！Discriminant Function Analysis with Three or More Groups
With more than two groups one can obtain more than one discriminant function. The first DF is that which maximally separates the groups (produces the largest ratio of among-groups to within groups SS on the resulting D scores). The second DF, orthogonal
to the first, maximally separates the groups on variance not yet explained by the first DF.
One can find a total of K-1 (number of groups minus 1) or p (number of predictor variables)
orthogonal discriminant functions, whichever is smaller.
We shall use the data from Experiment 1 of my dissertation to illustrate a discriminant function analysis with three groups. The analysis I reported when I published this research was a doubly multivariate repeated measures ANOVA (see Wuensch, K. L., Fostering house mice onto rats and deer mice: Effects on response to species odors. Animal Learning and Behavior, 1992, 20, 253-258). Wild-strain house mice were, at birth, cross-fostered onto house-mouse (Mus), deer mouse (Peromyscus) or rat (Rattus) nursing
mothers. Ten days after weaning, each subject was tested in an apparatus that allowed it to enter tunnels scented with clean pine shavings or with shavings bearing the scent of Mus,
Peromyscus, or Rattus. One of the variables measured was the number of visits to each tunnel during a twenty minute test. Also measured were how long each subject spent in each of the four tunnels and the latency to first visit of each tunnel. We shall use the visits data for our discriminant function analysis.
The data are in the SPSS data file, TUNNEL4b.sav. Download it from my SPSS-
Data page. The variables in this data file are:
， NURS (nursing group, 1 for Mus reared, 2 for Peromyscus reared, and 3 for Rattus
， V1, V2, V3, and V4 (labeled Clean-V, Mus-V, Pero-V, and Rat-V, these are the raw
data for number of visits to the clean, Mus-scented, Peromyscus-scented, and
， V_Clean, V_Mus, V_Pero, and V_Rat (the visits data after a square root
transformation to reduce positive skewness and stabilize the variances)
， T1, T2, T3, and T4 (time in seconds spent in each tunnel)
， T_Clean, T_Mus, T_Pero, and T_Rat (the time data after a square root
transformation to reduce positive skewness)
， L1, L2, L3, and L4 (the latency data in seconds) and
， L_Clean, L_Mus, L_Pero, and L_Rat (the latency data after a log transformation to
reduce positive skewness).
For this lesson we shall use only the NURS variable and the visits variables.
Obtaining Means and Standard Deviations for the Untransformed Data
Open the TUNNEL4b.sav file in SPSS. Click Analyze, Compare Means, Means.
！ Copyright 2008 Karl L. Wuensch - All rights reserved.
Scoot V1, V2, V3, and V4 into the Dependent List and Nurs into the Independent List. Click OK
The output produced here is a table of means and standard deviations for untransformed number of visits to each tunnel for each nursing group. Look at the means for the Mus group and the Peromyscus group. These two groups were very similar to one
another. Both visited the tunnels with moderate frequency, except for the rat-scented tunnel, which they avoided. Now look at the means for the Rattus-reared group. These
animals appear to have been much more active, visiting the tunnels more frequently than did animals in the other groups, and they did not avoid the rat-scented tunnel.
Look at the standard deviations for V4. There is troublesome heterogeneity of variance here.
Conducting the Discriminant Function Analysis
Now let us do the discriminant function analysis on the transformed data. Click Analyze, Classify, Discriminant. Put V_Clean, V_Mus, V_Pero, and V_Rat into the Independents box. Put Nurs into the Grouping Variable box.