Example Rotation

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[ PCQ Soft ] [ Tutorial ] [ FAQ ] [ Technical Notes ] [ Search ] [ Site Map ] or click on Back in the browser 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 Red Blue Green Black Magenta	Factor 1 2 3 4 1 & 3	Sort numbers 6 & 7 3, 4 & 5 1 & 2 9 8		Nationalities Canada, Britain US, US, Japan US, US France US	Notes 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.
		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.

		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.

		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.

		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.

		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.

		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.

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

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

		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.

		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.

Back to Top of Page 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



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