Example for Discriminant Analysis

A high school administrator wants to create a model to classify future students into one of three educational tracks. The administrator randomly selects 180 students and records an achievement test score, a motivation score, and the current track for each.

  1. Open the sample data set, EducationPlacement.MTW.
  2. Choose Stat > Multivariate > Discriminant Analysis.
  3. In Groups, enter Track.
  4. In Predictors, enter Test Score and Motivation.
  5. Under Discriminant Function, ensure that Linear is selected.
  6. Click OK.

Interpret the results

The Summary of Classification table shows the proportion of observations correctly placed into their true groups by the model. The school administrator uses the results to see how accurately the model classifies the students. Overall, 93.9% of students were placed into the correct educational track. Group 2 had the lowest proportion of correct placement, with only 53 of 60 students, or 88.3%, correctly placed into that educational track.

The Summary of Misclassified Observations table indicates into which group an observation should have been placed. The school administrator uses the results to see which individual students were misclassified. For example, student 4 should have been placed into group 2, but was incorrectly placed into group 1.

Discriminant Analysis: Track versus Test Score, Motivation

Linear Method for Response: Track

Predictors: Test Score, Motivation

Groups Group 1 2 3 Count 60 60 60
Summary of Classification True Group Put into Group 1 2 3 1 59 5 0 2 1 53 3 3 0 2 57 Total N 60 60 60 N correct 59 53 57 Proportion 0.983 0.883 0.950
Correct Classifications N Correct Proportion 180 169 0.939
Squared Distance Between Groups 1 2 3 1 0.0000 12.9853 48.0911 2 12.9853 0.0000 11.3197 3 48.0911 11.3197 0.0000
Linear Discriminant Function for Groups 1 2 3 Constant -9707.5 -9269.0 -8921.1 Test Score 17.4 17.0 16.7 Motivation -3.2 -3.7 -4.3
Summary of Misclassified Observations True Pred Squared Observation Group Group Group Distance Probability 4** 1 2 1 3.524 0.438 2 3.028 0.562 3 25.579 0.000 65** 2 1 1 2.764 0.677 2 4.244 0.323 3 29.419 0.000 71** 2 1 1 3.357 0.592 2 4.101 0.408 3 27.097 0.000 78** 2 1 1 2.327 0.775 2 4.801 0.225 3 29.695 0.000 79** 2 1 1 1.528 0.891 2 5.732 0.109 3 32.524 0.000 100** 2 1 1 5.016 0.878 2 8.962 0.122 3 38.213 0.000 107** 2 3 1 39.0226 0.000 2 7.3604 0.032 3 0.5249 0.968 116** 2 3 1 31.898 0.000 2 7.913 0.285 3 6.070 0.715 123** 3 2 1 30.164 0.000 2 5.662 0.823 3 8.738 0.177 124** 3 2 1 26.328 0.000 2 4.054 0.918 3 8.887 0.082 125** 3 2 1 28.542 0.000 2 3.059 0.521 3 3.230 0.479
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