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17 package org.apache.commons.math4.legacy.stat.inference;
18
19 import java.util.ArrayList;
20 import java.util.List;
21
22 import org.apache.commons.statistics.distribution.NormalDistribution;
23 import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
24 import org.apache.commons.math4.legacy.exception.NotPositiveException;
25 import org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException;
26 import org.apache.commons.math4.legacy.exception.NullArgumentException;
27 import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException;
28 import org.apache.commons.math4.legacy.exception.OutOfRangeException;
29 import org.apache.commons.math4.legacy.stat.descriptive.SummaryStatistics;
30 import org.apache.commons.math4.core.jdkmath.JdkMath;
31 import org.junit.Assert;
32 import org.junit.Test;
33
34
35
36
37
38
39 public class InferenceTestUtilsTest {
40 @Test
41 public void testChiSquare() {
42
43
44
45
46
47
48 long[] observed = {10, 9, 11};
49 double[] expected = {10, 10, 10};
50 Assert.assertEquals("chi-square statistic", 0.2, InferenceTestUtils.chiSquare(expected, observed), 10E-12);
51 Assert.assertEquals("chi-square p-value", 0.904837418036, InferenceTestUtils.chiSquareTest(expected, observed), 1E-10);
52
53 long[] observed1 = { 500, 623, 72, 70, 31 };
54 double[] expected1 = { 485, 541, 82, 61, 37 };
55 Assert.assertEquals( "chi-square test statistic", 9.023307936427388, InferenceTestUtils.chiSquare(expected1, observed1), 1E-10);
56 Assert.assertEquals("chi-square p-value", 0.06051952647453607, InferenceTestUtils.chiSquareTest(expected1, observed1), 1E-9);
57 Assert.assertTrue("chi-square test reject", InferenceTestUtils.chiSquareTest(expected1, observed1, 0.07));
58 Assert.assertFalse("chi-square test accept", InferenceTestUtils.chiSquareTest(expected1, observed1, 0.05));
59
60 try {
61 InferenceTestUtils.chiSquareTest(expected1, observed1, 95);
62 Assert.fail("alpha out of range, OutOfRangeException expected");
63 } catch (OutOfRangeException ex) {
64
65 }
66
67 long[] tooShortObs = { 0 };
68 double[] tooShortEx = { 1 };
69 try {
70 InferenceTestUtils.chiSquare(tooShortEx, tooShortObs);
71 Assert.fail("arguments too short, DimensionMismatchException expected");
72 } catch (DimensionMismatchException ex) {
73
74 }
75
76
77 long[] unMatchedObs = { 0, 1, 2, 3 };
78 double[] unMatchedEx = { 1, 1, 2 };
79 try {
80 InferenceTestUtils.chiSquare(unMatchedEx, unMatchedObs);
81 Assert.fail("arrays have different lengths, DimensionMismatchException expected");
82 } catch (DimensionMismatchException ex) {
83
84 }
85
86
87 expected[0] = 0;
88 try {
89 InferenceTestUtils.chiSquareTest(expected, observed, .01);
90 Assert.fail("bad expected count, NotStrictlyPositiveException expected");
91 } catch (NotStrictlyPositiveException ex) {
92
93 }
94
95
96 expected[0] = 1;
97 observed[0] = -1;
98 try {
99 InferenceTestUtils.chiSquareTest(expected, observed, .01);
100 Assert.fail("bad expected count, NotPositiveException expected");
101 } catch (NotPositiveException ex) {
102
103 }
104 }
105
106 @Test
107 public void testChiSquareIndependence() {
108
109
110
111 long[][] counts = { {40, 22, 43}, {91, 21, 28}, {60, 10, 22}};
112 Assert.assertEquals( "chi-square test statistic", 22.709027688, InferenceTestUtils.chiSquare(counts), 1E-9);
113 Assert.assertEquals("chi-square p-value", 0.000144751460134, InferenceTestUtils.chiSquareTest(counts), 1E-9);
114 Assert.assertTrue("chi-square test reject", InferenceTestUtils.chiSquareTest(counts, 0.0002));
115 Assert.assertFalse("chi-square test accept", InferenceTestUtils.chiSquareTest(counts, 0.0001));
116
117 long[][] counts2 = {{10, 15}, {30, 40}, {60, 90} };
118 Assert.assertEquals( "chi-square test statistic", 0.168965517241, InferenceTestUtils.chiSquare(counts2), 1E-9);
119 Assert.assertEquals("chi-square p-value",0.918987499852, InferenceTestUtils.chiSquareTest(counts2), 1E-9);
120 Assert.assertFalse("chi-square test accept", InferenceTestUtils.chiSquareTest(counts2, 0.1));
121
122
123 long[][] counts3 = { {40, 22, 43}, {91, 21, 28}, {60, 10}};
124 try {
125 InferenceTestUtils.chiSquare(counts3);
126 Assert.fail("Expecting DimensionMismatchException");
127 } catch (DimensionMismatchException ex) {
128
129 }
130
131
132 long[][] counts4 = {{40, 22, 43}};
133 try {
134 InferenceTestUtils.chiSquare(counts4);
135 Assert.fail("Expecting DimensionMismatchException");
136 } catch (DimensionMismatchException ex) {
137
138 }
139 long[][] counts5 = {{40}, {40}, {30}, {10}};
140 try {
141 InferenceTestUtils.chiSquare(counts5);
142 Assert.fail("Expecting DimensionMismatchException");
143 } catch (DimensionMismatchException ex) {
144
145 }
146
147
148 long[][] counts6 = {{10, -2}, {30, 40}, {60, 90} };
149 try {
150 InferenceTestUtils.chiSquare(counts6);
151 Assert.fail("Expecting NotPositiveException");
152 } catch (NotPositiveException ex) {
153
154 }
155
156
157 try {
158 InferenceTestUtils.chiSquareTest(counts, 0);
159 Assert.fail("Expecting OutOfRangeException");
160 } catch (OutOfRangeException ex) {
161
162 }
163 }
164
165 @Test
166 public void testChiSquareLargeTestStatistic() {
167 double[] exp = new double[] {
168 3389119.5, 649136.6, 285745.4, 25357364.76, 11291189.78, 543628.0,
169 232921.0, 437665.75
170 };
171
172 long[] obs = new long[] {
173 2372383, 584222, 257170, 17750155, 7903832, 489265, 209628, 393899
174 };
175 org.apache.commons.math4.legacy.stat.inference.ChiSquareTest csti =
176 new org.apache.commons.math4.legacy.stat.inference.ChiSquareTest();
177 double cst = csti.chiSquareTest(exp, obs);
178 Assert.assertEquals("chi-square p-value", 0.0, cst, 1E-3);
179 Assert.assertEquals( "chi-square test statistic",
180 114875.90421929007, InferenceTestUtils.chiSquare(exp, obs), 1E-9);
181 }
182
183
184 @Test
185 public void testChiSquareZeroCount() {
186
187 long[][] counts = { {40, 0, 4}, {91, 1, 2}, {60, 2, 0}};
188 Assert.assertEquals( "chi-square test statistic", 9.67444662263,
189 InferenceTestUtils.chiSquare(counts), 1E-9);
190 Assert.assertEquals("chi-square p-value", 0.0462835770603,
191 InferenceTestUtils.chiSquareTest(counts), 1E-9);
192 }
193
194 private double[] tooShortObs = { 1.0 };
195 private double[] emptyObs = {};
196 private SummaryStatistics emptyStats = new SummaryStatistics();
197
198 @Test
199 public void testOneSampleT() {
200 double[] observed =
201 {93.0, 103.0, 95.0, 101.0, 91.0, 105.0, 96.0, 94.0, 101.0, 88.0, 98.0, 94.0, 101.0, 92.0, 95.0 };
202 double mu = 100.0;
203 SummaryStatistics sampleStats = null;
204 sampleStats = new SummaryStatistics();
205 for (int i = 0; i < observed.length; i++) {
206 sampleStats.addValue(observed[i]);
207 }
208
209
210 Assert.assertEquals("t statistic", -2.81976445346,
211 InferenceTestUtils.t(mu, observed), 10E-10);
212 Assert.assertEquals("t statistic", -2.81976445346,
213 InferenceTestUtils.t(mu, sampleStats), 10E-10);
214 Assert.assertEquals("p value", 0.0136390585873,
215 InferenceTestUtils.tTest(mu, observed), 10E-10);
216 Assert.assertEquals("p value", 0.0136390585873,
217 InferenceTestUtils.tTest(mu, sampleStats), 10E-10);
218
219 try {
220 InferenceTestUtils.t(mu, (double[]) null);
221 Assert.fail("arguments too short, NullArgumentException expected");
222 } catch (NullArgumentException ex) {
223
224 }
225
226 try {
227 InferenceTestUtils.t(mu, (SummaryStatistics) null);
228 Assert.fail("arguments too short, NullArgumentException expected");
229 } catch (NullArgumentException ex) {
230
231 }
232
233 try {
234 InferenceTestUtils.t(mu, emptyObs);
235 Assert.fail("arguments too short, NumberIsTooSmallException expected");
236 } catch (NumberIsTooSmallException ex) {
237
238 }
239
240 try {
241 InferenceTestUtils.t(mu, emptyStats);
242 Assert.fail("arguments too short, NumberIsTooSmallException expected");
243 } catch (NumberIsTooSmallException ex) {
244
245 }
246
247 try {
248 InferenceTestUtils.t(mu, tooShortObs);
249 Assert.fail("insufficient data to compute t statistic, NumberIsTooSmallException expected");
250 } catch (NumberIsTooSmallException ex) {
251
252 }
253 try {
254 InferenceTestUtils.tTest(mu, tooShortObs);
255 Assert.fail("insufficient data to perform t test, NumberIsTooSmallException expected");
256 } catch (NumberIsTooSmallException ex) {
257
258 }
259
260 try {
261 InferenceTestUtils.t(mu, (SummaryStatistics) null);
262 Assert.fail("insufficient data to compute t statistic, NullArgumentException expected");
263 } catch (NullArgumentException ex) {
264
265 }
266 try {
267 InferenceTestUtils.tTest(mu, (SummaryStatistics) null);
268 Assert.fail("insufficient data to perform t test, NullArgumentException expected");
269 } catch (NullArgumentException ex) {
270
271 }
272 }
273
274 @Test
275 public void testOneSampleTTest() {
276 double[] oneSidedP =
277 {2d, 0d, 6d, 6d, 3d, 3d, 2d, 3d, -6d, 6d, 6d, 6d, 3d, 0d, 1d, 1d, 0d, 2d, 3d, 3d };
278 SummaryStatistics oneSidedPStats = new SummaryStatistics();
279 for (int i = 0; i < oneSidedP.length; i++) {
280 oneSidedPStats.addValue(oneSidedP[i]);
281 }
282
283 Assert.assertEquals("one sample t stat", 3.86485535541,
284 InferenceTestUtils.t(0d, oneSidedP), 10E-10);
285 Assert.assertEquals("one sample t stat", 3.86485535541,
286 InferenceTestUtils.t(0d, oneSidedPStats),1E-10);
287 Assert.assertEquals("one sample p value", 0.000521637019637,
288 InferenceTestUtils.tTest(0d, oneSidedP) / 2d, 10E-10);
289 Assert.assertEquals("one sample p value", 0.000521637019637,
290 InferenceTestUtils.tTest(0d, oneSidedPStats) / 2d, 10E-5);
291 Assert.assertTrue("one sample t-test reject", InferenceTestUtils.tTest(0d, oneSidedP, 0.01));
292 Assert.assertTrue("one sample t-test reject", InferenceTestUtils.tTest(0d, oneSidedPStats, 0.01));
293 Assert.assertFalse("one sample t-test accept", InferenceTestUtils.tTest(0d, oneSidedP, 0.0001));
294 Assert.assertFalse("one sample t-test accept", InferenceTestUtils.tTest(0d, oneSidedPStats, 0.0001));
295
296 try {
297 InferenceTestUtils.tTest(0d, oneSidedP, 95);
298 Assert.fail("alpha out of range, OutOfRangeException expected");
299 } catch (OutOfRangeException ex) {
300
301 }
302
303 try {
304 InferenceTestUtils.tTest(0d, oneSidedPStats, 95);
305 Assert.fail("alpha out of range, OutOfRangeException expected");
306 } catch (OutOfRangeException ex) {
307
308 }
309 }
310
311 @Test
312 public void testTwoSampleTHeterscedastic() {
313 double[] sample1 = { 7d, -4d, 18d, 17d, -3d, -5d, 1d, 10d, 11d, -2d };
314 double[] sample2 = { -1d, 12d, -1d, -3d, 3d, -5d, 5d, 2d, -11d, -1d, -3d };
315 SummaryStatistics sampleStats1 = new SummaryStatistics();
316 for (int i = 0; i < sample1.length; i++) {
317 sampleStats1.addValue(sample1[i]);
318 }
319 SummaryStatistics sampleStats2 = new SummaryStatistics();
320 for (int i = 0; i < sample2.length; i++) {
321 sampleStats2.addValue(sample2[i]);
322 }
323
324
325 Assert.assertEquals("two sample heteroscedastic t stat", 1.60371728768,
326 InferenceTestUtils.t(sample1, sample2), 1E-10);
327 Assert.assertEquals("two sample heteroscedastic t stat", 1.60371728768,
328 InferenceTestUtils.t(sampleStats1, sampleStats2), 1E-10);
329 Assert.assertEquals("two sample heteroscedastic p value", 0.128839369622,
330 InferenceTestUtils.tTest(sample1, sample2), 1E-10);
331 Assert.assertEquals("two sample heteroscedastic p value", 0.128839369622,
332 InferenceTestUtils.tTest(sampleStats1, sampleStats2), 1E-10);
333 Assert.assertTrue("two sample heteroscedastic t-test reject",
334 InferenceTestUtils.tTest(sample1, sample2, 0.2));
335 Assert.assertTrue("two sample heteroscedastic t-test reject",
336 InferenceTestUtils.tTest(sampleStats1, sampleStats2, 0.2));
337 Assert.assertFalse("two sample heteroscedastic t-test accept", InferenceTestUtils.tTest(sample1, sample2, 0.1));
338 Assert.assertFalse("two sample heteroscedastic t-test accept", InferenceTestUtils.tTest(sampleStats1, sampleStats2, 0.1));
339
340 try {
341 InferenceTestUtils.tTest(sample1, sample2, .95);
342 Assert.fail("alpha out of range, OutOfRangeException expected");
343 } catch (OutOfRangeException ex) {
344
345 }
346
347 try {
348 InferenceTestUtils.tTest(sampleStats1, sampleStats2, .95);
349 Assert.fail("alpha out of range, OutOfRangeException expected");
350 } catch (OutOfRangeException ex) {
351
352 }
353
354 try {
355 InferenceTestUtils.tTest(sample1, tooShortObs, .01);
356 Assert.fail("insufficient data, NumberIsTooSmallException expected");
357 } catch (NumberIsTooSmallException ex) {
358
359 }
360
361 try {
362 InferenceTestUtils.tTest(sampleStats1, (SummaryStatistics) null, .01);
363 Assert.fail("insufficient data, NullArgumentException expected");
364 } catch (NullArgumentException ex) {
365
366 }
367
368 try {
369 InferenceTestUtils.tTest(sample1, tooShortObs);
370 Assert.fail("insufficient data, NumberIsTooSmallException expected");
371 } catch (NumberIsTooSmallException ex) {
372
373 }
374
375 try {
376 InferenceTestUtils.tTest(sampleStats1, (SummaryStatistics) null);
377 Assert.fail("insufficient data, NullArgumentException expected");
378 } catch (NullArgumentException ex) {
379
380 }
381
382 try {
383 InferenceTestUtils.t(sample1, tooShortObs);
384 Assert.fail("insufficient data, NumberIsTooSmallException expected");
385 } catch (NumberIsTooSmallException ex) {
386
387 }
388
389 try {
390 InferenceTestUtils.t(sampleStats1, (SummaryStatistics) null);
391 Assert.fail("insufficient data, NullArgumentException expected");
392 } catch (NullArgumentException ex) {
393
394 }
395 }
396 @Test
397 public void testTwoSampleTHomoscedastic() {
398 double[] sample1 ={2, 4, 6, 8, 10, 97};
399 double[] sample2 = {4, 6, 8, 10, 16};
400 SummaryStatistics sampleStats1 = new SummaryStatistics();
401 for (int i = 0; i < sample1.length; i++) {
402 sampleStats1.addValue(sample1[i]);
403 }
404 SummaryStatistics sampleStats2 = new SummaryStatistics();
405 for (int i = 0; i < sample2.length; i++) {
406 sampleStats2.addValue(sample2[i]);
407 }
408
409
410 Assert.assertEquals("two sample homoscedastic t stat", 0.73096310086,
411 InferenceTestUtils.homoscedasticT(sample1, sample2), 10E-11);
412 Assert.assertEquals("two sample homoscedastic p value", 0.4833963785,
413 InferenceTestUtils.homoscedasticTTest(sampleStats1, sampleStats2), 1E-10);
414 Assert.assertTrue("two sample homoscedastic t-test reject",
415 InferenceTestUtils.homoscedasticTTest(sample1, sample2, 0.49));
416 Assert.assertFalse("two sample homoscedastic t-test accept", InferenceTestUtils.homoscedasticTTest(sample1, sample2, 0.48));
417 }
418
419 @Test
420 public void testSmallSamples() {
421 double[] sample1 = {1d, 3d};
422 double[] sample2 = {4d, 5d};
423
424
425 Assert.assertEquals(-2.2360679775, InferenceTestUtils.t(sample1, sample2),
426 1E-10);
427 Assert.assertEquals(0.198727388935, InferenceTestUtils.tTest(sample1, sample2),
428 1E-10);
429 }
430
431 @Test
432 public void testPaired() {
433 double[] sample1 = {1d, 3d, 5d, 7d};
434 double[] sample2 = {0d, 6d, 11d, 2d};
435 double[] sample3 = {5d, 7d, 8d, 10d};
436
437
438 Assert.assertEquals(-0.3133, InferenceTestUtils.pairedT(sample1, sample2), 1E-4);
439 Assert.assertEquals(0.774544295819, InferenceTestUtils.pairedTTest(sample1, sample2), 1E-10);
440 Assert.assertEquals(0.001208, InferenceTestUtils.pairedTTest(sample1, sample3), 1E-6);
441 Assert.assertFalse(InferenceTestUtils.pairedTTest(sample1, sample3, .001));
442 Assert.assertTrue(InferenceTestUtils.pairedTTest(sample1, sample3, .002));
443 }
444
445 private double[] classA =
446 {93.0, 103.0, 95.0, 101.0};
447 private double[] classB =
448 {99.0, 92.0, 102.0, 100.0, 102.0};
449 private double[] classC =
450 {110.0, 115.0, 111.0, 117.0, 128.0};
451
452 private List<double[]> classes = new ArrayList<>();
453 private OneWayAnova oneWayAnova = new OneWayAnova();
454
455 @Test
456 public void testOneWayAnovaUtils() {
457 classes.add(classA);
458 classes.add(classB);
459 classes.add(classC);
460 Assert.assertEquals(oneWayAnova.anovaFValue(classes),
461 InferenceTestUtils.oneWayAnovaFValue(classes), 10E-12);
462 Assert.assertEquals(oneWayAnova.anovaPValue(classes),
463 InferenceTestUtils.oneWayAnovaPValue(classes), 10E-12);
464 Assert.assertEquals(oneWayAnova.anovaTest(classes, 0.01),
465 InferenceTestUtils.oneWayAnovaTest(classes, 0.01));
466 }
467 @Test
468 public void testGTestGoodnesOfFit() throws Exception {
469 double[] exp = new double[]{
470 0.54d, 0.40d, 0.05d, 0.01d
471 };
472
473 long[] obs = new long[]{
474 70, 79, 3, 4
475 };
476 Assert.assertEquals("G test statistic",
477 13.144799, InferenceTestUtils.g(exp, obs), 1E-5);
478 double p_gtgf = InferenceTestUtils.gTest(exp, obs);
479 Assert.assertEquals("g-Test p-value", 0.004333, p_gtgf, 1E-5);
480
481 Assert.assertTrue(InferenceTestUtils.gTest(exp, obs, 0.05));
482 }
483
484 @Test
485 public void testGTestIndependence() throws Exception {
486 long[] obs1 = new long[]{
487 268, 199, 42
488 };
489
490 long[] obs2 = new long[]{
491 807, 759, 184
492 };
493
494 double g = InferenceTestUtils.gDataSetsComparison(obs1, obs2);
495
496 Assert.assertEquals("G test statistic",
497 7.3008170, g, 1E-4);
498 double p_gti = InferenceTestUtils.gTestDataSetsComparison(obs1, obs2);
499
500 Assert.assertEquals("g-Test p-value", 0.0259805, p_gti, 1E-4);
501 Assert.assertTrue(InferenceTestUtils.gTestDataSetsComparison(obs1, obs2, 0.05));
502 }
503
504 @Test
505 public void testRootLogLikelihood() {
506
507 Assert.assertTrue(InferenceTestUtils.rootLogLikelihoodRatio(904, 21060, 1144, 283012) > 0.0);
508
509
510 Assert.assertTrue(InferenceTestUtils.rootLogLikelihoodRatio(36, 21928, 60280, 623876) < 0.0);
511
512 Assert.assertEquals(JdkMath.sqrt(2.772589), InferenceTestUtils.rootLogLikelihoodRatio(1, 0, 0, 1), 0.000001);
513 Assert.assertEquals(-JdkMath.sqrt(2.772589), InferenceTestUtils.rootLogLikelihoodRatio(0, 1, 1, 0), 0.000001);
514 Assert.assertEquals(JdkMath.sqrt(27.72589), InferenceTestUtils.rootLogLikelihoodRatio(10, 0, 0, 10), 0.00001);
515
516 Assert.assertEquals(JdkMath.sqrt(39.33052), InferenceTestUtils.rootLogLikelihoodRatio(5, 1995, 0, 100000), 0.00001);
517 Assert.assertEquals(-JdkMath.sqrt(39.33052), InferenceTestUtils.rootLogLikelihoodRatio(0, 100000, 5, 1995), 0.00001);
518
519 Assert.assertEquals(JdkMath.sqrt(4730.737), InferenceTestUtils.rootLogLikelihoodRatio(1000, 1995, 1000, 100000), 0.001);
520 Assert.assertEquals(-JdkMath.sqrt(4730.737), InferenceTestUtils.rootLogLikelihoodRatio(1000, 100000, 1000, 1995), 0.001);
521
522 Assert.assertEquals(JdkMath.sqrt(5734.343), InferenceTestUtils.rootLogLikelihoodRatio(1000, 1000, 1000, 100000), 0.001);
523 Assert.assertEquals(JdkMath.sqrt(5714.932), InferenceTestUtils.rootLogLikelihoodRatio(1000, 1000, 1000, 99000), 0.001);
524 }
525
526 @Test
527 public void testKSOneSample() throws Exception {
528 final NormalDistribution unitNormal = NormalDistribution.of(0d, 1d);
529 final double[] sample = KolmogorovSmirnovTestTest.gaussian;
530 final double tol = 1e-10;
531 Assert.assertEquals(0.3172069207622391, InferenceTestUtils.kolmogorovSmirnovTest(unitNormal, sample), tol);
532 Assert.assertEquals(0.0932947561266756, InferenceTestUtils.kolmogorovSmirnovStatistic(unitNormal, sample), tol);
533 }
534
535 @Test
536 public void testKSTwoSample() throws Exception {
537 final double tol = 1e-10;
538 final double[] smallSample1 = {
539 6, 7, 9, 13, 19, 21, 22, 23, 24
540 };
541 final double[] smallSample2 = {
542 10, 11, 12, 16, 20, 27, 28, 32, 44, 54
543 };
544 Assert.assertEquals(0.105577085453247, InferenceTestUtils.kolmogorovSmirnovTest(smallSample1, smallSample2, false), tol);
545 final double d = InferenceTestUtils.kolmogorovSmirnovStatistic(smallSample1, smallSample2);
546 Assert.assertEquals(0.5, d, tol);
547 Assert.assertEquals(0.105577085453247, InferenceTestUtils.exactP(d, smallSample1.length, smallSample2.length, false), tol);
548 }
549 }