Multiple Discriminant Analysis in Excel with UNISTAT
The UNISTAT statistics add-in extends Excel with Multiple Discriminant Analysis capabilities.
For further information visit UNISTAT User's Guide section 8.2.1. Multiple Discriminant Analysis.
Here we provide a sample output from the UNISTAT Excel statistics add-in for data analysis.
Multiple Discriminant Analysis: Stepwise Statistics
Summary Table
Tolerance: 0.001
F-to-Enter: 3.8416 (5.0%)
F-to-Remove: 2.7056 (10.0%)
| Variable | Entered at Step | F-to-Enter | Probability | Wilks’ Lambda |
|---|---|---|---|---|
| Var3 | 1 | 16.9426 | 0.0000 | 0.5649 |
| Var1 | 2 | 4.7660 | 0.0046 | 0.4631 |
| Var5 | 3 | 4.2502 | 0.0085 | 0.3861 |
Step 0
| Variable | Entered at Step | Tolerance | F-to-Enter/Remove | Wilks’ Lambda |
|---|---|---|---|---|
| Var1 | 1.0000 | 6.4644 | 0.7729 | |
| Var2 | 1.0000 | 1.1458 | 0.9505 | |
| Var3 | 1.0000 | 16.9426 | 0.5649 | |
| Var4 | 1.0000 | 0.1583 | 0.9929 | |
| Var5 | 1.0000 | 8.5882 | 0.7192 | |
| Var6 | 1.0000 | 0.3047 | 0.9863 | |
| Var7 | 1.0000 | 1.5744 | 0.9332 |
Step 1
| Variable | Entered at Step | Tolerance | F-to-Enter/Remove | Wilks’ Lambda |
|---|---|---|---|---|
| Var1 | 0.8445 | 4.7660 | 0.4631 | |
| Var2 | 0.8974 | 1.8542 | 0.5204 | |
| Var3 | 1 | -1.0000 | 16.9426 | 1.0000 |
| Var4 | 0.9654 | 0.4390 | 0.5537 | |
| Var5 | 0.9656 | 3.6752 | 0.4830 | |
| Var6 | 0.9947 | 0.2616 | 0.5582 | |
| Var7 | 0.9233 | 3.2327 | 0.4916 |
Step 2
| Variable | Entered at Step | Tolerance | F-to-Enter/Remove | Wilks’ Lambda |
|---|---|---|---|---|
| Var1 | 2 | -1.0000 | 4.7660 | 0.5649 |
| Var2 | 0.6657 | 2.6896 | 0.4112 | |
| Var3 | 1 | -1.0000 | 14.4963 | 0.7729 |
| Var4 | 0.8601 | 1.3557 | 0.4354 | |
| Var5 | 0.8532 | 4.2502 | 0.3861 | |
| Var6 | 0.8707 | 0.0898 | 0.4611 | |
| Var7 | 0.8817 | 2.4184 | 0.4159 |
Step 3
| Variable | Entered at Step | Tolerance | F-to-Enter/Remove | Wilks’ Lambda |
|---|---|---|---|---|
| Var1 | 2 | -1.0000 | 5.3514 | 0.4830 |
| Var2 | 0.9691 | 2.7738 | 0.3411 | |
| Var3 | 1 | -1.0000 | 11.5667 | 0.5955 |
| Var4 | 0.9379 | 1.6458 | 0.3581 | |
| Var5 | 3 | -1.0000 | 4.2502 | 0.4631 |
| Var6 | 0.9992 | 0.0983 | 0.3843 | |
| Var7 | 0.9988 | 1.9661 | 0.3531 |
Linear Discriminant Analysis
Group Means
| Var1 | Var2 | Var3 | Var4 | Var5 | Var6 | Var7 | |
|---|---|---|---|---|---|---|---|
| 1 | 92.8235 | 42.5294 | 34.7647 | 14.6471 | 25.0000 | 9.4118 | 9.4706 |
| 2 | 99.8889 | 43.2778 | 35.9444 | 14.3889 | 26.2222 | 9.7222 | 9.9444 |
| 3 | 98.8824 | 42.6471 | 40.1765 | 14.5294 | 29.4706 | 9.5882 | 9.2353 |
| 4 | 99.7778 | 44.7778 | 38.5000 | 14.7778 | 30.5000 | 9.7222 | 9.5000 |
Group Standard Deviations
| Var1 | Var2 | Var3 | Var4 | Var5 | Var6 | Var7 | |
|---|---|---|---|---|---|---|---|
| 1 | 4.7728 | 2.8748 | 2.4375 | 2.0292 | 2.1213 | 1.0641 | 1.0676 |
| 2 | 5.8600 | 2.6303 | 1.8302 | 1.6852 | 2.7344 | 0.7519 | 0.6391 |
| 3 | 6.7443 | 6.6327 | 2.8556 | 2.0346 | 4.4458 | 1.3720 | 1.0914 |
| 4 | 4.3999 | 2.7982 | 2.6402 | 1.2154 | 4.8416 | 1.1785 | 1.0981 |
Within-Groups Covariance Matrix
| Var1 | Var2 | Var3 | Var4 | Var5 | Var6 | Var7 | |
|---|---|---|---|---|---|---|---|
| Var1 | 30.3807 | 14.0841 | 5.3566 | 3.9983 | 8.5968 | 2.1931 | 2.2541 |
| Var2 | 14.0841 | 16.4673 | 3.2039 | 3.0382 | 5.8744 | 1.0167 | 0.8402 |
| Var3 | 5.3566 | 3.2039 | 6.0754 | 0.8089 | 1.7017 | 0.1986 | 0.6761 |
| Var4 | 3.9983 | 3.0382 | 0.8089 | 3.1137 | 2.4880 | 0.2880 | 0.2439 |
| Var5 | 8.5968 | 5.8744 | 1.7017 | 2.4880 | 13.8462 | 0.5137 | 0.5430 |
| Var6 | 2.1931 | 1.0167 | 0.1986 | 0.2880 | 0.5137 | 1.2342 | 0.9178 |
| Var7 | 2.2541 | 0.8402 | 0.6761 | 0.2439 | 0.5430 | 0.9178 | 0.9809 |
Within-Groups Correlation Matrix
| Var1 | Var2 | Var3 | Var4 | Var5 | Var6 | Var7 | |
|---|---|---|---|---|---|---|---|
| Var1 | 1.0000 | 0.6297 | 0.3943 | 0.4111 | 0.4192 | 0.3582 | 0.4129 |
| Var2 | 0.6297 | 1.0000 | 0.3203 | 0.4243 | 0.3890 | 0.2255 | 0.2091 |
| Var3 | 0.3943 | 0.3203 | 1.0000 | 0.1860 | 0.1855 | 0.0725 | 0.2769 |
| Var4 | 0.4111 | 0.4243 | 0.1860 | 1.0000 | 0.3789 | 0.1469 | 0.1395 |
| Var5 | 0.4192 | 0.3890 | 0.1855 | 0.3789 | 1.0000 | 0.1243 | 0.1473 |
| Var6 | 0.3582 | 0.2255 | 0.0725 | 0.1469 | 0.1243 | 1.0000 | 0.8342 |
| Var7 | 0.4129 | 0.2091 | 0.2769 | 0.1395 | 0.1473 | 0.8342 | 1.0000 |
Total Covariance Matrix
| Var1 | Var2 | Var3 | Var4 | Var5 | Var6 | Var7 | |
|---|---|---|---|---|---|---|---|
| Var1 | 37.5986 | 14.9899 | 8.8754 | 3.7261 | 12.6333 | 2.4536 | 2.3594 |
| Var2 | 14.9899 | 16.5716 | 3.5524 | 2.9787 | 6.9315 | 1.0561 | 0.8480 |
| Var3 | 8.8754 | 3.5524 | 10.2865 | 0.8253 | 5.9631 | 0.2936 | 0.3184 |
| Var4 | 3.7261 | 2.9787 | 0.8253 | 2.9998 | 2.5306 | 0.2727 | 0.2137 |
| Var5 | 12.6333 | 6.9315 | 5.9631 | 2.5306 | 18.4143 | 0.6520 | 0.2472 |
| Var6 | 2.4536 | 1.0561 | 0.2936 | 0.2727 | 0.6520 | 1.1969 | 0.8936 |
| Var7 | 2.3594 | 0.8480 | 0.3184 | 0.2137 | 0.2472 | 0.8936 | 1.0054 |
Univariate Statistics
| Lambda | F-Statistic | Probability | |
|---|---|---|---|
| Var1 | 0.7729 | 6.4644 | 0.0007 |
| Var2 | 0.9505 | 1.1458 | 0.3372 |
| Var3 | 0.5649 | 16.9426 | 0.0000 |
| Var4 | 0.9929 | 0.1583 | 0.9239 |
| Var5 | 0.7192 | 8.5882 | 0.0001 |
| Var6 | 0.9863 | 0.3047 | 0.8219 |
| Var7 | 0.9332 | 1.5744 | 0.2039 |
Linear Discriminant Functions
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| Var1 | 2.4700 | 2.7236 | 2.4571 | 2.5292 |
| Var3 | 3.5919 | 3.5815 | 4.4302 | 4.0700 |
| Var5 | -0.1694 | -0.2374 | 0.0584 | 0.1322 |
| Constant | -176.3697 | -198.6425 | -212.7547 | -207.9029 |
Canonical Discriminant Analysis
Eigenvalues
| Eigenvalue | Percent | Cumulative | Correlation | |
|---|---|---|---|---|
| 1 | 0.9930 | 77.6% | 77.6% | 0.7059 |
| 2 | 0.2269 | 17.7% | 95.4% | 0.4300 |
| 3 | 0.0591 | 4.6% | 100.0% | 0.2363 |
Canonical Statistics
| Wilks’ Lambda | Chi-Square | DoF | Probability | |
|---|---|---|---|---|
| 1 | 0.3861 | 62.3265 | 9 | 0.0000 |
| 2 | 0.7696 | 17.1552 | 4 | 0.0018 |
| 3 | 0.9442 | 3.7618 | 1 | 0.0524 |
Standardised Coefficients
| Function 1 | Function 2 | Function 3 | |
|---|---|---|---|
| Var1 | -0.2772 | 1.1368 | -0.1364 |
| Var3 | 0.8791 | -0.2564 | -0.5884 |
| Var5 | 0.5402 | -0.1929 | 0.9407 |
Structure Matrix
| Function 1 | Function 2 | Function 3 | |
|---|---|---|---|
| Var1 | 0.2959 | 0.9549 | 0.0259 |
| Var3 | 0.8700 | 0.1560 | -0.4676 |
| Var5 | 0.5871 | 0.2360 | 0.7743 |
Unstandardised Coefficients
| Function 1 | Function 2 | Function 3 | |
|---|---|---|---|
| Var1 | -0.0503 | 0.2063 | -0.0247 |
| Var3 | 0.3567 | -0.1040 | -0.2387 |
| Var5 | 0.1452 | -0.0518 | 0.2528 |
| Constant | -12.4335 | -14.8654 | 4.3051 |
Canonical Discriminant Functions
| Function 1 | Function 2 | Function 3 | |
|---|---|---|---|
| 1 | -1.0728 | -0.6329 | 0.0296 |
| 2 | -0.8299 | 0.6382 | -0.1178 |
| 3 | 1.2017 | -0.1780 | -0.2820 |
| 4 | 0.7082 | 0.1277 | 0.3562 |
Canonical Discriminant Scores
| Function 1 | Function 2 | Function 3 | |
|---|---|---|---|
| 1 | -2.0221 | -1.8549 | 1.1219 |
| 2 | -2.2015 | -1.3909 | 0.0753 |
| 3 | -0.4010 | -0.6225 | 0.2112 |
| 4 | -1.5819 | -0.6707 | 1.4683 |
| 5 | -1.0034 | -0.0541 | 0.1476 |
| 6 | -0.6857 | -1.0857 | -0.4730 |
| 7 | -0.3451 | -1.3956 | 0.0574 |
| 8 | -0.4456 | -0.9831 | 0.0079 |
| 9 | -0.8309 | -1.0339 | -0.7258 |
| 10 | -0.8412 | -1.8067 | -0.1353 |
| 11 | 0.5181 | -0.3158 | -0.5792 |
| 12 | -0.8755 | -1.3945 | -0.9291 |
| 13 | -0.1896 | -0.6747 | -0.2803 |
| 14 | -0.5805 | -0.1585 | -0.8354 |
| 15 | -2.1316 | 1.8551 | -1.3142 |
| 16 | -2.3295 | -0.0505 | 1.1520 |
| 17 | -2.2906 | 0.8771 | 1.5339 |
| 18 | -2.5535 | 0.0529 | -0.0979 |
| 19 | -0.1896 | -0.6747 | -0.2803 |
| 20 | 0.5077 | -1.0886 | 0.0113 |
| 21 | -0.0947 | -0.5202 | -0.0523 |
| 22 | 0.6187 | -0.7283 | -0.5297 |
| 23 | -0.2901 | -0.2622 | -0.3298 |
| 24 | -1.7121 | 1.4937 | 0.2132 |
| 25 | -1.0387 | 2.2647 | -0.8795 |
| 26 | -0.4363 | 1.6963 | -0.8159 |
| 27 | -1.0868 | 1.6470 | 1.4277 |
| 28 | -2.1476 | 1.6492 | -0.5452 |
| 29 | -1.4949 | 0.8746 | -0.4569 |
| 30 | -1.1553 | 2.4713 | -0.1599 |
| 31 | -0.4684 | 1.2845 | 0.7222 |
| 32 | -1.3887 | -0.1048 | -0.5860 |
| 33 | -1.3269 | 1.5444 | 0.9468 |
| 34 | -0.5691 | -1.2923 | -1.1925 |
| 35 | -0.1117 | 1.1805 | 0.4835 |
| 36 | 0.0676 | -2.2728 | -0.3352 |
| 37 | 0.8930 | -1.0379 | 0.7449 |
| 38 | 1.0874 | 0.6107 | 0.7892 |
| 39 | -0.4446 | -2.8898 | 0.2412 |
| 40 | 2.0122 | 0.3504 | -0.1798 |
| 41 | 0.3833 | 0.5089 | -1.4224 |
| 42 | 2.2900 | 0.2979 | -1.4156 |
| 43 | 1.3046 | -0.0084 | 0.1191 |
| 44 | 2.0682 | -0.4228 | -0.3336 |
| 45 | 2.8100 | -0.4761 | 0.1613 |
| 46 | 3.1440 | 1.6876 | 0.6369 |
| 47 | 0.4300 | 0.0455 | 1.1128 |
| 48 | 1.7618 | -0.5250 | -0.0702 |
| 49 | 0.9514 | 0.3527 | -2.1527 |
| 50 | -0.1506 | 0.2529 | 0.1016 |
| 51 | 0.9835 | 0.7645 | -3.6907 |
| 52 | 0.8370 | -0.2647 | 0.8988 |
| 53 | -0.6079 | 0.7694 | 0.2908 |
| 54 | 1.3994 | 0.1460 | 0.3471 |
| 55 | 1.3388 | -0.4206 | 0.9129 |
| 56 | 2.2133 | -0.4746 | -0.0808 |
| 57 | 2.4855 | 0.0398 | -1.1381 |
| 58 | 0.5306 | -0.3670 | 1.1622 |
| 59 | -0.0912 | -0.2632 | -2.5627 |
| 60 | -2.2358 | -0.9787 | -0.7185 |
| 61 | 0.9319 | -0.1103 | 1.1268 |
| 62 | 1.8842 | 1.6908 | 0.8969 |
| 63 | -0.4284 | 0.3054 | 1.3374 |
| 64 | 0.5856 | 0.7665 | 0.7751 |
| 65 | 0.1294 | -0.6236 | 1.1976 |
| 66 | 1.4120 | 0.0948 | 2.0885 |
| 67 | 1.2989 | 0.5585 | 0.2976 |
| 68 | -0.8765 | 0.5121 | -1.1624 |
| 69 | 1.3435 | 0.9191 | 0.5010 |
| 70 | 1.4337 | -0.2662 | 1.1409 |
Classification by Case
| Actual Group | Misclassified | Estimated Group | Probability | |
|---|---|---|---|---|
| 1 | 1 | 1 | 0.3096 | |
| 2 | 1 | 1 | 0.6040 | |
| 3 | 1 | 1 | 0.9223 | |
| 4 | 1 | 1 | 0.5067 | |
| 5 | 1 | 1 | 0.9496 | |
| 6 | 1 | 1 | 0.8947 | |
| 7 | 1 | 1 | 0.7742 | |
| 8 | 1 | 1 | 0.9153 | |
| 9 | 1 | 1 | 0.8519 | |
| 10 | 1 | 1 | 0.6919 | |
| 11 | 1 | * | 3 | 0.9022 |
| 12 | 1 | 1 | 0.6735 | |
| 13 | 1 | 1 | 0.8308 | |
| 14 | 1 | * | 2 | 0.7502 |
| 15 | 1 | * | 2 | 0.2030 |
| 16 | 1 | 1 | 0.3649 | |
| 17 | 1 | * | 2 | 0.1778 |
| 18 | 2 | * | 1 | 0.4438 |
| 19 | 2 | * | 1 | 0.8308 |
| 20 | 2 | * | 3 | 0.7063 |
| 21 | 2 | * | 1 | 0.8070 |
| 22 | 2 | * | 3 | 0.8722 |
| 23 | 2 | * | 1 | 0.8304 |
| 24 | 2 | 2 | 0.6549 | |
| 25 | 2 | 2 | 0.3520 | |
| 26 | 2 | 2 | 0.6233 | |
| 27 | 2 | 2 | 0.3244 | |
| 28 | 2 | 2 | 0.4008 | |
| 29 | 2 | 2 | 0.8934 | |
| 30 | 2 | 2 | 0.3250 | |
| 31 | 2 | 2 | 0.7401 | |
| 32 | 2 | * | 1 | 0.8596 |
| 33 | 2 | 2 | 0.5316 | |
| 34 | 2 | * | 1 | 0.5355 |
| 35 | 2 | 2 | 0.7599 | |
| 36 | 3 | * | 1 | 0.2485 |
| 37 | 3 | * | 4 | 0.6722 |
| 38 | 3 | * | 4 | 0.9045 |
| 39 | 3 | * | 1 | 0.1367 |
| 40 | 3 | 3 | 0.8142 | |
| 41 | 3 | 3 | 0.4858 | |
| 42 | 3 | 3 | 0.4409 | |
| 43 | 3 | 3 | 0.9776 | |
| 44 | 3 | 3 | 0.8463 | |
| 45 | 3 | 3 | 0.4117 | |
| 46 | 3 | 3 | 0.0440 | |
| 47 | 3 | * | 4 | 0.8834 |
| 48 | 3 | 3 | 0.9235 | |
| 49 | 3 | 3 | 0.2789 | |
| 50 | 3 | * | 2 | 0.8830 |
| 51 | 3 | 3 | 0.0057 | |
| 52 | 3 | * | 4 | 0.9265 |
| 53 | 4 | * | 2 | 0.9720 |
| 54 | 4 | 4 | 0.9236 | |
| 55 | 4 | 4 | 0.7993 | |
| 56 | 4 | * | 3 | 0.7646 |
| 57 | 4 | * | 3 | 0.4884 |
| 58 | 4 | 4 | 0.8192 | |
| 59 | 4 | * | 3 | 0.0758 |
| 60 | 4 | * | 1 | 0.5658 |
| 61 | 4 | 4 | 0.8731 | |
| 62 | 4 | 4 | 0.2489 | |
| 63 | 4 | 4 | 0.5152 | |
| 64 | 4 | 4 | 0.8968 | |
| 65 | 4 | 4 | 0.6577 | |
| 66 | 4 | 4 | 0.3211 | |
| 67 | 4 | 4 | 0.9105 | |
| 68 | 4 | * | 2 | 0.7749 |
| 69 | 4 | 4 | 0.7889 | |
| 70 | 4 | 4 | 0.7298 |
Classification by Group
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| 1 | 13 | 3 | 1 | 0 |
| 76.47% | 17.65% | 5.88% | 0.00% | |
| 2 | 6 | 10 | 2 | 0 |
| 33.33% | 55.56% | 11.11% | 0.00% | |
| 3 | 2 | 1 | 10 | 4 |
| 11.76% | 5.88% | 58.82% | 23.53% | |
| 4 | 1 | 2 | 3 | 12 |
| 5.56% | 11.11% | 16.67% | 66.67% |
Correctly Classified: 64.29%
Distance Between Centroids
| Clusters | Distance |
|---|---|
| 3 – 4 | 0.8628 |
| 1 – 2 | 1.3025 |
| 2 – 4 | 1.6885 |
| 1 – 4 | 1.9639 |
| 2 – 3 | 2.1956 |
| 1 – 3 | 2.3404 |
