Table 9 ANOVA tests
From: The effects of class rarity on the evaluation of supervised healthcare fraud detection models
Term | Df | Sum Sq | Mean Sq | F value | Pr(>F) |
|---|---|---|---|---|---|
(a) Four factor: Train_Test | |||||
Datasets | 3 | 1.96516 | 0.65505 | 1600.558663 | 0 |
Learner | 2 | 0.66409 | 0.33205 | 811.3215437 | 1.29E−270 |
Pos count | 4 | 2.33669 | 0.58417 | 1427.367028 | 0 |
Ratio | 5 | 0.30092 | 0.06018 | 147.0525251 | 1.17E−136 |
Dataset:learner | 6 | 0.22145 | 0.03691 | 90.18221558 | 2.05E−102 |
Dataset:pos count | 7 | 0.05788 | 0.00827 | 20.2044874 | 1.61E−26 |
Learner:pos count | 8 | 0.03291 | 0.00411 | 10.0523189 | 7.04E−14 |
Dataset:ratio | 15 | 0.08724 | 0.00582 | 14.21108373 | 2.17E−35 |
Learner:ratio | 10 | 0.46537 | 0.04654 | 113.7087576 | 2.69E−194 |
Pos count:ratio | 20 | 0.05443 | 0.00272 | 6.649302133 | 3.98E−18 |
Dataset:learner:pos count | 14 | 0.02401 | 0.00171 | 4.189763574 | 2.52E−07 |
Dataset:learner:ratio | 30 | 0.11577 | 0.00386 | 9.428942232 | 2.99E−40 |
Dataset:pos count:ratio | 35 | 0.01306 | 0.00037 | 0.911606914 | 0.61790442 |
Learner:pos count:ratio | 40 | 0.10682 | 0.00267 | 6.52539348 | 3.70E−32 |
Dataset:learner:pos count:ratio | 70 | 0.04795 | 0.00068 | 1.673573178 | 4.56E−04 |
Residuals | 2430 | 0.99452 | 0.00041 | – | – |
(b) Four factor: Train_CV | |||||
Datasets | 7 | 26.98719 | 3.85531 | 2641.872038 | 0 |
Learner | 2 | 1.34356 | 0.67178 | 460.3389767 | 5.33E−194 |
Pos count | 3 | 6.30292 | 2.10097 | 1439.702651 | 0 |
Ratio | 5 | 1.25714 | 0.25143 | 172.2919289 | 3.65E−178 |
Dataset:learner | 14 | 0.79698 | 0.05693 | 39.00963177 | 2.86E−105 |
Dataset:pos count | 4 | 0.34344 | 0.08586 | 58.83679308 | 2.58E−49 |
Learner:pos count | 6 | 0.07181 | 0.01197 | 8.201310311 | 7.04E−09 |
Dataset:ratio | 35 | 0.32743 | 0.00936 | 6.410645904 | 3.43E−29 |
Learner:ratio | 10 | 1.36440 | 0.13644 | 93.49620948 | 1.03E−187 |
Pos count:ratio | 15 | 0.13786 | 0.00919 | 6.298014086 | 1.64E−13 |
Dataset:learner:pos count | 8 | 0.04741 | 0.00593 | 4.061371638 | 7.71E−05 |
Dataset:learner:ratio | 70 | 0.42329 | 0.00605 | 4.143770726 | 3.52E−28 |
Dataset:pos count:ratio | 20 | 0.01735 | 0.00087 | 0.594299086 | 0.919852682 |
Learner:pos count:ratio | 30 | 0.08452 | 0.00282 | 1.9304991 | 0.001663456 |
Dataset:learner:pos count:ratio | 40 | 0.07660 | 0.00192 | 1.312296909 | 0.089594623 |
Residuals | 13230 | 19.30669 | 0.00146 | – | – |
(c) Two factor: Train_Test and Train_CV | |||||
Evaluation method | 1 | 0.45439 | 0.45439 | 103.9411081 | 2.59E−24 |
Residuals | 12598 | 55.07319 | 0.00437 | – | – |