We will discuss the problem a discriminating between 3 or more populations. We will use the following data from the Carnegie Mellon Statistics Library, originally from Lubischew, A.A. (1962) On the use of discriminant functions in taxonomy. Biometrics 18: 455-477. The measurements are the width and angle of the aedeagus of each beetle. The data are on three species of the flea beetle Chaetocnema: concinna (Con), heikertingeri (Hei), and heptapotamica (Hep).
Width Angle Species 150 15 Con 147 13 Con 144 14 Con 144 16 Con 153 13 Con 140 15 Con 151 14 Con 143 14 Con 144 14 Con 142 15 Con 141 13 Con 150 15 Con 148 13 Con 154 15 Con 147 14 Con 137 14 Con 134 15 Con 157 14 Con 149 13 Con 147 13 Con 148 14 Con 120 14 Hei 123 16 Hei 130 14 Hei 131 16 Hei 116 16 Hei 122 15 Hei 127 15 Hei 132 16 Hei 125 14 Hei 119 13 Hei 122 13 Hei 120 15 Hei 119 14 Hei 123 15 Hei 125 15 Hei 125 14 Hei 129 14 Hei 130 13 Hei 129 13 Hei 122 12 Hei 129 15 Hei 124 15 Hei 120 13 Hei 119 16 Hei 119 14 Hei 133 13 Hei 121 15 Hei 128 14 Hei 129 14 Hei 124 13 Hei 129 14 Hei 145 8 Hep 140 11 Hep 140 11 Hep 131 10 Hep 139 11 Hep 139 10 Hep 136 12 Hep 129 11 Hep 140 10 Hep 137 9 Hep 141 11 Hep 138 9 Hep 143 9 Hep 142 11 Hep 144 10 Hep 138 10 Hep 140 10 Hep 130 9 Hep 137 11 Hep 137 10 Hep 136 9 Hep 140 10 Hep