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概述

双因素方差分析指的是，对包含两个自变量的试验数据进行显著性分析。

分析方法

双因素分析的方法建立在单因素方差分析的基础上。

对于单因素分析，我们拿到的是一组数据或者一维数据，例如：

1，2，5，6，7

而双因素试验的数据是个矩阵，因为它有两个影响因素，每个因素假如分别有m和n个水平的话，组合起来，就有m*n组数据，例如：

上述表格研究的是不同湿度（25%、50%）和温度（20，25，30）对灌木直径的影响，每种处理条件有5个数据。

进行双因素方差分析时，原理是首先将所有数据混在一起，不区分来源，计算出总的变异度，然后以单因素方差分析的方法计算出每个因素的变异度，最后用总的变异度减去两个因素的变异度就是两个因素交叉影响的变异度，这样就能得出需要的三个结论：

湿度变化对直径是否有显著影响？（如果平均值变大，结论描述就是‘湿度增加是否显著增大直径’）

温度变化对直径是否有显著影响？

湿度和温度是否存在显著的交叉作用？

maven依赖

	<!-- https://mvnrepository.com/artifact/org.apache.commons/commons-math3 --><dependency><groupId>org.apache.commons</groupId><artifactId>commons-math3</artifactId><version>3.6.1</version></dependency>

代码

package com.math.statistics;import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;import JSci.maths.statistics.FDistribution;
/**** 双因素方差分析* 独立测量* @author miaoyibo**/
public class TwoWayVariance {private List<double[]> data=new ArrayList<double[]>();private int row;private int col;/**** 总变异（方差）*/private double ss_total;/**** 总的自由度*/private int free_total;/**** 所有数据总和*/private double sum;/**** 所有数据个数*/private int num;/**** 处理间变异（方差）*/private double ss_group;private int free_group;/**** 处理内变异*/private double ss_inner;private int free_inner;private double ss_row;private double ss_col;private double ss_cross;private int free_row=row-1;private int free_col=col-1;private double fValue_row;private double fValue_col;private double fValue_cross;public TwoWayVariance(List<double[]> data, int row, int col) {this.data = data;this.row = row;this.col = col;cal();}public double[] getFValues() {double[] dd=new double[3];dd[0]=fValue_row;dd[1]=fValue_col;dd[2]=fValue_cross;return dd;}public double[] getPValues() {double[] dd=new double[3];dd[0]=getPValue_Row();dd[1]=getPValue_Col();dd[2]=getPValue_Cross();return dd;}private void cal() {if(data==null||data.isEmpty()||row*col!=data.size()) {throw new NullPointerException("数据格式异常");}calStageI();calStageII();double msinner=getMSInner();free_row=row-1;free_col=col-1;double msA=ss_row/free_row;double msB=ss_col/free_col;double msAB=ss_cross/(free_group-free_row-free_col);fValue_row=msA/msinner;fValue_col=msB/msinner;fValue_cross=msAB/msinner;}private double getPValue_Row() {FDistribution fd=new FDistribution(free_row, free_inner);double cumulative = fd.cumulative(fValue_row);return (1-cumulative)*2;}private double getPValue_Col() {FDistribution fd=new FDistribution(free_col, free_inner);double cumulative = fd.cumulative(fValue_col);return (1-cumulative)*2;}private double getPValue_Cross() {FDistribution fd=new FDistribution(free_group-free_row-free_col, free_inner);double cumulative = fd.cumulative(fValue_cross);return (1-cumulative)*2;}private void calStageI() {double gsum=0;double squareSum=0;for(double[] dd:data) {double isum=0;for(int i=0;i<dd.length;i++) {sum=sum+dd[i];isum=isum+dd[i];squareSum=squareSum+dd[i]*dd[i];num++;					}gsum=(isum*isum)/dd.length+gsum;}free_total=num-1;ss_total=squareSum-((sum*sum)/num);free_group=data.size()-1;ss_group=gsum-((sum*sum)/num);ss_inner=ss_total-ss_group;free_inner=free_total-free_group;}private void calStageII() {int r=0;double s=0;int n=0;double ss=0;Map<Integer,Double> sumMap=new HashMap<Integer, Double>();Map<Integer,Integer> countMap=new HashMap<Integer, Integer>();for(double[] dd:data) {	double cs=0;for(int i=0;i<dd.length;i++) {s=s+dd[i];cs=cs+dd[i];n++;}if(sumMap.get(r)==null) {sumMap.put(r, cs);countMap.put(r, dd.length);}else {sumMap.put(r, sumMap.get(r)+cs);countMap.put(r, countMap.get(r)+dd.length);}r++;if(r==col) {ss=ss+(s*s)/n;r=0;s=0;n=0;}}ss_row=ss-((sum*sum)/num);double sm = 0;for(int key:sumMap.keySet()) {Double d1 = sumMap.get(key);Integer n1 = countMap.get(key);sm=sm+((d1*d1)/n1);}ss_col=sm-((sum*sum)/num);ss_cross=ss_group-ss_row-ss_col;}private double getMSInner() {return ss_inner/free_inner;}public List<double[]> getData() {return data;}public void setData(List<double[]> data) {this.data = data;}public int getRow() {return row;}public void setRow(int row) {this.row = row;}public int getCol() {return col;}public void setCol(int col) {this.col = col;}public double getSs_total() {return ss_total;}public void setSs_total(double ss_total) {this.ss_total = ss_total;}public int getFree_total() {return free_total;}public void setFree_total(int free_total) {this.free_total = free_total;}public double getSum() {return sum;}public void setSum(double sum) {this.sum = sum;}public int getNum() {return num;}public void setNum(int num) {this.num = num;}public double getSs_group() {return ss_group;}public void setSs_group(double ss_group) {this.ss_group = ss_group;}public int getFree_group() {return free_group;}public void setFree_group(int free_group) {this.free_group = free_group;}public double getSs_inner() {return ss_inner;}public void setSs_inner(double ss_inner) {this.ss_inner = ss_inner;}public int getFree_inner() {return free_inner;}public void setFree_inner(int free_inner) {this.free_inner = free_inner;}public double getSs_row() {return ss_row;}public void setSs_row(double ss_row) {this.ss_row = ss_row;}public double getSs_col() {return ss_col;}public void setSs_col(double ss_col) {this.ss_col = ss_col;}public double getSs_cross() {return ss_cross;}public void setSs_cross(double ss_cross) {this.ss_cross = ss_cross;}public int getFree_row() {return free_row;}public void setFree_row(int free_row) {this.free_row = free_row;}public int getFree_col() {return free_col;}public void setFree_col(int free_col) {this.free_col = free_col;}public double getfValue_row() {return fValue_row;}public void setfValue_row(double fValue_row) {this.fValue_row = fValue_row;}public double getfValue_col() {return fValue_col;}public void setfValue_col(double fValue_col) {this.fValue_col = fValue_col;}public double getfValue_cross() {return fValue_cross;}public void setfValue_cross(double fValue_cross) {this.fValue_cross = fValue_cross;}
}

Demo

	public static void main(String[] args) {List<double[]> data=new ArrayList<double[]>();double[] d1= {3,1,1,6,4};double[] d2= {2,5,9,7,7};double[] d3= {9,9,13,6,8};double[] d4= {1,2,1,1,3};double[] d5= {3,8,3,3,3};double[] d6= {2,2,2,5,2};data.add(d1);data.add(d2);data.add(d3);data.add(d4);data.add(d5);data.add(d6);TwoWayVariance tw=new TwoWayVariance(data, 2, 3);double[] fValues = tw.getFValues();double[] pValues = tw.getPValues();for(int i=0;i<=2;i++) {}System.out.println("湿度对应的F分数为："+fValues[0]+";P值为："+pValues[0]);System.out.println("温度对应的F分数为："+fValues[1]+";P值为："+pValues[1]);System.out.println("湿度和温度交叉作用对应的F分数为："+fValues[2]+";P值为："+pValues[2]);}

结果：

湿度对应的F分数为：18.75781249999998;P值为：4.5524754487313857E-4
温度对应的F分数为：7.882812499999992;P值为：0.004671659099831249
湿度和温度交叉作用对应的F分数为：4.367187499999995;P值为：0.04825210413060654