Discriminant Function      

Function Plot Plot after VARIMAX

 

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 c² Probability
1 13.2635 34.5502 0.0000
2 0.9285 8.5375 0.2013
Likelihood test í 44.7936 Prob. 0.0 Trace BW (Inv) 14.1956
PMax / (1+PMax) 0.9299
Wilks Lambada 0.0364
F Test 10.3086 Prob. 0.0 (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