Classify observations into predefined groups and identify which variables best separate the groups.
Linear Discriminant Analysis (LDA) is a supervised classification and dimensionality-reduction technique that finds linear combinations of variables that best separate two or more predefined groups. Unlike cluster analysis (which discovers groups), LDA requires that group membership be known in advance and uses that information to find the discriminant functions that maximally separate the groups. The technique has both descriptive value (which variables contribute most to group separation?) and predictive value (can we classify new cases into the correct group?).
LDA is used in psychology to differentiate diagnostic groups (e.g., clinical vs. non-clinical samples) based on psychological test scores; in medicine to classify patients into disease subtypes based on biomarkers; in marketing to identify which customer attributes best predict product category choice; and in educational research to separate high from low performers based on entrance test scores. LDA is closely related to MANOVA — in fact, a significant MANOVA is a prerequisite for meaningful LDA.
StatRyx computes the standardised discriminant coefficients (analogous to beta weights in regression), Wilks' Lambda for each discriminant function, the structure matrix (correlations between original variables and discriminant functions), group centroids (means on the discriminant function scores), a classification table with overall and per-group classification accuracy, and cross-validated (leave-one-out) accuracy estimates.
| Variable | Standardised Coeff. (Function 1) | Standardised Coeff. (Function 2) | Structure r (F1) |
|---|---|---|---|
| Verbal Reasoning | 0.74 | 0.21 | .81 |
| Numerical Ability | 0.58 | −0.43 | .67 |
| Spatial Reasoning | 0.31 | 0.69 | .44 |
| Working Memory | 0.49 | 0.17 | .58 |
A linear discriminant analysis was conducted to determine which combination of five cognitive test scores best distinguished students classified as gifted, average, or below-average. The first discriminant function was significant, Wilks' Λ = 0.43, χ²(10) = 87.6, p < .001, and accounted for 76% of the between-group variance. The overall classification accuracy was 81.3% (cross-validated: 78.9%).
Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.
No coding required. Describe your group variable and predictors in plain English and StatRyx handles eigendecomposition, assumption checks, classification, and all output tables.
A common guideline is at least 20 observations per group and at least 5 times as many observations as discriminating variables. Smaller samples produce unstable discriminant functions that may not replicate, and cross-validated accuracy is essential for evaluating real-world predictive performance.
The structure matrix shows the correlation between each original variable and each discriminant function. These correlations are called 'structure coefficients' or 'discriminant loadings.' They indicate which variables are most strongly associated with each discriminant dimension, analogous to factor loadings in EFA.
Both methods classify binary or multi-group outcomes, but LDA assumes multivariate normality and equal covariance matrices within groups. Logistic regression makes no distributional assumptions and is generally more robust when those assumptions are violated. With large samples and well-behaved data, both methods typically give similar classification accuracy.
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