├── README.md ├── src ├── main │ ├── TTest │ │ ├── TTestUtil.scala │ │ ├── OneSampleTTest.scala │ │ ├── PairTwoSampleTTest.scala │ │ └── TwoSampleIndependentTTest.scala │ ├── KolmogorovSmirnovTest │ │ └── KolmogorovSmirnovTest.scala │ ├── ANOVA │ │ └── OneWayANOVA.scala │ └── MannWhitneyUTest │ │ └── MannWhitneyUTest.scala └── test │ ├── ANOVASuite.scala │ ├── MannWhitneyUTestSuite.scala │ └── TTestSuite.scala └── LICENSE /README.md: -------------------------------------------------------------------------------- 1 | # Spark.statistics 2 | 3 | Assembly of fundamental statistics implemented based on Apache Spark 4 | 5 | ## Requirements 6 | 7 | This documentation is for Spark 1.3+. Other version will probably work yet not tested. 8 | 9 | ## Features 10 | 11 | `Spark.statistics` intends to provide fundamental statistics functions. 12 | 13 | Currently we support: 14 | * One Sample T Test, 15 | * Independent Samples T Test 16 | * Paired Samples T Test 17 | * One way ANOVA 18 | 19 | Hopefully more features will come in quickly, next on the list: 20 | * Post Hoc comparison 21 | * Log likelihood 22 | * Kolmogorov-Smirnov 23 | 24 | 25 | ## Example 26 | 27 | ### Scala API 28 | 29 | ```scala 30 | val sample1 = Array(100d, 200d, 300d, 400d) 31 | val sample2 = Array(101d, 205d, 300d, 400d) 32 | 33 | val rdd1 = sc.parallelize(sample1) 34 | val rdd2 = sc.parallelize(sample2) 35 | 36 | new TwoSampleIndependentTTest().tTest(rdd1, rdd2, 0.05)) 37 | new TwoSampleIndependentTTest().tTest(rdd1, rdd2) 38 | ``` 39 | -------------------------------------------------------------------------------- /src/main/TTest/TTestUtil.scala: -------------------------------------------------------------------------------- 1 | /* 2 | * Licensed to the Apache Software Foundation (ASF) under one or more 3 | * contributor license agreements. See the NOTICE file distributed with 4 | * this work for additional information regarding copyright ownership. 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 6 | * (the "License"); you may not use this file except in compliance with 7 | * the License. You may obtain a copy of the License at 8 | * 9 | * http://www.apache.org/licenses/LICENSE-2.0 10 | * 11 | * Unless required by applicable law or agreed to in writing, software 12 | * distributed under the License is distributed on an "AS IS" BASIS, 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 | * See the License for the specific language governing permissions and 15 | * limitations under the License. 16 | */ 17 | package org.apache.spark.mllib.stat 18 | 19 | import org.apache.commons.math3.distribution.TDistribution 20 | import org.apache.spark.rdd.RDD 21 | 22 | /** 23 | * Created by yuhao on 12/31/15. 24 | */ 25 | trait TTestBasic { 26 | 27 | private[stat] def t(m: Double, mu: Double, v: Double, n: Long): Double = { 28 | val t = math.abs((m - mu) / math.sqrt(v / n)) 29 | val TDistribution = new TDistribution(null, n - 1.0D) 30 | return 2.0D * TDistribution.cumulativeProbability(-t) 31 | } 32 | 33 | } 34 | -------------------------------------------------------------------------------- /src/test/ANOVASuite.scala: -------------------------------------------------------------------------------- 1 | package test 2 | 3 | import java.util 4 | 5 | import main.ANOVA.OneWayANOVA 6 | import org.apache.commons.math3.stat.inference.TestUtils 7 | import org.apache.log4j.{Level, Logger} 8 | import org.apache.spark.mllib.stat.OneSampleTTest 9 | import org.apache.spark.{SparkContext, SparkConf} 10 | 11 | /** 12 | * Created by yuhao on 1/4/16. 13 | */ 14 | object ANOVASuite { 15 | 16 | Logger.getLogger("org").setLevel(Level.WARN) 17 | Logger.getLogger("akka").setLevel(Level.WARN) 18 | val conf = new SparkConf().setAppName("TallSkinnySVD").setMaster("local") 19 | val sc = new SparkContext(conf) 20 | 21 | def main(args: Array[String]) { 22 | OneWayANOVA 23 | } 24 | 25 | def OneWayANOVA(): Unit ={ 26 | val sample1 = Array(100d, 200d, 300d, 400d) 27 | val sample2 = Array(101d, 200d, 300d, 400d) 28 | val sample3 = Array(102d, 200d, 300d, 400d) 29 | val data = new util.ArrayList[Array[Double]]() 30 | data.add(sample1) 31 | data.add(sample2) 32 | data.add(sample3) 33 | 34 | val rdd1 = sc.parallelize(sample1) 35 | val rdd2 = sc.parallelize(sample2) 36 | val rdd3 = sc.parallelize(sample3) 37 | val rddData = Seq(rdd1, rdd2, rdd3) 38 | 39 | assert(TestUtils.oneWayAnovaFValue(data) == new OneWayANOVA().anovaFValue(rddData)) 40 | assert(TestUtils.oneWayAnovaPValue(data) == new OneWayANOVA().anovaPValue(rddData)) 41 | } 42 | 43 | } 44 | -------------------------------------------------------------------------------- /src/test/MannWhitneyUTestSuite.scala: -------------------------------------------------------------------------------- 1 | package test 2 | 3 | import org.apache.commons.math3.stat.inference.MannWhitneyUTest 4 | import org.apache.log4j.{Level, Logger} 5 | import org.apache.spark.{SparkContext, SparkConf} 6 | 7 | /** 8 | * Created by yuhao on 2/8/16. 9 | */ 10 | object MannWhitneyUTestSuite { 11 | 12 | Logger.getLogger("org").setLevel(Level.WARN) 13 | Logger.getLogger("akka").setLevel(Level.WARN) 14 | val conf = new SparkConf().setAppName("TallSkinnySVD").setMaster("local") 15 | val sc = new SparkContext(conf) 16 | 17 | def main(args: Array[String]) { 18 | testMannWhitneyU 19 | testMannWhitneyUTest 20 | } 21 | 22 | private def testMannWhitneyU(): Unit ={ 23 | val sample1 = Array(1d, 3d, 5, 7) 24 | val sample2 = Array(2, 4, 6, 8d) 25 | 26 | val rdd1 = sc.parallelize(sample1) 27 | val rdd2 = sc.parallelize(sample2) 28 | 29 | val result = new MannWhitneyUTest() 30 | .mannWhitneyU(sample1, sample2) 31 | val result2 = org.apache.spark.mllib.stat.test.MannWhitneyUTest.mannWhitneyU(rdd1, rdd2) 32 | assert(result == result2) 33 | } 34 | 35 | private def testMannWhitneyUTest(): Unit ={ 36 | val sample1 = Array(1d, 3d, 5, 7) 37 | val sample2 = Array(2, 4, 6, 8d) 38 | 39 | val rdd1 = sc.parallelize(sample1) 40 | val rdd2 = sc.parallelize(sample2) 41 | 42 | val result = new MannWhitneyUTest() 43 | .mannWhitneyUTest(sample1, sample2) 44 | val result2 = org.apache.spark.mllib.stat.test.MannWhitneyUTest.mannWhitneyUTest(rdd1, rdd2) 45 | println(result) 46 | println(result2) 47 | assert(result == result2) 48 | } 49 | 50 | 51 | 52 | } 53 | -------------------------------------------------------------------------------- /src/main/KolmogorovSmirnovTest/KolmogorovSmirnovTest.scala: -------------------------------------------------------------------------------- 1 | /* 2 | * Licensed to the Apache Software Foundation (ASF) under one or more 3 | * contributor license agreements. See the NOTICE file distributed with 4 | * this work for additional information regarding copyright ownership. 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 6 | * (the "License"); you may not use this file except in compliance with 7 | * the License. You may obtain a copy of the License at 8 | * 9 | * http://www.apache.org/licenses/LICENSE-2.0 10 | * 11 | * Unless required by applicable law or agreed to in writing, software 12 | * distributed under the License is distributed on an "AS IS" BASIS, 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 | * See the License for the specific language governing permissions and 15 | * limitations under the License. 16 | */ 17 | package org.apache.spark.mllib.stat.test 18 | 19 | import org.apache.commons.math3.util.FastMath 20 | 21 | /** 22 | * We just found out KolmogorovSmirnovTest was included in Spark 1.6. 23 | * Instead of providing a new implementation, it better aligns with 24 | * users' interests if we can provide improvement or new functions based 25 | * on the Spark version. If you find something potentially useful yet missing 26 | * from Spark, please go ahead and create an issue in the project. 27 | * 28 | */ 29 | object KolmogorovSmirnovTest { 30 | 31 | def ksSum (t: Double, tolerance: Double, maxIterations: Int): Double = { 32 | if (t == 0.0) { 33 | return 0.0 34 | } 35 | val x: Double = -2 * t * t 36 | var sign: Int = -1 37 | var i: Long = 1 38 | var partialSum: Double = 0.5d 39 | var delta: Double = 1 40 | while (delta > tolerance && i < maxIterations) { 41 | delta = FastMath.exp(x * i * i) 42 | partialSum += sign * delta 43 | sign *= -1 44 | i += 1 45 | } 46 | partialSum * 2 47 | } 48 | } 49 | 50 | -------------------------------------------------------------------------------- /src/test/TTestSuite.scala: -------------------------------------------------------------------------------- 1 | /* 2 | * Licensed to the Apache Software Foundation (ASF) under one or more 3 | * contributor license agreements. See the NOTICE file distributed with 4 | * this work for additional information regarding copyright ownership. 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 6 | * (the "License"); you may not use this file except in compliance with 7 | * the License. You may obtain a copy of the License at 8 | * 9 | * http://www.apache.org/licenses/LICENSE-2.0 10 | * 11 | * Unless required by applicable law or agreed to in writing, software 12 | * distributed under the License is distributed on an "AS IS" BASIS, 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 | * See the License for the specific language governing permissions and 15 | * limitations under the License. 16 | */ 17 | 18 | package org.apache.spark.mllib.stat 19 | 20 | import org.apache.commons.math3.stat.inference.TestUtils 21 | import org.apache.log4j.{Level, Logger} 22 | import org.apache.spark.{SparkConf, SparkContext} 23 | 24 | 25 | /** 26 | * Created by yuhao on 12/31/15. 27 | */ 28 | object TTestSuite { 29 | 30 | Logger.getLogger("org").setLevel(Level.WARN) 31 | Logger.getLogger("akka").setLevel(Level.WARN) 32 | val conf = new SparkConf().setAppName("TallSkinnySVD").setMaster("local") 33 | val sc = new SparkContext(conf) 34 | 35 | def main(args: Array[String]) { 36 | OneSampleTTest 37 | twoIndependentSampleTTest 38 | pairedTwoSampleTTest 39 | } 40 | 41 | def OneSampleTTest(): Unit ={ 42 | val observed = Array(100d, 200d, 300d, 400d) 43 | val mu = 2.5d 44 | 45 | assert(TestUtils.tTest(mu, observed, 0.05) == new OneSampleTTest().tTest(mu, sc.parallelize(observed), 0.05)) 46 | assert(TestUtils.tTest(mu, observed) == new OneSampleTTest().tTest(mu, sc.parallelize(observed))) 47 | } 48 | 49 | def twoIndependentSampleTTest(): Unit ={ 50 | val sample1 = Array(100d, 200d, 300d, 400d) 51 | val sample2 = Array(101d, 205d, 300d, 400d) 52 | 53 | val rdd1 = sc.parallelize(sample1) 54 | val rdd2 = sc.parallelize(sample2) 55 | 56 | assert(TestUtils.tTest(sample1, sample2, 0.05) == new TwoSampleIndependentTTest().tTest(rdd1, rdd2, 0.05)) 57 | assert(TestUtils.tTest(sample1, sample2) == new TwoSampleIndependentTTest().tTest(rdd1, rdd2)) 58 | } 59 | 60 | def pairedTwoSampleTTest(): Unit ={ 61 | val sample1 = Array(100d, 200d, 300d, 400d) 62 | val sample2 = Array(101d, 202d, 300d, 400d) 63 | 64 | val rdd1 = sc.parallelize(sample1) 65 | val rdd2 = sc.parallelize(sample2) 66 | 67 | assert(TestUtils.pairedTTest(sample1, sample2, 0.05) == new PairTwoSampleTTest().tTest(rdd1, rdd2, 0.05)) 68 | assert(TestUtils.pairedTTest(sample1, sample2) == new PairTwoSampleTTest().tTest(rdd1, rdd2)) 69 | } 70 | 71 | } 72 | -------------------------------------------------------------------------------- /src/main/ANOVA/OneWayANOVA.scala: -------------------------------------------------------------------------------- 1 | package main.ANOVA 2 | 3 | import org.apache.commons.math3.distribution.FDistribution 4 | import org.apache.spark.rdd.RDD 5 | 6 | 7 | /** 8 | * Created by yuhao on 1/1/16. 9 | */ 10 | class OneWayANOVA { 11 | 12 | /** 13 | * Performs an ANOVA test, evaluating the null hypothesis that there 14 | * is no difference among the means of the data categories. 15 | * 16 | * @param categoryData Collection of RDD[Double], each containing data for one category 17 | * @param alpha significance level of the test 18 | * @return true if the null hypothesis can be rejected with 19 | * confidence 1 - alpha 20 | */ 21 | def anovaTest(categoryData: Iterable[RDD[Double]], alpha: Double): Boolean = { 22 | anovaPValue(categoryData) < alpha 23 | } 24 | 25 | /** 26 | * Computes the ANOVA F-value for a collection of RDD[double]. 27 | * 28 | * This implementation computes the F statistic using the definitional 29 | * formula 30 | * F = msbg/mswg 31 | * where 32 | * msbg = between group mean square 33 | * mswg = within group mean square 34 | * 35 | * @param categoryData Collection of RDD[Double], each containing data for one category 36 | * @return Fvalue 37 | */ 38 | def anovaFValue(categoryData: Iterable[RDD[Double]]): Double = { 39 | getAnovaStats(categoryData).F 40 | } 41 | 42 | 43 | 44 | /** 45 | * Computes the ANOVA P-value for a collection of double[] 46 | * arrays. 47 | * 48 | * @param categoryData Collection of RDD[Double], each containing data for one category 49 | * @return Pvalue 50 | */ 51 | def anovaPValue(categoryData: Iterable[RDD[Double]]): Double = { 52 | val anovaStats = getAnovaStats(categoryData) 53 | 54 | val fdist: FDistribution = new FDistribution(null, anovaStats.dfbg, anovaStats.dfwg) 55 | return 1.0 - fdist.cumulativeProbability(anovaStats.F) 56 | } 57 | 58 | private case class ANOVAStats(dfbg: Double, dfwg: Double, F: Double) 59 | 60 | private def getAnovaStats(categoryData: Iterable[RDD[Double]]): ANOVAStats = { 61 | var dfwg: Long = 0 62 | var sswg: Double = 0 63 | var totsum: Double = 0 64 | var totsumsq: Double = 0 65 | var totnum: Long = 0 66 | 67 | for (data <- categoryData) { 68 | val sum: Double = data.sum() 69 | val sumsq: Double = data.map(i => i * i).sum() 70 | val num = data.count() 71 | totnum += num 72 | totsum += sum 73 | totsumsq += sumsq 74 | dfwg += num - 1 75 | val ss: Double = sumsq - ((sum * sum) / num) 76 | sswg += ss 77 | } 78 | 79 | val sst: Double = totsumsq - ((totsum * totsum) / totnum) 80 | val ssbg: Double = sst - sswg 81 | val dfbg: Int = categoryData.size - 1 82 | val msbg: Double = ssbg / dfbg 83 | val mswg: Double = sswg / dfwg 84 | val F: Double = msbg / mswg 85 | ANOVAStats(dfbg, dfwg, F) 86 | } 87 | 88 | 89 | } 90 | -------------------------------------------------------------------------------- /src/main/TTest/OneSampleTTest.scala: -------------------------------------------------------------------------------- 1 | /* 2 | * Licensed to the Apache Software Foundation (ASF) under one or more 3 | * contributor license agreements. See the NOTICE file distributed with 4 | * this work for additional information regarding copyright ownership. 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 6 | * (the "License"); you may not use this file except in compliance with 7 | * the License. You may obtain a copy of the License at 8 | * 9 | * http://www.apache.org/licenses/LICENSE-2.0 10 | * 11 | * Unless required by applicable law or agreed to in writing, software 12 | * distributed under the License is distributed on an "AS IS" BASIS, 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 | * See the License for the specific language governing permissions and 15 | * limitations under the License. 16 | */ 17 | 18 | package org.apache.spark.mllib.stat 19 | 20 | import org.apache.commons.math3.distribution.TDistribution 21 | import org.apache.spark.rdd.RDD 22 | 23 | /** 24 | * Created by yuhao on 12/31/15. 25 | */ 26 | class OneSampleTTest extends TTestBasic { 27 | /** 28 | * Performs a two-sided t-test evaluating the null hypothesis that the mean of the population from 29 | * which sample is drawn equals mu 30 | * Returns true iff the null hypothesis can be 31 | * rejected with confidence 1 - alpha. To 32 | * perform a 1-sided test, use alpha * 2 33 | 34 | * To test the (2-sided) hypothesis sample mean = mu at 35 | * the 95% level, use tTest(mu, sample, 0.05) 36 | * 37 | * To test the (one-sided) hypothesis sample mean < mu 38 | * at the 99% level, first verify that the measured sample mean is less 39 | * than mu and then use 40 | * tTest(mu, sample, 0.02) 41 | * 42 | * @param mu constant value to compare sample mean against 43 | * @param sample array of sample data values 44 | * @param alpha significance level of the test 45 | * @return p-value 46 | */ 47 | def tTest(mu: Double, sample: RDD[Double], alpha:Double): Boolean = { 48 | tTest(mu, sample) < alpha 49 | } 50 | 51 | /** 52 | * Returns the observed significance level, or 53 | * p-value, associated with a one-sample, two-tailed t-test 54 | * comparing the mean of the input array with the constant mu. 55 | * 56 | * The number returned is the smallest significance level 57 | * at which one can reject the null hypothesis that the mean equals 58 | * mu in favor of the two-sided alternative that the mean 59 | * is different from mu. For a one-sided test, divide the 60 | * returned value by 2. 61 | * 62 | * @param mu constant value to compare sample mean against 63 | * @param sample array of sample data values 64 | * @return p-value 65 | */ 66 | def tTest(mu: Double, sample: RDD[Double]): Double = { 67 | val n = sample.count() 68 | val mean = sample.sum() / n 69 | val variance = sample.map(d => (d - mean) * (d - mean)).sum() / (n - 1) 70 | t(mean, mu, variance, n) 71 | } 72 | 73 | } 74 | -------------------------------------------------------------------------------- /src/main/TTest/PairTwoSampleTTest.scala: -------------------------------------------------------------------------------- 1 | /* 2 | * Licensed to the Apache Software Foundation (ASF) under one or more 3 | * contributor license agreements. See the NOTICE file distributed with 4 | * this work for additional information regarding copyright ownership. 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 6 | * (the "License"); you may not use this file except in compliance with 7 | * the License. You may obtain a copy of the License at 8 | * 9 | * http://www.apache.org/licenses/LICENSE-2.0 10 | * 11 | * Unless required by applicable law or agreed to in writing, software 12 | * distributed under the License is distributed on an "AS IS" BASIS, 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 | * See the License for the specific language governing permissions and 15 | * limitations under the License. 16 | */ 17 | package org.apache.spark.mllib.stat 18 | 19 | 20 | import org.apache.spark.rdd.RDD 21 | 22 | /** 23 | * Created by yuhao on 12/31/15. 24 | */ 25 | class PairTwoSampleTTest extends TTestBasic { 26 | /** 27 | * Returns the observed significance level, or 28 | * p-value, associated with a paired, two-sample, two-tailed t-test 29 | * based on the data in the input arrays. 30 | * 31 | * The number returned is the smallest significance level 32 | * at which one can reject the null hypothesis that the mean of the paired 33 | * differences is 0 in favor of the two-sided alternative that the mean paired 34 | * difference is not equal to 0. For a one-sided test, divide the returned 35 | * value by 2. 36 | * 37 | * This test is equivalent to a one-sample t-test computed using 38 | * {@link #tTest(double, double[])} with mu = 0 and the sample 39 | * array consisting of the signed differences between corresponding elements of 40 | * sample1 and sample2. 41 | * 42 | * @param sample1 array of sample data values 43 | * @param sample2 array of sample data values 44 | * @return p-value for t-test 45 | */ 46 | def tTest(sample1: RDD[Double], sample2: RDD[Double]): Double = { 47 | val n = sample1.count() 48 | require(n == sample2.count()) 49 | 50 | val meanDifference = sample1.zip(sample2).map(p => p._1 - p._2).sum() / n 51 | 52 | val sum1 = sample1.zip(sample2).map(p => (p._1 - p._2 - meanDifference) * (p._1 - p._2 - meanDifference)).sum() 53 | val sum2 = sample1.zip(sample2).map(p => p._1 - p._2 - meanDifference).sum() 54 | val varianceDifference = (sum1 - sum2 * sum2 / n) / (n - 1) 55 | 56 | t(meanDifference, 0, varianceDifference, n) 57 | } 58 | 59 | /** 60 | * Performs a paired t-test evaluating the null hypothesis that the 61 | * mean of the paired differences between sample1 and 62 | * sample2 is 0 in favor of the two-sided alternative that the 63 | * mean paired difference is not equal to 0, with significance level 64 | * alpha. 65 | * Returns true iff the null hypothesis can be rejected with 66 | * confidence 1 - alpha. To perform a 1-sided test, use 67 | * alpha * 2 68 | * 69 | * @param sample1 array of sample data values 70 | * @param sample2 array of sample data values 71 | * @param alpha significance level of the test 72 | * @return true if the null hypothesis can be rejected with 73 | * confidence 1 - alpha 74 | */ 75 | def tTest(sample1: RDD[Double], sample2: RDD[Double], alpha: Double): Boolean = { 76 | tTest(sample1, sample2) < alpha 77 | } 78 | 79 | } 80 | -------------------------------------------------------------------------------- /src/main/TTest/TwoSampleIndependentTTest.scala: -------------------------------------------------------------------------------- 1 | /* 2 | * Licensed to the Apache Software Foundation (ASF) under one or more 3 | * contributor license agreements. See the NOTICE file distributed with 4 | * this work for additional information regarding copyright ownership. 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 6 | * (the "License"); you may not use this file except in compliance with 7 | * the License. You may obtain a copy of the License at 8 | * 9 | * http://www.apache.org/licenses/LICENSE-2.0 10 | * 11 | * Unless required by applicable law or agreed to in writing, software 12 | * distributed under the License is distributed on an "AS IS" BASIS, 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 | * See the License for the specific language governing permissions and 15 | * limitations under the License. 16 | */ 17 | package org.apache.spark.mllib.stat 18 | 19 | import org.apache.commons.math3.distribution.TDistribution 20 | import org.apache.commons.math3.util.FastMath 21 | import org.apache.spark.rdd.RDD 22 | 23 | /** 24 | * Created by yuhao on 12/31/15. 25 | */ 26 | class TwoSampleIndependentTTest { 27 | /** 28 | * Performs a two-sided t-test evaluating the null hypothesis that sample1 29 | * and sample2 are drawn from populations with the same mean, 30 | * with significance level alpha. This test does not assume 31 | * that the subpopulation variances are equal. 32 | * Returns true iff the null hypothesis that the means are 33 | * equal can be rejected with confidence 1 - alpha. To 34 | * perform a 1-sided test, use alpha * 2 35 | * To test the (2-sided) hypothesis mean 1 = mean 2 at 36 | * the 95% level, use 37 | * tTest(sample1, sample2, 0.05). 38 | * To test the (one-sided) hypothesis mean 1 < mean 2, 39 | * at the 99% level, first verify that the measured mean of sample 1 40 | * is less than the mean of sample 2 and then use 41 | * tTest(sample1, sample2, 0.02) 42 | * @param sample1 array of sample data values 43 | * @param sample2 array of sample data values 44 | * @param alpha significance level of the test 45 | * @return true if the null hypothesis can be rejected with 46 | * confidence 1 - alpha 47 | */ 48 | def tTest(sample1: RDD[Double], sample2: RDD[Double], alpha: Double): Boolean = { 49 | tTest(sample1, sample2) < alpha 50 | } 51 | 52 | /** 53 | * Returns the observed significance level, or 54 | * p-value, associated with a two-sample, two-tailed t-test 55 | * comparing the means of the input arrays. 56 | * 57 | * The number returned is the smallest significance level 58 | * at which one can reject the null hypothesis that the two means are 59 | * equal in favor of the two-sided alternative that they are different. 60 | * For a one-sided test, divide the returned value by 2. 61 | * 62 | * @param sample1 array of sample data values 63 | * @param sample2 array of sample data values 64 | * @return p-value for t-test 65 | */ 66 | def tTest(sample1: RDD[Double], sample2: RDD[Double]): Double = { 67 | val n1 = sample1.count() 68 | val n2 = sample2.count() 69 | val m1 = sample1.sum() / n1 70 | val m2 = sample2.sum() / n2 71 | val v1 = sample1.map(d => (d - m1) * (d - m1)).sum() / (n1 - 1) 72 | val v2 = sample2.map(d => (d - m2) * (d - m2)).sum() / (n2 - 1) 73 | val t: Double = math.abs((m1 - m2) / FastMath.sqrt((v1 / n1) + (v2 / n2))) 74 | val degreesOfFreedom: Double = (((v1 / n1) + (v2 / n2)) * ((v1 / n1) + (v2 / n2))) / 75 | ((v1 * v1) / (n1 * n1 * (n1 - 1d)) + (v2 * v2) / (n2 * n2 * (n2 - 1d))) 76 | 77 | // pass a null rng to avoid unneeded overhead as we will not sample from this distribution 78 | val distribution: TDistribution = new TDistribution(null, degreesOfFreedom) 79 | 2.0 * distribution.cumulativeProbability(-t) 80 | } 81 | 82 | } 83 | -------------------------------------------------------------------------------- /src/main/MannWhitneyUTest/MannWhitneyUTest.scala: -------------------------------------------------------------------------------- 1 | /* 2 | * Licensed to the Apache Software Foundation (ASF) under one or more 3 | * contributor license agreements. See the NOTICE file distributed with 4 | * this work for additional information regarding copyright ownership. 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 6 | * (the "License"); you may not use this file except in compliance with 7 | * the License. You may obtain a copy of the License at 8 | * 9 | * http://www.apache.org/licenses/LICENSE-2.0 10 | * 11 | * Unless required by applicable law or agreed to in writing, software 12 | * distributed under the License is distributed on an "AS IS" BASIS, 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 | * See the License for the specific language governing permissions and 15 | * limitations under the License. 16 | */ 17 | package org.apache.spark.mllib.stat.test 18 | 19 | import breeze.linalg.max 20 | import org.apache.commons.math3.distribution.NormalDistribution 21 | import org.apache.commons.math3.exception.{ConvergenceException, MaxCountExceededException, NoDataException, NullArgumentException} 22 | import org.apache.commons.math3.stat.ranking.{NaNStrategy, NaturalRanking, TiesStrategy} 23 | import org.apache.commons.math3.util.FastMath 24 | import org.apache.spark.rdd.RDD 25 | 26 | /** 27 | * An implementation of the Mann-Whitney U test (also called Wilcoxon rank-sum test). 28 | * 29 | */ 30 | object MannWhitneyUTest { 31 | 32 | 33 | /** 34 | * Computes the Mann-Whitney 36 | * U statistic comparing mean for two independent samples possibly of 37 | * different length. 38 | * This statistic can be used to perform a Mann-Whitney U test evaluating 39 | * the null hypothesis that the two independent samples has equal mean. 40 | * 41 | * @param x the first sample 42 | * @param y the second sample 43 | * @return Mann-Whitney U statistic (maximum of Ux and Uy) 44 | */ 45 | def mannWhitneyU(x: RDD[Double], y: RDD[Double]): Double = { 46 | val zz = x.union(y) 47 | val originalPositions = zz.zipWithIndex().sortByKey().map(_._2) // original positions sorted 48 | val rank = originalPositions.zipWithIndex() // original position and rank 49 | val xLength = x.count() 50 | val yLength = y.count() 51 | val sumRankX = rank.filter( p => p._1 < xLength).map(_._2).sum() + xLength 52 | 53 | val U1: Double = sumRankX - (xLength * (xLength + 1)) / 2 54 | val U2: Double = xLength.toLong * yLength - U1 55 | return math.max(U1, U2) 56 | } 57 | 58 | /** 59 | * @param Umin smallest Mann-Whitney U value 60 | * @param n1 number of subjects in first sample 61 | * @param n2 number of subjects in second sample 62 | * @return two-sided asymptotic p-value 63 | */ 64 | private def calculateAsymptoticPValue(Umin: Double, n1: Long, n2: Long): Double = { 65 | val n1n2prod: Long = n1.toLong * n2 66 | val EU: Double = n1n2prod / 2.0 67 | val VarU: Double = n1n2prod * (n1 + n2 + 1) / 12.0 68 | val z: Double = (Umin - EU) / FastMath.sqrt(VarU) 69 | val standardNormal: NormalDistribution = new NormalDistribution(null, 0, 1) 70 | return 2 * standardNormal.cumulativeProbability(z) 71 | } 72 | 73 | /** 74 | * Returns the asymptotic observed significance level, or 76 | * p-value, associated with a Mann-Whitney 78 | * U statistic comparing mean for two independent samples. 79 | * 80 | * @param x the first sample 81 | * @param y the second sample 82 | * @return asymptotic p-value 83 | */ 84 | 85 | def mannWhitneyUTest(x: RDD[Double], y: RDD[Double]): Double = { 86 | val Umax: Double = mannWhitneyU(x, y) 87 | val Umin: Double = x.count() * y.count() - Umax 88 | return calculateAsymptoticPValue(Umin, x.count(), y.count()) 89 | } 90 | } 91 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. 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