which the unrotated solution might be the best =
final solution.  It might be helpful if Sam Hopper could provide us with mo=
re information about the nature of the study and perhaps the Q sample that =
is being used.  This might provide a key that would help explain these unus=
ual results.

As to Sam Hopper's desire "to look at subgroups within my data," this is ge=
nerally not a good idea.  For one thing, males-females, Republicans-Democra=
ts, and like divisions are mere categories which are supplanted by the oper=
ant categories represented by the Q factors.  Conventional categories are n=
ot accurate guides as to the way nature actually operates and ought to be r=
eplaced by more precise designations (such as Q factors) when these reveal =
themselves.  Conventional categories are only useful in designing P sets, a=
nd to return to categories once the Q factors have been revealed is to plac=
e the lever in the wrong location.  Moreover, given that P samples are neit=
her large nor randomly selected means that the categories that comprise the=
m are ill suited for inferential purposes.  That said, it is always possibl=
e to keep the Q factors intact and then compare subcategories of persons us=
ing t, F, or other tests of this kind.  For instance, a t-test could be use=
d to determine whether the average factor-1 loadings for males is significa=
ntly greater than the average factor-1 loadings for females.  Or quantitati=
ve variables (such as IQ) could be correlated with the loadings for the var=
ious factors.  Such test results would still be on shaky ground given the s=
mall and probably unrepresentative character of the person sample.  In Q st=
udies, it is best (and certainly safest) to focus on the factor arrays-whic=
h is where the subjectivity is-and to play down the matrix of factor loadin=
gs and the objective demographic characteristics of the respondents that ar=
e associated with the loadings.  To focus on the latter is to move back tow=
ard R methodology and all its logic, which Q methodology is ill suited to d=
o.
___________________________________________
*  _____  ______  ____  __ __  ____  ___ _  *  Steven R. Brown
| |  ___||_    _||  _ ||  |  ||  _ ||   | | |  Political Science
| |___  |  |  |  |  _| |  |  ||  _| |     | |  Kent State University
| |_____|  |__|  |____| \___/ |____||_|___| |  (sbrown@kent.edu)
*___________________________________________*_________________________
Economists have forecasted nine out of the past five recessions.




On 6/5/09 9:37 AM, "Sam Hopper"  wrote:

Dear all
I just have a couple of questions regarding my results and I wondered if

anyone could help. The first is regarding eigenvalue's/% of variance
explained - the prerotation values are:
Factor  Eigenvalue      As Percentage   Cumulative percentage
1       20.78                61.12      61.12
2       1.74                 5.13       66.26
3       1.13                 3.34       69.60
4       1.00                 2.95       72.55

ect...

but the post rotation ones are higher (see below), why is this, I'm going

to have to explain it in a viva potentially.

 QSORT             1         2         3         4

  1 1            0.4356    0.6995X   0.1473   -0.1207
  2 2            0.6738X   0.4643   -0.0180    0.1879
  3 3            0.7053X   0.5243    0.0358    0.0964
  4 4            0.5475    0.6437X  -0.1134   -0.1321
  5 5            0.1918    0.6030X   0.3802   -0.0802
  6 6            0.5815    0.6357X   0.0655    0.0106
  7 7            0.8032X   0.3382    0.0457    0.2553
  8 8            0.5793X   0.5234   -0.0133    0.0006
  9 9            0.7499X   0.3172   -0.0290    0.3484
 10 10           0.6242X   0.5898    0.0382    0.0342
 11 11           0.6167X   0.4980    0.1298   -0.0137
 12 12           0.7740X   0.3658    0.0986    0.2421
 13 13           0.3465    0.4923X  -0.0391    0.2337
 14 14           0.6139X   0.5119   -0.0139    0.0914
 15 15           0.5519    0.6386X   0.2492   -0.1189
 16 16           0.7346X   0.4022    0.1266    0.2470
 17 17           0.8324X   0.2080    0.1408    0.4370
 18 18           0.8249X   0.3016    0.1740    0.3439
 19 19           0.7487X   0.4959    0.1330    0.0894
 20 2800         0.6644X   0.4046    0.1106    0.2713
 21 2809         0.0840    0.2934X   0.9208X   0.0424
 22 2830         0.8255X   0.2794    0.0717    0.3035
 23 2876         0.7728X   0.4232    0.1197    0.1627
 24 2878         0.6264X   0.4768    0.1398    0.0909
 25 2880         0.2799    0.7442X   0.2099   -0.1633
 26 2884         0.6981X   0.5118    0.0937    0.0570
 27 29 21        0.3420    0.7810X   0.1600   -0.2195
 28 30 74        0.6144X   0.6092    0.0311    0.0211
 29 3120         0.7232X   0.4899    0.0517    0.0845
 30 3357         0.6375X   0.5772    0.1268   -0.0659
 31 3371         0.6214X   0.4536    0.2503   -0.0161
 32 3380        -0.5689X   0.4873    0.0069   -0.8105X
 33 3382         0.7587X   0.3588   -0.0038    0.2617
 34 3383         0.6317X   0.4697    0.2232    0.2220

 % expl.Var.         41        26         4         5



Secondly, I would like to look at subgroups within my data, but dont want

to delete sorts from the file to do this. Is there a way of "ignoring"

certain participants sorts or making a new file (with copied data) so I c
an
delete the unwanted sorts?

Thank you very much for any help!
Sam


--_000_C65230A06F75sbrownkentedu_
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Content-Transfer-Encoding: quoted-printable








There seems to be something definitely amiss about this situation.  It=
 is impossible, as Peter Schmolck notes, to rotate the first four unrotated=
 factors and end up explaining more variance (or even explaining less varia=
nce).  If only the first four unrotated factors are admitted into the =
varimax phase, then the rotated factors should explain exactly 72.55% of th=
e variance, just as the unrotated factors did.  However, I do agree wi=
th Bob Braswell that if (say) all eight principal components were allowed i=
nto the varimax rotation, that it would then be possible that four of those=
 rotated factors could account for more variability than the first four unr=
otated factors by virtue of gaining some of the variance from those factors=
 not retained in the final four.  But Sam Hopper claims to have kept o=
nly four factors for the varimax phase.  This doesn’t add up and=
 I would be inclined to re-run the analysis.



Even without this problem, however, Sam Hopper’s rotated solution loo=
ks problematic.  Factors 3 and 4, for example, are only defined by a s=
ingle Q sort and should therefore probably not be retained unless there is =
something special about those two individuals.  (The two sets of facto=
r scores for these two factors will be nothing more than the Q sorts for th=
ose two persons.)  Moreover, the defining Q sort for factor 4 carries =
a negative loading, so that factor should probably be reflected.  In a=
ddition, it very much looks like factors 1 and 2 are highly correlated with=
 one another.  This may be one of those rare cases in which the unrota=
ted solution might be the best final solution.  It might be helpful if=
 Sam Hopper could provide us with more information about the nature of the =
study and perhaps the Q sample that is being used.  This might provide=
 a key that would help explain these unusual results.



As to Sam Hopper’s desire “to look at subgroups within my data,=
” this is generally not a good idea.  For one thing, males-femal=
es, Republicans-Democrats, and like divisions are mere categories which are=
 supplanted by the operant categories represented by the Q factors.  C=
onventional categories are not accurate guides as to the way nature actuall=
y operates and ought to be replaced by more precise designations (such as Q=
 factors) when these reveal themselves.  Conventional categories are o=
nly useful in designing P sets, and to return to categories once the Q fact=
ors have been revealed is to place the lever in the wrong location.  M=
oreover, given that P samples are neither large nor randomly selected means=
 that the categories that comprise them are ill suited for inferential purp=
oses.  That said, it is always possible to keep the Q factors intact a=
nd then compare subcategories of persons using t, F, or other tests of this=
 kind.  For instance, a t-test could be used to determine whether the =
average factor-1 loadings for males is significantly greater than the avera=
ge factor-1 loadings for females.  Or quantitative variables (such as =
IQ) could be correlated with the loadings for the various factors.  Su=
ch test results would still be on shaky ground given the small and probably=
 unrepresentative character of the person sample.  In Q studies, it is=
 best (and certainly safest) to focus on the factor arrays—which is w=
here the subjectivity is—and to play down the matrix of factor loadin=
gs and the objective demographic characteristics of the respondents that ar=
e associated with the loadings.  To focus on the latter is to move bac=
k toward R methodology and all its logic, which Q methodology is ill suited=
 to do.

 ___________________________________________

*=A0 _____=A0 ______=A0 ____=A0 __ __=A0 ____=A0 ___ _=A0 *=A0 Steven R. Brown

| |=A0 ___||_=A0=A0=A0 _||=A0 _ ||=A0 |=
=A0 ||=A0 _ ||=A0=A0 | | |=A0 Political Science=


| |___=A0 |=A0 | =A0|=A0 | =A0_| |=A0 | =
=A0||=A0 _| |=A0=A0=A0=A0 | |=A0 Kent State Uni=
versity

| |_____|=A0 |__|=A0 |____| \___/ |____||=
_|___| |=A0=A0(sbro=
wn@kent.edu)

*________________________________________=
___*_________________________

Economists have forecasted nine out o=
f the past five recessions.









On 6/5/09 9:37 AM, "Sam Hopper" <hopper_sam@HOTMAIL.COM> wrote:  



Dear all

I just have a couple of questions regarding my results and I wondered if


anyone could help. The first is regarding eigenvalue's/% of variance

explained - the prerotation values are:

Factor  Eigenvalue      As Percentage  &=
nbsp;Cumulative percentage

1       20.78      &=
nbsp;         61.12  &nbs=
p;   61.12

2       1.74      &n=
bsp;          5.13  =
     66.26

3       1.13      &n=
bsp;          3.34  =
     69.60

4       1.00      &n=
bsp;          2.95  =
     72.55



ect...



but the post rotation ones are higher (see below), why is this, I'm going


to have to explain it in a viva potentially.



 QSORT           &nb=
sp; 1         2   &n=
bsp;     3       &nb=
sp; 4



  1 1           =
; 0.4356    0.6995X   0.1473   -0.1=
207

  2 2           =
; 0.6738X   0.4643   -0.0180    0.1=
879

  3 3           =
; 0.7053X   0.5243    0.0358   &nbs=
p;0.0964

  4 4           =
; 0.5475    0.6437X  -0.1134   -0.1321
  5 5           =
; 0.1918    0.6030X   0.3802   -0.0=
802

  6 6           =
; 0.5815    0.6357X   0.0655   &nbs=
p;0.0106

  7 7           =
; 0.8032X   0.3382    0.0457   &nbs=
p;0.2553

  8 8           =
; 0.5793X   0.5234   -0.0133    0.0=
006

  9 9           =
; 0.7499X   0.3172   -0.0290    0.3=
484

 10 10           0.6=
242X   0.5898    0.0382    0.0342
 11 11           0.6=
167X   0.4980    0.1298   -0.0137

 12 12           0.7=
740X   0.3658    0.0986    0.2421
 13 13           0.3=
465    0.4923X  -0.0391    0.2337

 14 14           0.6=
139X   0.5119   -0.0139    0.0914

 15 15           0.5=
519    0.6386X   0.2492   -0.1189

 16 16           0.7=
346X   0.4022    0.1266    0.2470
 17 17           0.8=
324X   0.2080    0.1408    0.4370
 18 18           0.8=
249X   0.3016    0.1740    0.3439
 19 19           0.7=
487X   0.4959    0.1330    0.0894
 20 2800         0.6644X  =
; 0.4046    0.1106    0.2713

 21 2809         0.0840  =
  0.2934X   0.9208X   0.0424

 22 2830         0.8255X  =
; 0.2794    0.0717    0.3035

 23 2876         0.7728X  =
; 0.4232    0.1197    0.1627

 24 2878         0.6264X  =
; 0.4768    0.1398    0.0909

 25 2880         0.2799  =
  0.7442X   0.2099   -0.1633

 26 2884         0.6981X  =
; 0.5118    0.0937    0.0570

 27 29 21        0.3420   =
; 0.7810X   0.1600   -0.2195

 28 30 74        0.6144X  &nbs=
p;0.6092    0.0311    0.0211

 29 3120         0.7232X  =
; 0.4899    0.0517    0.0845

 30 3357         0.6375X  =
; 0.5772    0.1268   -0.0659

 31 3371         0.6214X  =
; 0.4536    0.2503   -0.0161

 32 3380        -0.5689X  &nbs=
p;0.4873    0.0069   -0.8105X

 33 3382         0.7587X  =
; 0.3588   -0.0038    0.2617

 34 3383         0.6317X  =
; 0.4697    0.2232    0.2220



 % expl.Var.         41  =
      26       =
  4         5







Secondly, I would like to look at subgroups within my data, but dont want


to delete sorts from the file to do this. Is there a way of "ignoring&=
quot;



certain participants sorts or making a new file (with copied data) so I c
an

delete the unwanted sorts?



Thank you very much for any help!

Sam








--_000_C65230A06F75sbrownkentedu_--