An item on a wellbeing scale has a loading of .32 on Factor 1 (hedonic pleasure) and .38 on Factor 2 (meaning and purpose). What is the most appropriate action?
AKeep the item — loadings above .30 on any factor indicate it is measuring something meaningful
BAssign the item to whichever factor has the higher loading and proceed
CFlag the item as having a high cross-loading and consider revising or dropping it, as it does not clearly measure either construct
DApply oblique rotation to force the item onto a single factor
High cross-loadings — significant loadings on two or more factors simultaneously — indicate an ambiguous item that does not clearly measure any single construct. Such an item clouds the factor structure and makes the constructs harder to interpret and name. The goal of factor analysis in scale development is simple structure: high loadings on one factor and near-zero loadings on others. Rotation (oblique or orthogonal) can improve interpretability but cannot rescue a genuinely ambiguous item.
Question 2 Multiple Choice
In exploratory factor analysis, a factor with an eigenvalue greater than 1.0 (the Kaiser criterion) is typically retained. What does the eigenvalue represent in this context?
AThe average correlation among items loading on that factor
BThe number of items that load significantly on the factor
CThe amount of total variance in the observed variables that the factor accounts for, measured in units of a single variable's variance
DThe probability that the factor reflects a true latent construct rather than random noise
Eigenvalues in factor analysis represent the variance explained by a factor, measured in units of the variance of a single standardized variable (which equals 1). A factor with eigenvalue > 1 explains more variance than any single observed variable, justifying its retention as a meaningful summary. Eigenvalue ≤ 1 means the factor explains less than one variable's worth of variance — adding it explains nothing useful beyond what's already in the data.
Question 3 True / False
Applying rotation (varimax or promax) to extracted factors changes the total variance explained by the factor solution.
TTrue
FFalse
Answer: False
Rotation redistributes variance among factors but preserves total variance explained. Think of rotation as rotating the coordinate axes in factor space: the data points (item positions) don't change, only the axes used to describe them. Varimax (orthogonal) and promax (oblique) rotations reapportion the variance differently across factors to improve interpretability — making some loadings larger and others smaller — without changing the total communality. This is why rotation is about interpretability, not fit.
Question 4 True / False
A factor loading of .70 means the factor accounts for 70% of that item's variance.
TTrue
FFalse
Answer: False
A loading of .70 means the item correlates .70 with the factor. The proportion of variance explained (communality from that factor) is the squared loading: .70² = .49, or 49%. This is analogous to r² in regression. The loading itself is a correlation, not a proportion of variance. Students frequently confuse the loading with r² — always square the loading to get the variance explained.
Question 5 Short Answer
Why does a well-designed psychological scale want items with high loadings on one factor and near-zero loadings on all others?
Think about your answer, then reveal below.
Model answer: High loadings on one factor indicate the item strongly and specifically measures that underlying construct. Near-zero loadings on other factors indicate the item is not contaminated by other constructs. This 'simple structure' makes the factors interpretable (each factor has a clear identity), the scale unidimensional (all items measure the same thing), and scores on the scale a valid reflection of the target construct rather than a blend of multiple constructs.
This is the measurement validity argument. If an item loads on two factors, its observed responses reflect a mixture of two latent constructs, making it impossible to know which construct it is measuring. A scale built on such items produces scores that are ambiguous composites. Simple structure — each item loading on one factor — means each factor can be cleanly named and each item unambiguously contributes to exactly one construct's measurement.