Discriminant analysis is what you run when the groups already exist and you want to know how — and how well — your measurements separate them. Magic Stat runs canonical linear discriminant analysis and reports the functions, the loadings, the group means and the classification accuracy.
Linear discriminant analysis takes a set of numeric measurements and a categorical grouping, and finds the linear combinations of the measurements that separate the groups most strongly. The result is a small number of discriminant functions — at most one fewer than the number of groups — each a weighted mixture of your variables.
It answers three practical questions at once: do the groups separate at all, which variables drive the separation, and how well can an observation be assigned to its group. The output here covers all three — functions with their eigenvalues and a test of significance, standardised coefficients and structure loadings, group means, and a classification table with the overall accuracy.
The assumptions are real: multivariate normal measurements within each group, and equal covariance across groups (the pooled covariance). When groups clearly differ in spread or in shape, linear boundaries are the wrong model. This dialog fits linear discriminant analysis; for a quadratic boundary, use the qda function in R's MASS package.
One warning about the accuracy figure. The classification table here is built from the same data used to fit the model — resubstitution — which is optimistic. It describes how separable these groups are, not how a classifier would perform on new samples. For an honest generalisation estimate, use cross-validation, or the cross-validated accuracy that the PLS-DA dialog reports.
Grouping variable: a categorical column with two or more levels. Variables: two or more numeric columns used to discriminate those groups.
Conventions: proportional priors and pooled covariance, matching the classic reference implementation; eigenvalues are reported in the same convention as that implementation, and the structure loadings are invariant to the arbitrary sign of the functions.
They share the same mathematics but ask different questions. MANOVA tests whether group means differ on a set of variables; discriminant analysis describes how they differ and classifies observations. If you want the test, run MANOVA; if you want the functions and the classification, run discriminant analysis.
Discriminant analysis assumes normal predictors within groups and equal covariance; logistic regression assumes neither and gives you odds ratios. For two groups with non-normal predictors, logistic regression is often the better fit. Use discriminant analysis when its assumptions hold or when you specifically want the canonical functions.
The classification table is resubstitution — fitted and evaluated on the same data — so it is optimistic. Treat it as a measure of separation, not of future performance, and prefer a cross-validated estimate when you need to claim predictive accuracy.
This dialog fits pooled covariance; if the groups differ in spread, that assumption is violated and a quadratic model (MASS::qda in R) is more appropriate. The app also offers PLS-DA, which makes no distributional assumption about the predictors.
No. The analysis runs on your computer. The only automatic signal is an anonymous installation counter, with no data in it.