在spark mllib 1.1加入版本stat包，其中包括一些统计数据有关的功能。本文分析中卡方检验和实施的主要原则：

 

一个、根本

　　在stat包实现Pierxunka方检验，它包括以下类别

　　　　（1）适配度检验（Goodness of Fit test）：验证一组观察值的次数分配是否异于理论上的分配。

　　　　（2）独立性检验（independence test） ：验证从两个变量抽出的配对观察值组是否互相独立（比如：每次都从A国和B国各抽一个人，看他们的反应是否与国籍无关）

　　计算公式：

　　　　当中O表示观測值，E表示期望值

　　具体原理能够參考：

 

二、java api调用example

　　

 

三、源代码分析

　　1、外部api

　　　　通过Statistics类提供了4个外部接口　　

// Goodness of Fit testdef chiSqTest(observed: Vector, expected: Vector): ChiSqTestResult = {    ChiSqTest.chiSquared(observed, expected)  }//Goodness of Fit testdef chiSqTest(observed: Vector): ChiSqTestResult = ChiSqTest.chiSquared(observed)//independence testdef chiSqTest(observed: Matrix): ChiSqTestResult = ChiSqTest.chiSquaredMatrix(observed)//independence testdef chiSqTest(data: RDD[LabeledPoint]): Array[ChiSqTestResult] = {    ChiSqTest.chiSquaredFeatures(data)}

　　2、Goodness of Fit test实现

　　这个比較简单。关键是依据(observed-expected)²/expected计算卡方值

/*   * Pearon's goodness of fit test on the input observed and expected counts/relative frequencies.   * Uniform distribution is assumed when `expected` is not passed in.   */  def chiSquared(observed: Vector,      expected: Vector = Vectors.dense(Array[Double]()),      methodName: String = PEARSON.name): ChiSqTestResult = {    // Validate input arguments    val method = methodFromString(methodName)    if (expected.size != 0 && observed.size != expected.size) {      throw new IllegalArgumentException("observed and expected must be of the same size.")    }    val size = observed.size    if (size > 1000) {      logWarning("Chi-squared approximation may not be accurate due to low expected frequencies "        + s" as a result of a large number of categories: $size.")    }    val obsArr = observed.toArray　　// 假设expected值没有设置，默认取1.0 / size    val expArr = if (expected.size == 0) Array.tabulate(size)(_ => 1.0 / size) else expected.toArray　　/ 假设expected、observed值都必需要大于1    if (!obsArr.forall(_ >= 0.0)) {      throw new IllegalArgumentException("Negative entries disallowed in the observed vector.")    }    if (expected.size != 0 && ! expArr.forall(_ >= 0.0)) {      throw new IllegalArgumentException("Negative entries disallowed in the expected vector.")    }    // Determine the scaling factor for expected    val obsSum = obsArr.sum    val expSum = if (expected.size == 0.0) 1.0 else expArr.sum    val scale = if (math.abs(obsSum - expSum) < 1e-7) 1.0 else obsSum / expSum    // compute chi-squared statistic    val statistic = obsArr.zip(expArr).foldLeft(0.0) { case (stat, (obs, exp)) =>      if (exp == 0.0) {        if (obs == 0.0) {          throw new IllegalArgumentException("Chi-squared statistic undefined for input vectors due"            + " to 0.0 values in both observed and expected.")        } else {          return new ChiSqTestResult(0.0, size - 1, Double.PositiveInfinity, PEARSON.name,            NullHypothesis.goodnessOfFit.toString)        }      }　　// 计算(observed-expected)2/expected      if (scale == 1.0) {        stat + method.chiSqFunc(obs, exp)      } else {        stat + method.chiSqFunc(obs, exp * scale)      }    }    val df = size - 1    val pValue = chiSquareComplemented(df, statistic)    new ChiSqTestResult(pValue, df, statistic, PEARSON.name, NullHypothesis.goodnessOfFit.toString)  }

　　3、independence test实现

　　　　先通过以下的公式计算expected值，矩阵共同拥有 r 行 c 列

　　　　　

　　　　然后依据(observed-expected)²/expected计算卡方值

/*   * Pearon's independence test on the input contingency matrix.   * TODO: optimize for SparseMatrix when it becomes supported.   */  def chiSquaredMatrix(counts: Matrix, methodName:String = PEARSON.name): ChiSqTestResult = {    val method = methodFromString(methodName)    val numRows = counts.numRows    val numCols = counts.numCols    // get row and column sums    val colSums = new Array[Double](numCols)    val rowSums = new Array[Double](numRows)    val colMajorArr = counts.toArray    var i = 0    while (i < colMajorArr.size) {      val elem = colMajorArr(i)      if (elem < 0.0) {        throw new IllegalArgumentException("Contingency table cannot contain negative entries.")      }      colSums(i / numRows) += elem      rowSums(i % numRows) += elem      i += 1    }    val total = colSums.sum    // second pass to collect statistic    var statistic = 0.0    var j = 0    while (j < colMajorArr.size) {      val col = j / numRows      val colSum = colSums(col)      if (colSum == 0.0) {        throw new IllegalArgumentException("Chi-squared statistic undefined for input matrix due to"          + s"0 sum in column [$col].")      }      val row = j % numRows      val rowSum = rowSums(row)      if (rowSum == 0.0) {        throw new IllegalArgumentException("Chi-squared statistic undefined for input matrix due to"          + s"0 sum in row [$row].")      }      val expected = colSum * rowSum / total      statistic += method.chiSqFunc(colMajorArr(j), expected)      j += 1    }    val df = (numCols - 1) * (numRows - 1)    val pValue = chiSquareComplemented(df, statistic)    new ChiSqTestResult(pValue, df, statistic, methodName, NullHypothesis.independence.toString)  }

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