| GROUP 1 Var. Covar. Matrix | ||||||
| HCO3 | SO4 | CL | CA | MG | NA | |
| HCO3 | 65.3 | 121.5 | -8072.2 | -1692.4 | -345.0 | -5829.1 |
| SO4 | 121.5 | 382.4 | -20141.1 | -4250.3 | -955.9 | -14399.9 |
| CL | -8072.2 | -20141.1 | 2022586.0 | 423189.0 | 70236.3 | 1498598.0 |
| CA | -1692.4 | -4250.3 | 423189.0 | 91478.9 | 14168.3 | 310958.5 |
| MG | -345.0 | -955.9 | 70236.3 | 14168.3 | 3943.4 | 50721.4 |
| NA | -5829.1 | -14399.9 | 1498598.0 | 310958.5 | 50721.4 | 1115148.0 |
| GROUP 2 Var. Covar. Matrix | ||||||
| HCO3 | SO4 | CL | CA | MG | NA | |
| HCO3 | 162.3 | -1077.2 | -19342.9 | -955.4 | -1295.3 | -17999.2 |
| SO4 | -1077.2 | 8272.3 | 154682.0 | 6957.4 | 7440.8 | 146931.8 |
| CL | -19342.9 | 154682.0 | 6235841.0 | 86280.9 | 126328.9 | 6124021.0 |
| CA | -955.4 | 6957.4 | 86280.9 | 7188.1 | 6061.1 | 78926.6 |
| MG | -1295.3 | 7440.8 | 126328.9 | 6061.1 | 12849.8 | 113941.8 |
| NA | -17999.2 | 146931.8 | 6124021.0 | 78926.6 | 113941.8 | 6026071.0 |
| GROUP 3 Var. Covar. Matrix | ||||||
| HCO3 | SO4 | CL | CA | MG | NA | |
| HCO3 | 50.5 | -46.5 | -10777.6 | -2013.2 | -796.9 | -8071.5 |
| SO4 | -46.5 | 334.5 | -12521.9 | -1946.1 | -930.4 | -9184.6 |
| CL | -10777.6 | -12521.9 | 7455291.5 | 1206246.9 | 520862.4 | 5720832.5 |
| CA | -2013.2 | -1946.1 | 1206246.9 | 200201.5 | 85443.8 | 919593.3 |
| MG | -796.9 | -930.4 | 520862.4 | 85443.8 | 36681.5 | 398154.0 |
| NA | -8071.5 | -9184.6 | 5720832.5 | 919593.3 | 398154.0 | 4398151.0 |
| Correlation Matrix | ||||||
| HCO3 | SO4 | CL | CA | MG | NA | |
| HCO3 | 1.0000 | 0.4036 | -0.3513 | -0.5900 | -0.4216 | -0.2546 |
| SO4 | 0.4036 | 1.0000 | 0.1635 | -0.3218 | 0.1159 | 0.2838 |
| CL | -0.3513 | 0.1635 | 1.0000 | 0.7549 | 0.7221 | 0.9860 |
| CA | -0.5900 | -0.3218 | 0.7549 | 1.0000 | 0.7136 | 0.6385 |
| MG | -0.4216 | 0.1159 | 0.7221 | 0.7136 | 1.0000 | 0.6525 |
| NA | -0.2546 | 0.2838 | 0.9860 | 0.6385 | 0.6525 | 1.0000 |
| (W) Within Sample Matrix | ||||||
| HCO3 | SO4 | CL | CA | MG | NA | |
| HCO3 | 278.1 | -1002.2 | -38192.7 | -4661.0 | -2437.2 | -31899.8 |
| SO4 | -1002.2 | 8989.2 | 122019.0 | 761.0 | 5554.5 | 123347.3 |
| CL | -38192.7 | 122019.0 | 15713718.5 | 1715716.8 | 717427.7 | 13343451.5 |
| CA | -4661.0 | 761.0 | 1715716.8 | 298868.5 | 105673.2 | 1309478.4 |
| MG | -2437.2 | 5554.5 | 717427.7 | 105673.2 | 53474.8 | 562817.2 |
| NA | -31899.8 | 123347.3 | 13343451.5 | 1309478.4 | 562817.2 | 11539370.0 |
| (B) Between Sample Matrix | ||||||
| HCO3 | SO4 | CL | CA | MG | NA | |
| HCO3 | 456.0 | 2751.6 | -2000.3 | -5632.7 | -208.1 | 6828.2 |
| SO4 | 2751.6 | 16604.0 | -11577.1 | -33916.7 | -1258.7 | 41629.4 |
| CL | -2000.3 | -11577.1 | 2115755.9 | 336875.9 | -11281.6 | 1786324.9 |
| CA | -5632.7 | -33916.7 | 336875.9 | 115830.4 | 764.2 | 184748.2 |
| MG | -208.1 | -1258.7 | -11281.6 | 764.2 | 165.6 | -13628.7 |
| NA | 6828.2 | 41629.4 | 1786324.9 | 184748.2 | -13628.7 | 1667942.4 |
| UNIVARIATE F TEST | ||||
| Variables | Error MS | Tretment MS | F Ratio | Probability |
| HCO3 | 8.44 | 139.05 | 16.47 | 0.000 |
| SO4 | 307.48 | 4494.59 | 14.62 | 0.000 |
| CL | 39180.66 | 7856859.25 | 200.53 | 0.000 |
| CA | 2145.01 | 149434.23 | 69.67 | 0.000 |
| MG | 3.07 | 26737.40 | 8720.26 | 0.000 |
| NA | 30887.82 | 5769685.00 | 186.79 | 0.000 |
| Variable Means | ||||
| Variables | 1 GROUP | 2 GROUP | 3 GROUP | G. Mean |
| HCO3 | 5.60 | 15.17 | 3.77 | 8.04 |
| SO4 | 23.10 | 80.72 | 11.85 | 37.74 |
| CL | 1896.21 | 1375.43 | 1106.37 | 1482.33 |
| CA | 276.50 | 87.38 | 180.93 | 186.60 |
| MG | 75.03 | 73.43 | 80.48 | 76.25 |
| NA | 1572.34 | 1302.85 | 857.08 | 1261.37 |
| Variables Std. Dev. | ||||
| Variables | 1 GROUP | 2 GROUP | 3 GROUP | |
| HCO3 | 3.299 | 5.697 | 3.179 | |
| SO4 | 7.983 | 40.675 | 8.179 | |
| CL | 580.602 | 1116.767 | 1221.089 | |
| CA | 123.477 | 37.916 | 200.101 | |
| MG | 25.637 | 50.695 | 85.652 | |
| NA | 431.113 | 1097.823 | 937.886 | |
| (B/W) Matrix | ||||||
| HCO3 | SO4 | CL | CA | MG | NA | |
| HCO3 | 7.31 | 44.12 | -10.71 | -87.14 | -3.46 | 127.89 |
| SO4 | 0.92 | 5.54 | -11.83 | -12.51 | -0.37 | 7.04 |
| CL | -0.20 | -1.22 | -14.02 | 0.29 | 0.18 | -15.89 |
| CA | 0.27 | 1.63 | 17.73 | -0.52 | -0.23 | 20.33 |
| MG | 0.33 | 1.99 | 3.06 | -3.40 | -0.18 | 8.83 |
| NA | 0.20 | 1.20 | 14.31 | -0.20 | -0.18 | 16.06 |
Significance Test for Discriminant Functions
| S No. | Latent Root | ~2c~² | Probability |
| 1 | 13.2635 | 34.5502 | 0.0000 |
| 2 | 0.9285 | 8.5375 | 0.2013 |
| Likelihood test í | 44.7936 | 0 | Prob.Trace BW (Inv) | 14.1956 |
| PMax / (1+PMax) | 0.9299 | |||
| Wilks Lambada | 0.0364 | |||
| F Test | 10.3086 | 0 | Prob. | (Exact) |
Misclassification Probabilities
| 1 Group | 2 Group | 3 Group | Total | |
| 1 Group | 5 | 2 | 7 | |
| 71.40% | 0.00% | 28.60% | ||
| 2 Group | 5 | 1 | 6 | |
| 0.00% | 83.30% | 16.70% | ||
| 3 Group | 6 | 6 | ||
| 0.00% | 0.00% | 100.00% | ||
| TOTAL Misclassification 3 OUT OF 19 Misclassification % 15.8 | ||||
