Which statement distinguishes a discriminant function variate from a discriminant score as described?

Which statement distinguishes a discriminant function variate from a discriminant score as described?

• A. The discriminant function variate is a score for an individual case on a discriminant function, obtained by applying the variate equation to that case's scores.
• B. The discriminant function variate is a dummy variable used to recode categories.
• C. The discriminant score is the eigenvalue of the discriminant function.
• D. The discriminant score is the mean difference between groups on the original variables.

Answer: (A)

In discriminant analysis, you build a discriminant function as a linear combination of the predictor variables, and then apply that function to each case to get a single numeric value for that case. That per-case value is the discriminant score, the amount by which the case is scored on the function. The statement that the discriminant function variate is a score for an individual case on a discriminant function, obtained by applying the variate equation to that case's scores, captures exactly this idea: the variate is the computed score for that specific case derived from the discriminant equation. The other statements describe different concepts. A dummy variable used to recode categories is not about the discriminant function’s per-case score. An eigenvalue pertains to the strength of separation in some discriminant analyses but is not a score for an individual case. A mean difference between groups on the original variables speaks to differences in the observed measurements, not to the score produced by the discriminant function.

In discriminant analysis, you build a discriminant function as a linear combination of the predictor variables, and then apply that function to each case to get a single numeric value for that case. That per-case value is the discriminant score, the amount by which the case is scored on the function. The statement that the discriminant function variate is a score for an individual case on a discriminant function, obtained by applying the variate equation to that case's scores, captures exactly this idea: the variate is the computed score for that specific case derived from the discriminant equation.

The other statements describe different concepts. A dummy variable used to recode categories is not about the discriminant function’s per-case score. An eigenvalue pertains to the strength of separation in some discriminant analyses but is not a score for an individual case. A mean difference between groups on the original variables speaks to differences in the observed measurements, not to the score produced by the discriminant function.