Latent factors estimated from a set of items. How to read a rotated loadings table, what communalities tell you, why the sign of a factor means nothing and the sign of an item means everything, and how to report it in APA 7.
Exploratory factor analysis estimates latent variables that could account for the correlations among your items. The model runs in one direction: the factor is assumed to cause the responses, and each item's variance is split into what the common factors explain and what is unique to that item.
That split is the difference from principal components. PCA is a mathematical repackaging of total observed variance, with components built out of the items. EFA models shared variance only and treats the rest as item-specific error.
If your question is what underlying construct produces these answers, EFA is the correct tool. If it is whether these columns can be compressed, PCA is. The two frequently give similar-looking output and answer different questions.
Quanta rotates the solution using varimax, which rotates the factor axes to make each item load strongly on one factor and weakly on the others. Rotation does not change how much variance the solution explains; it changes how interpretable the arrangement is.
The run opens with four figures: factors extracted, items in analysis, cases with listwise deletion named, and the variance carried by the first factor.
The Varimax-rotated loadings card is badged either Converged or Max iterations. Read that badge before anything else. A solution that hit the iteration ceiling has not settled and should not be interpreted.
Each item gets a loading on every factor plus a communality. Loadings are correlations between item and factor: above about |.40| is usually treated as meaningful, though the threshold is a convention rather than a rule. Quanta highlights each item's highest-loading factor so the structure is visible without scanning.
Communality is the share of that item's variance the factors account for. A communality of .65 means the factor solution explains 65% of that item's variance and 35% is unique to the item. Low communalities, below roughly .30, flag items the solution is not capturing: they are candidates for removal, or a sign that a factor is missing.
This trips up almost everyone reading their first loadings table. A factor's direction is not determined by the data. Multiply every loading on a factor by −1 and you have an equally valid solution describing the same structure. So a column of loadings that is uniformly negative is not a problem and means nothing on its own.
What is meaningful is an item whose sign runs opposite to the rest of its group.
A real example. In an 18-item run, the Self-Management items load on the second factor at −.694, −.701, −.744 and −.712, while two items in the same block load at +.686 and +.744. Both carry an _R suffix. In the first factor's block, five items sit between −.547 and −.603 and one reverse-worded item sits at +.556.
Those items are not measuring something different. They are reverse-worded items that were never rescored, and the factor analysis is reporting exactly that. Notice the magnitudes are comparable to their neighbours: these are good items pointing backwards.
Fix the scoring and rerun before interpreting structure. Left uncorrected, the consequences vary with how many factors you extract. Here, with two factors, the mis-scored items stayed in their proper groups and merely flipped sign. With more factors extracted they can separate out and form what looks like a genuine additional dimension, which is the version that reaches publication. See reverse-coded items.
Quanta asks you for a factor count. That number is a decision, not an output, and it changes the solution more than any other choice you make.
Theory first. If your instrument was built to measure four domains, four is the hypothesis worth testing. Extracting two and finding that the four collapse is itself a finding about the instrument.
Eigenvalues and the scree. Run a principal components analysis first and read the eigenvalue sequence. The point where it levels off is the usual guide, and it is more informative than the eigenvalue-greater-than-one rule, which over-extracts.
Interpretability. A factor you cannot name is not a factor you should keep. Extracting more will always explain more variance, in the same way that adding predictors always raises R squared.
Check what you got against what you expected. If a four-domain instrument returns two factors whose members cut across the intended domains, the instrument is not behaving as designed in this sample. That belongs in the paper.
Lay the data out with one row per respondent and one column per item.
Rescore reverse-worded items first. This is the single most consequential preparation step for factor analysis.
Open Data Reduction and choose Factor Analysis (EFA), then set your items and the number of factors in the Setup panel on the right.
Watch the case count. Listwise deletion drops any respondent missing a single item, so a long instrument can lose a meaningful share of the sample.
Check the convergence badge, then the communalities, then the loadings. That order catches the problems that make the loadings meaningless before you start interpreting them.
Use the action bar to add the result to a report, copy the table, or copy the APA text. Every result carries the ReliCheck Intelligence card for a plain-language explanation computed on your Mac.
Report the number of items and cases, the extraction and rotation methods, how you chose the number of factors, the variance explained, and the loadings table.
An exploratory factor analysis with varimax rotation was conducted on 18 items (N = 250). A two-factor solution was extracted, with the first factor accounting for 50.3% of the variance. Communalities ranged from .40 to .65, and all items loaded above |.40| on at least one factor.
State the rotation method. Varimax is orthogonal, which assumes the factors are uncorrelated; that assumption is often wrong for psychological constructs and a reader needs to know you made it.
Give the full loadings table with communalities, and state your loading threshold. Reporting only loadings above a cutoff, without saying what the cutoff was, hides cross-loading items.
Say how the number of factors was decided. "Two factors were extracted" without a reason is the most common omission in this analysis.
Report reverse scoring explicitly. A loadings table where some items run opposite to their group is either a scoring error or a substantive finding, and only you can tell a reader which.
Every result carries a ReliCheck Intelligence card with one action: explain this result in plain language. It runs entirely on your Mac with Apple Intelligence. No upload, no API key, nothing to configure. The model only explains the result Quanta has already computed and validated. It never computes a statistic, and it never applies a decision on your behalf.
From the action bar you can add the result to a report, copy the table, or copy the APA text. Exported reports carry the APA table, its note, and a caution specific to that analysis beneath it.
Quanta's factor analysis and PCA are validated against an independent Python implementation and against closed-form values, recovering known simple structure. The engine is pure Swift with no R or Python at runtime. Full record on the validation page.
Data Reduction is part of every Quanta subscription, $9.99 a month or $79.99 a year after the 30-day trial. One price for everyone. See pricing.
The analysis, the report builder, and the on-device explanations all work with the network off. Your dataset is never uploaded.
Principal components compression rather than latent structure · McDonald's omega reliability from a single-factor model · Reverse-coded items what an opposite-signed loading means · the complete list on the analyses page.