Factor Analysis Results Interpreter
Define Variables, Factors & Input Loadings
This tool helps interpret pre-calculated factor loadings. It does not perform factor extraction or rotation from raw data. You need to input the factor loading matrix obtained from other statistical software (e.g., R, Python, SPSS).
Factor Interpretation
Input factor loadings and click "Interpret" to see results.
Understanding Factor Analysis & Export
Factor Analysis Explained (Briefly)
Factor Analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors (or latent variables).
It's primarily used for:
- Data Reduction: To reduce a large number of variables into a smaller, more manageable set of underlying factors.
- Identifying Latent Constructs: To uncover the underlying structure or dimensions that are believed to cause the observed correlations among variables (e.g., 'intelligence' as a factor underlying various cognitive test scores).
Key Outputs (Typically from Statistical Software):
- Factor Loadings: These are correlations between the original variables and the extracted factors. A high loading (close to +1 or -1) indicates that the variable is strongly related to that factor. This tool focuses on interpreting these.
- Eigenvalues: Indicate the amount of variance in all original variables accounted for by each factor. Often used to decide how many factors to retain (e.g., Kaiser's criterion: keep factors with eigenvalues > 1).
- Communality (h²): The proportion of variance in an original variable that is explained by all the extracted factors combined.
- Variance Explained: The percentage of total variance in the original variables that is accounted for by each factor and by all factors together.
- Factor Rotation: Techniques like Varimax or Promax are often applied to the initial factor solution to make the factor structure simpler and more interpretable (e.g., by making variables load highly on only one factor).
Interpreting Factors: After extraction and rotation, you examine the pattern of high factor loadings to understand what common theme or construct each factor represents. Variables that load highly (e.g., > |0.4|) on a particular factor are considered to be indicators of that underlying factor. You then try to give a meaningful name to each factor based on the variables that define it.