Turn messy variables into meaningful factors for insight. Choose extraction, rotations, and readable diagnostics here. Download tables, share visuals, and improve your decisions fast.
Factor analysis starts with variables that share meaningful covariance carefully. If you paste raw scores, the tool standardizes columns and builds a correlation matrix, so units do not dominate results. Missing values are not allowed, and each row must have the same number of columns. If you paste a correlation matrix, ensure it is symmetric with ones on the diagonal. Use at least 3 rows for raw data, and provide sample size when using a matrix.
KMO summarizes how much variance is common rather than unique. Values around 0.60 suggest acceptable adequacy, while 0.80 or higher indicates strong shared structure. Bartlett’s test evaluates whether the correlation matrix differs from an identity matrix. A small p-value supports extraction, but it depends on sample size and should complement substantive judgment. Watch for near-singular matrices, which can inflate partial correlations.
Eigenvalues quantify variance captured by each component. The Kaiser rule keeps components with eigenvalues greater than 1, which is fast and transparent. Also inspect cumulative variance; many applied studies aim for roughly 60% or more, depending on domain complexity. Manual factor counts are useful when theory suggests a fixed dimensional model. If eigenvalues drop sharply after the first components, fewer factors may be defensible.
Loadings act like correlations between variables and factors. Larger absolute loadings, such as 0.50 to 0.70, indicate variables that define a factor clearly. Communality is the sum of squared loadings for a variable and shows explained variance; low communalities can flag weak indicators. Uniqueness reports the remaining variance not captured by extracted factors. Use the cutoff control to spot cross-loadings that complicate naming.
Rotation does not change overall explained variance; it redistributes it across factors to simplify interpretation. Varimax, an orthogonal option, keeps factors uncorrelated and often produces sharper “high-or-low” patterns. After rotation, label factors using the strongest loading variables, document decisions, and validate with new data or confirmatory modeling when possible. When factors remain hard to interpret, revisit variable selection and measurement quality.
Use more observations than variables, and preferably several times more. For quick screening, n should exceed p, but larger samples improve KMO, stabilize loadings, and reduce chance patterns, especially when communalities are modest.
Yes. Paste a square matrix and include variable labels if available. Enter sample size to enable Bartlett’s test. Ensure symmetry and ones on the diagonal, otherwise results may be misleading.
A negative loading means the variable moves opposite the factor direction. Magnitude matters more than sign for structure. You can flip a factor’s sign without changing fit, so interpret using the full loading pattern.
Common cutoffs are 0.30 for exploratory work, 0.40 for clearer structure, and 0.50 when you need strong indicators. If many cross-loadings remain above the cutoff, reconsider variables or factor count.
Rotation redistributes variance across extracted factors but does not change the total variance explained by the retained factors. It is mainly used to produce a simpler, more interpretable loading pattern.
Bartlett’s test requires a sample size. When you paste a correlation matrix, the tool cannot infer n, so you must enter it. For raw data, n is derived from the number of rows.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.