# Statistics: Orthogonal and Oblique Factor Rotation

Factor rotation is a technique used to transform factors gained from the factor analysis (FA) so that the factor loadings that are small would be minimized, and factor loadings that are large would be maximized in order to enhance the interpretability of these factors (Field, 2013; Warner, 2013, p. 848).

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The major difference between orthogonal and oblique rotation is that the orthogonal rotation preserves the orthogonality of the factors (i.e., the correlations between them remain equal to zero), whereas the oblique rotation allows the new factors to be correlated.

Some advantages of orthogonal rotations are that they provide results that are simpler due to the preserved orthogonality of factors and might be easier to interpret. Orthogonal rotations also produce lower sampling errors, and the results from these rotations are more likely to be replicated in further studies (Kieffer, 1998, p. 12). An important limitation is that “underlying factors” are rarely completely uncorrelated if they correspond to something, in reality, so orthogonal rotations tend to oversimplify the model (Field, 2013; Kieffer, 1998).

On the contrary, oblique rotations allow for the best fit of the model to the gathered data, and they may better correspond to the scholar’s view about the world (Kieffer, 1998; Warner, 2013). However, a limitation is that these results are more difficult to interpret, for oblique rotations produce more data to be assessed (Kieffer, 1998, p. 16).

A researcher might want to use oblique rotation if they believe that the orthogonal rotation oversimplifies the data because “hidden factors,” as was noted, will rarely be uncorrelated if they are to reflect something in reality (Field, 2013, sec. 17.4.6). Also, a substantial reason might be that the positioning of clusters of the original variables is such that an orthogonal rotation will be unsuccessful in maximizing the factor loadings, whereas an oblique rotation will be much more effective (Field, 2013, sec. 17.4.6).

## References

Field, A. (2013). Discovering statistics using IBM SPSS Statistics (4th ed.). Thousand Oaks, CA: SAGE Publications.

Kieffer, K. M. (1998). Orthogonal versus oblique factor rotation: A review of the literature regarding the pros and cons. Web.

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Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.

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