A variable that has no unique variance (or random variance) would have a communality of 1.

A variable that has no unique variance (or random variance) would have a communality of 1.

• A. 0
• B. 0.5
• C. 1
• D. 2

Answer: (C)

Communality is the portion of a variable’s variance that is explained by the common factors in a factor-analytic model. If a variable has no unique (random) variance, all of its variance is shared with the factors, so its communality is 1. In other words, the total variance is fully accounted for by the common factors. If any unique variance existed, the communality would be less than 1. A value of 0 would mean none of the variance is explained by shared factors (all variance is unique). A value like 0.5 means only half is shared, and a value of 2 isn’t possible since communality cannot exceed 1.

Communality is the portion of a variable’s variance that is explained by the common factors in a factor-analytic model. If a variable has no unique (random) variance, all of its variance is shared with the factors, so its communality is 1. In other words, the total variance is fully accounted for by the common factors. If any unique variance existed, the communality would be less than 1. A value of 0 would mean none of the variance is explained by shared factors (all variance is unique). A value like 0.5 means only half is shared, and a value of 2 isn’t possible since communality cannot exceed 1.