• Variables
  
  • Dependent variable - nonmetric categorical (2 or more groups)
  • Independent variables - metric
    
    
• Objectives
  
  • Determine if statistically significant differences exist between the average score profiles of two or more a priori defined groups.
  • Determine that combination of independent variables which best discriminates among 2 or more apriori defined groups of the dependent variable
  • Determine which independent variables account most for the differences in average score profiles for each group.
    
    
• Statistical procedure - Maximize the between-group variance and minimize the within-group variance. When the variance between groups is large relative to the variance within-groups, then good discrimination has been achieved.
  
  
• Null hypothesis - The group means of two or more groups are statistically identical.

• The discriminant function
  
  Z = W1·X1 + W2·Z2 + ... + Wn·Zn
  
  • Z = discriminant scores
  • W = discriminant weights
  • X = independent variables
    
    
• Centroid - The mean of a statistically determined group of the dependent variable. It is the average discriminant score for a particular group.
  
• Cutting score - the criterion against which individual observations are classified according to their discriminant scores
  
• Group - those observations that fall into a specific category of the dependent variable
  
• Hit ratio - the percentage of statistical observations correctly classified by the discriminant function.
  
• Split sample approach
  
  
  • Analysis sample - the sample used for developing the discriminant function
    
  • Hold-out (or validation) sample - the sample used to validate the discriminant function

• Multivariate normality
• No prior probabilities with regard to group identity
• When the sample size is large violations of these assumptions is not adverse.

• Step 1 - Derivation of the discriminant function
  
  After the dependent variable is selected from among all variables, the sample data are split into analysis and hold-out samples, and the statistical procedure is run against only the data from the analysis sample.
  
  
• Step 2 - Validation
  
  Having estimated the determinant function in Step 1 the determinant function is examined for statistical significance. If statistical significance is found, the power of the function to classify correctly is tested using the observations remaining in the hold-out sample .
  
  
• Step 3 - Interpretation

Anderson, T. W. 1958. Introduction to multivariate statistical analysis. New York: John Wiley & Sons, Inc.

Crask, M. and W. Perreault. 1977. Validation of discriminant analysis in marketing research. Journal of Marketing Research, 14 (February).

Frank, R. E., W. F. Massey, and D. G. Morrison. 1965. Bias in mulitple discriminant analysis. Journal of Marketing Research 2, no. 3 (August) pp. 250-58.

Green, Paul E. and Donald S. Tull. 1975. Research for Marketing Decisions. Englewood Cliffs: Prentice-Hall, Inc.

Morrision, Donald G. 1969. On the interpretation of discriminant analysis. Journal of Marketing Research 6, no. 2 (May). pp. 156-63.

Overall, J. E. and J. Klett. 1972. Applied Multivariate Analysis. New York: McGraw-Hill, Inc.