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An Example of Judgmental Rotation

Consider for a moment that Judgmental Rotation is an active process and that the researcher's theoretical interests are the primary guides. The graphic controls in PCQ allow the researcher to put the theoretical considerations into motion within a graphical framework. Remember that the inter-relationships of the sorts -- the points shown in the graph -- are not changed in any way in rotation. It is the grid that is rotated so that variance is shifted from one factor to another. (Please refer to the FAQ and Technical Notes for more information about variance.) The shifting of variance is analogous to tuning a violin or focusing a camera lens.

This worked example of a Judgmental Rotation is an adaptation of the Lipset Q study, to be found in Brown's Political Subjectivity

For convince, colors have been assigned to each sort. The assignments are based upon the final outcome of the rotation:


Color Key

1 & 3

Sort numbers
6 & 7
3, 4 & 5
1 & 2

Canada, Britain
US, US, Japan


Sort 5 is negative

Sort 8 is confounded



Note: The "before" image is shown on the left and the "after" image is on the right.


rotate01.gif (2383 bytes)

Rotation 1: Factor 1.0 by Factor 2.0, -27
Strategy: To center the factor axes in the observed clusters.
Observations: Before the rotation, variance was divided between
 F1 and F2. After it, variance for the sorts shown in red and green
 has been concentrated on F1, and variance for the sorts shown
 in blue on F2.

Also, note that the factor designations are incremented after a 
rotation has been accepted. Thus,  rotating Factor 1.0 and 
Factor 2.0 yields Factor 1.1 and Factor 2.1.



rotate02.gif (2392 bytes)

Rotation 2: Factor 1.1 by Factor 3.0, +35
Strategy: To shift sorts shown in green from F1 to F3.
Observations: Before the rotation, sorts shown in green 
were associated with F1 in negative relationship with sorts 
shown in red. After it, the green sorts define F3.

Also note that the blue and black sorts are almost not effected be this rotation.



rotate03.gif (2382 bytes)

Rotation 3: Factor 1.2 by Factor 5.0, +27
Strategy: To maximize the loadings for the red sorts on F1
Observations: Note this rotation also makes one of the 
green sorts significant on F1.




rotate04.gif (2378 bytes)

Rotation 4: Factor 2.1 by Factor 4.0, -13
Strategy: To center F2 on the blue sorts
Observations: Two of the blue sorts have positive loadings 
on F2 while one has a negative loading. This configuration 
is referred to as a bipolar factor.




rotate05.gif (2400 bytes)

Rotation 5: Factor 4.1 by Factor 6.0, +30
Strategy: To begin collecting variance sort 9, shown in black
Observations: This rotation illustrates an interesting possibility. 
In the unrotated factor structure, sort 9, provided by an individual 
from France, is not associated with any factor. Judgmental Rotation 
provides the means to include this sort in the analysis.




rotate06.gif (2339 bytes)

Rotation 6: Factor 3.1 by Factor 6.1, +12
Strategy: To shift variance from F6 to F3 by centering on the 
green sorts.
Observations: This rotation, plus rotations 7 and 8, amount 
to fine tuning.




rotate07.gif (2313 bytes)

Rotation 7: Factor 2.2 by Factor 5.0, +10
Strategy: To shift variance from F5 to F2 by centering on 
the blue sorts.




rotate08.gif (2312 bytes)

Rotation 8: Factor 2.3 by Factor 6.2, -27
Strategy: To center F2 on the blue sorts




rotate09.gif (2420 bytes)

Rotation 9: Factor 4.1 by Factor 5.1, -41
Strategy: To shift variance to the black sort.
Observations: Since the relationships between the sorts 
is not changed in rotation, shifting variance from one factor 
to another has only the result of increasing or decreasing a 
sort's loadings. In this case, the researcher suspects that 
the black sort's point of view may be interesting enough to 
warrant the shift.




rotate10.gif (2385 bytes)

Rotation 10: Factor 4.2 by Factor 7.0, -30
Strategy: To finish defining F4 with the black sort.
Observations: Since F4 is defined by one sort, the 
original Q sort is used in the factor score array.





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Results of the Rotations

Since there are four factors remaining, the relationships of the sorts can be visualized in six images.


Before Judgmental Rotation

After Judgmental Rotation

unrotated-01.gif (2777 bytes)

final-01.gif (2737 bytes)

unrotated-02.gif (2136 bytes)

final-02.gif (2173 bytes)

unrotated-03.gif (1526 bytes)

final-03.gif (1538 bytes)


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Copyright 2000, 2001, 2002, 2003, 2004 Michael Stricklin & Ricardo Almeida (All Rights Reserved)

Last update on 09 March 2010.