Orthogonality

Orthogonality in Measurement

Orthogonality is used in measurement to set up analytic devices that will produce solutions with no relationship to each other. The most common application exists in exploratory factor analysis whereby a principal components analysis is conducted with a varimax rotation. The definition of the varimax rotation procedure becomes the production of factors that are orthogonal (uncorrelated) with each other. Suppose a scale has 15 items, the rotation in SPSS will produce 15 different linear combinations (vectors or factors) each uncorrelated with each other. Generally, the factors are listed in terms of size (percentage of variance accounted for) and each individual item is referenced to the factor in terms of a factor loading.

Most often, only one or two of the factors represent significant linear predictions that account for a significant portion of available variability. Suppose that one is measuring the credibility of a communicator. A common solution to items measuring the credibility of a communicator involves an exploratory factor analysis generating two important factors: (a) trust and (b) expertise. Usually, a set of standards are applied to select the items for each factor where a minimum loading may be required (like .50) and a maximum for any other factor (like .30). The reason for this is the assumption that an item must load on a factor of interest but not load on any other factor. Conceptually, the factors should contain items that are associated with only a single factor and are considered “pure” in terms of the ability to be a part of one solution.

Trust, as a factor in credibility, represents such elements as honesty, integrity, and lack of deception. Expertise in communicator credibility often becomes associated with knowledge, experience, and authoritativeness. The factor analysis indicates that two separate evaluations are made by the persons completing the scales. The orthogonality of the evaluations indicates that the two judgments are independent of each other; basically, that trust and expertise evaluations are made without consideration of each other when taking into account one of the outcomes.

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