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Disregarding signs,
column 2 has the largest absolute sum and is the best candidate for
reflection. To change the signs, multiply each correlation in column
2 and row 2 by the quantity -1. This way all the negative correlations
in column 2 and row 2 are made positive and all the positive correlations are
made negative. The table on the right shows the impact of this operation:
There are two results.
Reflection produces a positive sum for the column, but it also produces a
change in signs across the row and therefore changes the sums of all the
other columns. Then all the columns are summed again, which produces a change
in the Table sum from -216 to +248. Notice that column 4 is still negative,
and it should be reflected next. The objective of reflection is to produce
the largest positive sum for the entire table, with the fewest number of
negative correlations. In the literature, this goal is called a "positive
manifold." Achieving it is important because the Table sum determines
how much variance can be accounted for when a factor is extracted.
Q: What is a centroid?
A: A centroid can be thought
of as a kind of grand average of the relationships between all the sorts, as
they are represented by their correlation coefficients. In other words,
Centroid Analysis is a way of defining centers of gravity embedded in a
correlation matrix. In physics, a center of gravity turns out to be where the
weight tends to fall on average. For us this concept can be represented as a
vector that spans the longest dimension of the data space. The factor
loadings, then, are values expressing each sorts relationship with the
centroid. Each loading represents a sorts contribution to the length of the
centroid, and thus can be expressed as the correlation of that sort with the
centroid.
Q: Why does PCQ restrict the
number of factors?
A: As a practical
matter, the results of a Q study can be thought of as dimensions of
communicability embedded in the concourse from which the Q sample is a
representation. This implies that, while a communication situation will have
several dimensions, more than nine of them is unlikely. PCQ was designed with
this concept in mind. A researcher seeking more dimensions is advised to use
principal component factor analysis, which can be found in many commercially
available statistical software programs. Since principal component factor analysis
produces factors that account for 100 percent of the correlation table
variance, often there are as many factors as there are variables.
Q: Why is it called "Judgmental Rotation"?
A: Very often the
researcher has specific theoretical goals in mind in conducting a
communication experiment using a Q study: reasons for selecting a particular
Q sample, for selecting the people to provide the Q sorts. In PCQ for
Windows, rotations can be performed that take the theory into account. For
example, suppose that a group of nurses, including the chief of nursing, have
provided sorts. Rotating to maximize the chief of nursing's sort may reveal
relationships hither to unrecognized. Since it is the researcher who decides
to rotate in this way, it is called "Judgmental Rotation."
Q: Why
is it called Varimax?
A: This approach to
factor rotation is strictly mathematical. Through an iterative process,
variance is distributed across the factor structure in such a way that each
sort has highest degree of association with only one factor, all sorts and
all factors being taken into consideration.
Q: How can I save or print a graph?
A: A number of
freeware programs will capture graphical images. Once a screen has been
captured, the image can either be saved as a file or printed. Please note:
Start the screen capture program before beginning a Judgmental Rotation.
Q: How do I modify what will be
saved in the Log Report file?
A: At the PCQ File
Menu, select Preferences. Click the tables you want to have saved in the Log
Report.
Q: How can I submit a bug report?
A: We welcome your
help in uncovering bugs. Please click here to send your
message.
Q: How do I find out
about updates?
A: If you have
purchased PCQ for Windows or have registered for
notifications, you will be notified by email of updates.
Q: Why are there limits on the
number of sorts and items?
A: If you are curious
about the computational power of contemporary personal computers, many more sorts
and items are possible. (In a test, PCQ for Windows has factored 600 sorts,
each with 100 items.) However, from a theoretical standpoint, very few
Q Studies contain more than 100 items and 100 sorts. In considering sorts, it
is important to remember that Q Methodology experiments with communication
possibilities in the Q sample. The people who perform the sorts are, in a
defensible way, the measuring devices. Thus, 50 sorters produce 50
independent measurements of the Q sample. As a practical matter, 200 items is
equivalent to four decks of Bridge cards, and a Q sample with more than 40
items or so will reduce the willingness of people to sort them.
Q: Why does the program only allow
"forced" pile distributions?
A: Another way to
think about pile distributions would be "symmetrical". A preference
for symmetry is understandable because a Q sample has been constructed for
experimental purposes with an understanding that a sorter is likely to have
strong preferences -- both positively and negatively -- for few statements.
Also, since the sorts are normalized in correlation, forced and unforced
distributions yield very similar factor structures.
Q: What is a Q sample?
A: A Q sample is a
representative subset of a range of communication on any topic. It may be
comprised of statements, phrases, pictures or other symbols that are
representative of the much larger flow of communication -- referred to as a concourse -- associated with a
topic.
Q: What does the act of sorting signify?
A: Generally
speaking, sorting is a model of human communication in action. When sorting,
a person is literally "in conversation" with her/himself regarding
the statements in the Q sample. When completed the statements have been put
into positions (or rank ordered) assigned by the sorter. Significantly, the
positions of the statements are relative one to the others in a way that can
only be provided by the sorter. Using Q technique the rank orders of every
sort can be formally analyzed.
Q: PCQ for Windows says the
significance level is .36 for my study. I want to set it higher. How do I do
that?
A: You can change the
significance level in more than one place, the most convenient being during
the Rotation process. You may set the level either
or higher or lower than the number calculated by the program. The value you
set will be used until you change it, both during rotation and when
generating the Final Report. PCQ for Windows will not allow the level to be
set higher than .90 or less than .10.
Q: What
does "significance level mean"?
A: Another
way to think of this question would be to ask, "By what criteria is a
sort associated with a factor?" In Q technique, it is the significance
level that provides an answer. It is usually set equal to or greater than the
value of two standard deviations away from the mean. The choice of two standard
deviations is not entirely arbitrary because this translates into the
conventionally accepted probability statistic p < 0.01, which means 99
percent of the area under a normal curve. The significance level, then,
answers the question, "Given a certain number of items, at what
magnitude would 99 out of 100 loadings be excluded from the factor?" The
significance level is, therefore, a statistic directly related to the number
of items in the Q sample; i.e., as the number of items increases, the theoretical
significance level decreases, and, conversely, the smaller the number of
items, the higher the theoretical significance level. In non-technical terms,
the effect of raising or lowering the significance level raises or lowers the
difficulty of gaining association with a factor. Setting the level lower
means easier membership; setting it higher means more restricted membership.
For example, a typical Q sample might contain 48 items. The program
calculates the theoretical significance level as being ± .31, meaning a sort
must have a factor loading of at least .31 to become associated with a
factor.
Q: Will the program use both
Varimax and judgmental rotations for the Final Log Report?
A: The program is
flexible regarding rotation. You may choose to perform both Varimax and
Graphical (Judgmental) rotations. Tip: Choose Varimax first to get a
mathematical solution. Then, if you wish you may select the Graphical method
and choose to start with either the Unrotated or the Varimax factor loadings.
For example, you may use Varimax factor loadings and later choose to begin
with the Unrotated loadings. Please remember, though, that the Final Log Report will be based upon the last rotations
you performed.
Q: Why are there so many tables?
A: If you are
thinking about the size of the Final Log Report file, you can choose which
tables you want to exclude. Choose the File Menu and click on Preferences. Many of the tables
are generated to help you analyze the factor arrays. For example, take a look
at a table of Descending Array of Differences between any two factors to see
which items have been order differently.
Q: What does the Correlation
Table tell us?
A: Since the
correlations of the sorts are the raw data for factor analysis, one can
examine the correlation table to identify the relationships between any of
the sorts.
Q: I don't understand the Q study summary
of factors in the Log File.
A: This summary
contains much information. First, each factor is described in a listing of
the sorts contributing to the factor. Contributing sorts are defined as those
having an absolute value greater than the significance level. Factors with no
sorts are listed next. Any sorts with significant loadings on more than one
factor are designated as "confounded." Any sorts with no
significant loadings are listed next. A factor with both positive and
negative sorts is designated as "bipolar." The last line states how
many of the sorts have been accounted for in how many factors.
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