proc candisc data=sashelp.iris out=outcan distance anova;
class Species;
var SepalLength SepalWidth PetalLength PetalWidth;
run;The CANDISC Procedure
| Total Sample Size | 150 | DF Total | 149 |
|---|---|---|---|
| Variables | 4 | DF Within Classes | 147 |
| Classes | 3 | DF Between Classes | 2 |
| Number of Observations Read | 150 |
|---|---|
| Number of Observations Used | 150 |
| Class Level Information | ||||
|---|---|---|---|---|
| Species | Variable Name |
Frequency | Weight | Proportion |
| Setosa | Setosa | 50 | 50.0000 | 0.333333 |
| Versicolor | Versicolor | 50 | 50.0000 | 0.333333 |
| Virginica | Virginica | 50 | 50.0000 | 0.333333 |
The CANDISC Procedure
| Squared Distance to Species | |||
|---|---|---|---|
| From Species | Setosa | Versicolor | Virginica |
| Setosa | 0 | 89.86419 | 179.38471 |
| Versicolor | 89.86419 | 0 | 17.20107 |
| Virginica | 179.38471 | 17.20107 | 0 |
| F Statistics, NDF=4, DDF=144 for Squared Distance to Species | |||
|---|---|---|---|
| From Species | Setosa | Versicolor | Virginica |
| Setosa | 0 | 550.18889 | 1098 |
| Versicolor | 550.18889 | 0 | 105.31265 |
| Virginica | 1098 | 105.31265 | 0 |
| Prob > Mahalanobis Distance for Squared Distance to Species | |||
|---|---|---|---|
| From Species | Setosa | Versicolor | Virginica |
| Setosa | 1.0000 | <.0001 | <.0001 |
| Versicolor | <.0001 | 1.0000 | <.0001 |
| Virginica | <.0001 | <.0001 | 1.0000 |
The CANDISC Procedure
| Univariate Test Statistics | ||||||||
|---|---|---|---|---|---|---|---|---|
| F Statistics, Num DF=2, Den DF=147 | ||||||||
| Variable | Label | Total Standard Deviation |
Pooled Standard Deviation |
Between Standard Deviation |
R-Square | R-Square / (1-RSq) |
F Value | Pr > F |
| SepalLength | Sepal Length (mm) | 8.2807 | 5.1479 | 7.9506 | 0.6187 | 1.6226 | 119.26 | <.0001 |
| SepalWidth | Sepal Width (mm) | 4.3587 | 3.3969 | 3.3682 | 0.4008 | 0.6688 | 49.16 | <.0001 |
| PetalLength | Petal Length (mm) | 17.6530 | 4.3033 | 20.9070 | 0.9414 | 16.0566 | 1180.16 | <.0001 |
| PetalWidth | Petal Width (mm) | 7.6224 | 2.0465 | 8.9673 | 0.9289 | 13.0613 | 960.01 | <.0001 |
| Average R-Square | |
|---|---|
| Unweighted | 0.7224358 |
| Weighted by Variance | 0.8689444 |
| Multivariate Statistics and F Approximations | |||||
|---|---|---|---|---|---|
| S=2 M=0.5 N=71 | |||||
| Statistic | Value | F Value | Num DF | Den DF | Pr > F |
| NOTE: F Statistic for Roy's Greatest Root is an upper bound. | |||||
| NOTE: F Statistic for Wilks' Lambda is exact. | |||||
| Wilks' Lambda | 0.02343863 | 199.15 | 8 | 288 | <.0001 |
| Pillai's Trace | 1.19189883 | 53.47 | 8 | 290 | <.0001 |
| Hotelling-Lawley Trace | 32.47732024 | 582.20 | 8 | 203.4 | <.0001 |
| Roy's Greatest Root | 32.19192920 | 1166.96 | 4 | 145 | <.0001 |
The CANDISC Procedure
| Canonical Correlation |
Adjusted Canonical Correlation |
Approximate Standard Error |
Squared Canonical Correlation |
Eigenvalues of Inv(E)*H = CanRsq/(1-CanRsq) |
Test of H0: The canonical correlations in the current row and all that follow are zero | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Eigenvalue | Difference | Proportion | Cumulative | Likelihood Ratio |
Approximate F Value |
Num DF | Den DF | Pr > F | |||||
| 1 | 0.984821 | 0.984508 | 0.002468 | 0.969872 | 32.1919 | 31.9065 | 0.9912 | 0.9912 | 0.02343863 | 199.15 | 8 | 288 | <.0001 |
| 2 | 0.471197 | 0.461445 | 0.063734 | 0.222027 | 0.2854 | 0.0088 | 1.0000 | 0.77797337 | 13.79 | 3 | 145 | <.0001 | |
The CANDISC Procedure
| Total Canonical Structure | |||
|---|---|---|---|
| Variable | Label | Can1 | Can2 |
| SepalLength | Sepal Length (mm) | 0.791888 | 0.217593 |
| SepalWidth | Sepal Width (mm) | -0.530759 | 0.757989 |
| PetalLength | Petal Length (mm) | 0.984951 | 0.046037 |
| PetalWidth | Petal Width (mm) | 0.972812 | 0.222902 |
| Between Canonical Structure | |||
|---|---|---|---|
| Variable | Label | Can1 | Can2 |
| SepalLength | Sepal Length (mm) | 0.991468 | 0.130348 |
| SepalWidth | Sepal Width (mm) | -0.825658 | 0.564171 |
| PetalLength | Petal Length (mm) | 0.999750 | 0.022358 |
| PetalWidth | Petal Width (mm) | 0.994044 | 0.108977 |
| Pooled Within Canonical Structure | |||
|---|---|---|---|
| Variable | Label | Can1 | Can2 |
| SepalLength | Sepal Length (mm) | 0.222596 | 0.310812 |
| SepalWidth | Sepal Width (mm) | -0.119012 | 0.863681 |
| PetalLength | Petal Length (mm) | 0.706065 | 0.167701 |
| PetalWidth | Petal Width (mm) | 0.633178 | 0.737242 |
The CANDISC Procedure
| Total-Sample Standardized Canonical Coefficients | |||
|---|---|---|---|
| Variable | Label | Can1 | Can2 |
| SepalLength | Sepal Length (mm) | -0.686779533 | 0.019958173 |
| SepalWidth | Sepal Width (mm) | -0.668825075 | 0.943441829 |
| PetalLength | Petal Length (mm) | 3.885795047 | -1.645118866 |
| PetalWidth | Petal Width (mm) | 2.142238715 | 2.164135931 |
| Pooled Within-Class Standardized Canonical Coefficients | |||
|---|---|---|---|
| Variable | Label | Can1 | Can2 |
| SepalLength | Sepal Length (mm) | -.4269548486 | 0.0124075316 |
| SepalWidth | Sepal Width (mm) | -.5212416758 | 0.7352613085 |
| PetalLength | Petal Length (mm) | 0.9472572487 | -.4010378190 |
| PetalWidth | Petal Width (mm) | 0.5751607719 | 0.5810398645 |
| Raw Canonical Coefficients | |||
|---|---|---|---|
| Variable | Label | Can1 | Can2 |
| SepalLength | Sepal Length (mm) | -.0829377642 | 0.0024102149 |
| SepalWidth | Sepal Width (mm) | -.1534473068 | 0.2164521235 |
| PetalLength | Petal Length (mm) | 0.2201211656 | -.0931921210 |
| PetalWidth | Petal Width (mm) | 0.2810460309 | 0.2839187853 |
| Class Means on Canonical Variables | ||
|---|---|---|
| Species | Can1 | Can2 |
| Setosa | -7.607599927 | 0.215133017 |
| Versicolor | 1.825049490 | -0.727899622 |
| Virginica | 5.782550437 | 0.512766605 |