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Judgmental Rotation Tutorial
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Introduction
PERHAPS THE EASIEST way
to approach learning Judgmental Rotation is by way of analogy. Since the
purpose of this tutorial is to introduce you to Judgmental Rotation in
practical terms, let us consider a musician, say, a violinist. What is the
objective of tuning a violin? What does the reference tone for tuning it
sound like? We say the violin is in
tune when the four strings are in precise relationship with each other in
terms of a given tone. The choice of that tone -- it is almost universally
the 440-cycles-per-second "A" in the middle of a piano keyboard --
is partly convention and partly arbitrary:
So, what does one do to
tune a violin? First, pick up the bow and adjust the tension. Pick up the
instrument and pull it up and under the chin. Pluck the "A" string,
comparing its tone with the reference tone, 440-A. Tighten or loosen the
string until the sound it produces matches the reference tone. The violinist listens
to the combined tones and adjusts the string until it produces a pure sound
in combination with the reference tone. The process is repeated with the
other three strings: Pluck, listen, tighten or loosen until the strings
produce a pure sound in combination. This works because well-tuned violin
strings are precisely relative to each other and precisely relative to the
reference tone. Now draw the bow across the strings to produce continuous
tones because it is easier to make fine adjustments when hearing continuous
tones. An expert can tune an
instrument quickly because the ear and fingers have become trained through
experience. But, for untrained ears and fingers, many minutes may be needed.
Indeed, beginning string players struggle as they learn to listen and to hear
a pure combination of tones. A person unfamiliar with
music might think this analogy is obscure and wonder what is going on here.
As a matter of fact, though, engineers tune ships, buildings, bridges and
computer structures in ways parallel to tuning a violin or an entire
orchestra. Or, consider a photographer focusing a camera lens until the image
is sharp. Or, consider adding spices to a recipe -- the ubiquitous "salt
to taste". In all of these there are reference points and adjustment processes
that are used to bring complicated components into balance. And so it is, too, in
Judgmental Rotation. Much as with tuning a violin, Judgmental rotation can be
described as both abstract and concrete at the same time. The logic of it,
though, is completely theoretical. The numbers are theoretical; the graphical
representation is nothing more than a geometric projection of the factor
loadings, which are also theoretical. In a way, judgmental rotation is an
example of pure communication play, to apply Stephenson's concept, in the
sense that the researcher is in search of balancing the factors as guided by
theory, tuning them in terms of the preferred reference points.
Visualizing the factors
on a graph helps the researcher see the relationships between the sorts as
they are individually and collectively associated with the factors. But it is
a pointless exercise if there are no reference points, in the physical sense
of graphing, and no guides, in the abstract sense of theoretical
considerations. PCQ provides the physical reference points in the graph
plotted on the screen. The researcher provides the guiding theory. The program shows the
sorts in relation to one another in the form of a graph having two
dimensions, called axes. By convention, the two dimensions are labeled Factor
X, read vertically, and Factor Y, read horizontally. Please note that the
dimensions are always at right angles, that is, at 90° angles, because
mathematically this maintains a condition begun in the factoring stage
wherein the two factors are uncorrelated. In PCQ all the factors
can be visualized, but only two at a time. The process is parallel to the
violinist listening to the sounds produced by two strings at once. With PCQ,
though, rotating the X axis and Y axis is the visual parallel to the
tightening and loosening adjustments the violinist makes. But adjustments in
rotating factors involves many more components. Remember that when the
factors were extracted, each sort was assigned a numerical value establishing
its relationship to each factor. The values are called "factor
loadings". For example, if a study has 9 factors and 33 sorts, each sort
has 9 loadings associated with it. This means there are (9 * 33 = 297)
relationships involved in the complete factor structure. A common objective in
Judgmental Rotation -- there are others -- is to account for as many of the
sorts as possible in as few factors as possible. Or, put another way, one
seeks to have fewer dimensions which are identified by all the sorts. The
result of rotating the Lipset
Q study data, for example, produced four factors accounting for all the
sorts. This section contains two
major parts: (1) a tutorial introducing the practical
qualities, commands
and processes of
Judgmental Rotation, and (2) a step-by-step example showing how
Judgmental Rotation can become a tool for the researcher. Back to Top of
Page
Practical
Qualities
Judgmental Rotation in
PCQ has these components: (1) Cartesian graph, (2) commands, and (3) tables.
They are inter-related and are designed to provide you with a real-time
working environment. The thumbnail shows the three screen areas. |
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The graph displays the x,
y positions of each sort. The vertical axis is Factor X, and the horizontal
axis is Factor Y. Factor X and Factor Y loadings
are listed in the table to the left of the graph. |
Back to Top of
Page
Rotation controls and the results they produce
Here is the command area,
as shown on screen. |
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Once arrived at the
graphic rotation screen, use these commands. |
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Select factors
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Click on the left window and
select Factor X, then click on the other window and select Factor Y. To
display the factors on the graph, click on Start. |
Set rotation angle |
After clicking on Start,
you have three ways to select an angle of rotation.
The program will respond
automatically and move the X by Y axes to the position you have selected. Please note that only the
axis lines move; the points representing each sort remain stationary. |
Operation commands |
Start: Click on this button to display
loadings of the selected factors. Undo: Click here to Undo the most
recently Accepted rotation. Click it again to undo the previous rotation. Cancel: Click here if you want to select
other factors. Preview: Click here to display the
loadings that would result if you Accept the rotation of the currently
selected factors. Accept: When you are satisfied, click to
record the rotation. |
Show or Hide sort
numbers |
This feature is useful
for visual inspection, particularly with a large number of sorts. You may
choose to show the sort numbers for all sorts, only the sorts with significant
loadings, or only the sorts with less than significant loadings. |
Change significance
level |
Default is the
theoretical value |
General Commands |
History: A pop-up listing of rotations
performed in the current session. Labels: A pop-up listing of sort labels
that were entered with the Q sort data. Matrix: Click on this command to examine
the status of the rotation. The Matrix displays three tables:
While the Matrix is on
the screen, you may choose to show the sort labels. Please note that the
Matrix shows values as they were after the last rotation was accepted. Use
the Preview command to display the effect of rotating the two factors
displayed in the graph. Finish: Click here when all done. You
will be returned to Rotation Dialog. For example, suppose you want to start
over or abandon rotation, click Finish. |
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Copyright © 2000, 2001,
2002, 2003, 2004 Michael Stricklin & Ricardo Almeida (All Rights
Reserved) |
Last update on 27 April
2004. |
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