Exam 1

  1. Metainformation

    Tag Value
    fileFactor-analysis_uu-Explained-variance-008-en_uu-Explained-variance-008-en
    nameuu-Explained-variance-008-en
    sectionFactor analysis/Explained variance
    typeschoice
    solutionTRUE, FALSE, FALSE, FALSE
    TypeCalculation
    LanguageEnglish
    LevelStatistical Literacy

    Question

    In a higher-order principal component analysis of ten tests, the researcher finally adopted a two-factor solution. The Eigenvalue λ1\lambda_1 of the Factor 1 is 4.1 and the Eigenvalue λ2\lambda_2 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?


    1. TRUE: As good because the explained variance is higher than 50%.
    2. FALSE: As moderate because the explained variance is between 30% and 50%.
    3. FALSE: As poor because the explained variance is below 30%.
    4. FALSE: We cannot make a valid statement about quality with the data provided.

    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.