Discriminant Analysis

Discriminant Analysis classifies subjects into known groups based on multiple measurements and identifies which variables best discriminate between groups.

Step 1 — Provide your data

  • One categorical grouping variable (known group membership)
  • Two or more predictor variables (numeric)

Supports Excel Import, Sample Data Generator, and Manual Entry.

Step 2 — Results

Overall significance:

  • Wilks' Lambda with chi-square, df, p-value

Discriminant functions:

  • Eigenvalues and canonical correlations
  • Standardised coefficients per predictor
  • Structure matrix (predictor-function correlations)
  • Group centroids

Classification:

  • Confusion matrix
  • Overall and per-group accuracy
  • Prior probabilities

A UniversalChatBot is available for discussion.

Statistical methods used

Discriminant functions — from generalised eigenvalue problem: W^-1 * B * v = lambda * v

Number of functions = min(g-1, p).

Canonical correlations: sqrt(lambda / (1 + lambda))

Wilks' Lambda: det(W) / det(W + B)

Chi-square: -((N-1) - (p+g)/2) * ln(Lambda) with df = p*(g-1).

Classification — Linear discriminant function with pooled covariance and sample-based priors.

Accuracy — apparent (resubstitution) rate; may be optimistically biased.

H0: all group mean vectors equal. H1: at least one differs. alpha = 0.05.