Three-Group Discriminant
Function Analysis
The Research
• Mus reared by Mus, Peromyscus, or
Rattus
• Tested in an apparatus where they had
access to four scented tunnels
– Clean pine shavings
– Mus scented shavings
– Peromyscus scented shavings
– Rattus scented shavings
The Variables
• Predicted: Species of the foster mother
Mus, Peromyscus, or Rattus
• Predictors: Number of visits to the four
differently scented tunnels.
Mus musculus
Peromyscus maniculatus
Rattus norvegicus
ANOVAs
Tests of Equality of Group Means
Wilks'
Lambda
F
df1
df2
Sig.
v_clean
.784
4.542
2
33
.018
v_mus
.868
2.515
2
33
.096
v_pero
.861
2.658
2
33
.085
v_rat
.418 22.981
2
33
.000
Box’s M
Test Results
Box's M
F
Approx.
df1
df2
Sig.
17.268
.709
20
3909.028
.821
Eigenvalues
Eigenvalues
Function Eigenvalue % of Variance Cumulative % Canonical
Correlation
1
1.641a
93.6
93.6
.788
2
.111a
6.4
100.0
.316
Tests of DFs
Wilks' Lambda
Test of
Function(s)
Wilks‘
Lambda
Chisquare
df
Sig.
1 through 2
.341
33.916
8
.000
2
.900
3.324
3
.344
Standardized Weights
Standardized Canonical Discriminant
Function Coefficients
Function
v_clean
v_mus
v_pero
v_rat
1
-.205
.081
-.420
1.285
2
-1.559
.121
1.243
.222
Loadings
Structure Matrix
Function
1
2
v_rat
.921
.048
v_mus
.301
-.179
v_clean
.396
-.402
v_pero
.303
.309
Interpretation of DFs
• Scoring high on DF1 = many visits, more
to the rat-scented tunnel than the others
– Ratto-mania
• Scoring high on DF2 = more visits to the
Peromyscus tunnel than to the clean
tunnel
– Pero-curious
Group Means on DFs
Functions at Group Centroids
nurs
Function
1
2
Mus
-.539
.429
Pero
-1.158
-.336
Rat
1.697
-.093
69.4% Overall Success Rate
Classification Resultsa
nurs
Mus
Count Pero
%
Total
12
4
8
0
12
2
0
10
12
Mus
58.3
25.0
16.7
100.0
Pero
33.3
66.7
.0
100.0
Rat
16.7
.0
83.3
100.0
Rat
Original
Predicted Group
Membership
Mus
Pero
Rat
7
3
2
ANOVA with LSD
• AKA, “Fisher’s Procedure”
• Done on each of the original continuous
variables
• and each of the discriminant functions
Gender Differences in Sex
Roles
Another Example
Predicing Gender from Measures
of Masculinity and of Femininity
Wilks' Lambda
Test of
Function(s)
Wilks‘
Lambda
Chi-square
df
Sig.
1 through 2
.737
1248.547
4
.000
2
.990
41.444
1
.000
Notice that the second discriminant
function is significant too.
Structure Matrix
Function
1
2
Femininity
.858*
.513
Masculinity
-.581
.814*
High scores on DF2 = high in both
Femininity and Masculinity
Functions at Group Centroids
gender
Function
1
2
Male
-.729
-.018
Female
.499
-.036
Other
.176
.355
DF1 separates all three groups.
DF2 separates the Other Group from the
male and female groups.
REGWQ on DF 1
Subset for alpha =
0.05
Gender
1
N
Male
Ryan-Einot-GabrielWelsch Range
Other
Female
Sig.
2
3
1586 -.7294695
304
.1757751
2212
.4988711
1.000
1.000
1.000
Each gender significantly different from each other gender.
REGWQ on DF2
Gender
Subset for alpha =
N
0.05
1
2
Female
2212 -.0359468
Ryan-Einot-Gabriel-
Male
1586 -.0178940
Welsch Range
Other
Sig.
304
.3549156
.611
“Other” Gender significantly different from other two
genders.
1.000
Classification
• 57.4% correct with equal priors
• 69.7% with proportional priors