Tag | Value |
---|---|
file | Factor-analysis_uu-Explained-variance-008-en_uu-Explained-variance-008-en |
name | uu-Explained-variance-008-en |
section | Factor analysis/Explained variance |
type | schoice |
solution | TRUE, FALSE, FALSE, FALSE |
Type | Calculation |
Language | English |
Level | Statistical Literacy |
In a higher-order principal component analysis of ten tests, the researcher finally adopted a two-factor solution. The Eigenvalue of the Factor 1 is 4.1 and the Eigenvalue of Factor 2 is 1.3.
Apply the following criteria for qualitative assessment of the factor solution:
Based on explained variance and the above criteria, how do you rate the two-factor solution?
Explanation: In the explanation, it is given that 10 variables were included in this factor analysis. This means that the maximum Eigenvalue is equal to 10.00 (with full overlap of the factor with all variables). A factor with an Eigenvalue of 4.1, thus explains 41% (4.1 / 10.0) of the total variance. Since no oblique rotation was applied in this example, the factors have no overlap. For this reason, the following calculation can be used to calculate the explained variance of the factors:
4.1/10.0 + 1.3/ 10.0 = .41 + .13 = .54
In total, as much as 54% of the variance is explained by the two factors.