Question

An orthogonal rotation of factors identified in a factor analysis produces a communality of .30 for one of the tests included in the analysis. This means that ____% of variability in scores on that test is explained by the factor analysis.A. 9B. 49C. 30D. 70

Answer 1

An orthogonal rotation of factors identified in a factor analysis produces a communality of .30 for one of the tests included in the analysis. This means that 30% of variability in scores on that test is explained by the factor analysis.

It's important to note that a communality of .30 indicates that the factor analysis accounts for a moderate amount of the variability in scores on the test. This information can be useful in understanding the relationship between the factors and the test scores.

Therefore, the correct answer is C, 30%.

Answer 2

A commonality of .30 in an orthogonal rotation of factors means that 30% of the test score variability is explained by the factor analysis.

Step-by-step explanation:

When an orthogonal rotation of factors produces a communality of .30 for a test in a factor analysis, it means that this communality value represents the proportion of variance in that test scores which can be explained by the common factors extracted in the analysis. To convert this to a percentage, we simply multiply the communality by 100. Therefore, a commonality of .30 corresponds to 30% of the variability in test scores being explained by the factor analysis. This would correspond to option C. The remaining 70% represents the unique variance in the test scores, which includes error variance and specific variance that the extracted factors do not account for.