数据分析之独立样本的T-Test分析
比较两个独立样本数据之间是否有显著性差异，将实验数据与标准数据对比，查看
实验结果是否符合预期。T-Test在生物数据分析，实验数据效果验证中很常见的数
据处理方法。http://www.statisticslectures.com/tables/ttable/ - T-table查找表
独立样本T-test条件：
1. 每个样本相互独立没有影响
2. 样本大致符合正态分布曲线
3. 具有同方差异性
单侧检验(one-tail Test)与双侧检验(Two-Tail Test)
基本步骤：
1.双侧检验, 条件声明 alpha值设置为0.05
根据t-table, alpha = 0.05, df = 38时, 对于t-table的值为2.0244
2. 计算自由度(Degree of Freedom)
Df = （样本1的总数 + 样本2的总数）- 2
3. 声明决策规则
如果计算出来的结果t-value的结果大于2.0244或者小于-2.0244则拒绝
4. 计算T-test统计值
5. 得出结论
如果计算结果在双侧区间之内，说明两组样本之间没有显著差异。
可重复样本的T-Test计算
同样一组数据在不同的条件下得到结果进行比对，发现是否有显著性差异，最常见
的对一个人在饮酒与不饮酒条件下驾驶车辆测试，很容易得出酒精对驾驶员有显著
影响
算法实现：
对独立样本的T-Test计算最重要的是计算各自的方差与自由度df1与df2
对可重复样本的对比t-test计算
程序实现：
package com.gloomyfish.data.mining.analysis; public class TTestAnalysisAlg { private double alpahValue = 0.05; // default private boolean dependency = false; // default public TTestAnalysisAlg() { System.out.println("t-test algorithm"); } public double getAlpahValue() { return alpahValue; } public void setAlpahValue(double alpahValue) { this.alpahValue = alpahValue; } public boolean isDependency() { return dependency; } public void setDependency(boolean dependency) { this.dependency = dependency; } public double analysis(double[] data1, double[] data2) { double tValue = 0; if (dependency) { // Repeated Measures T-test. // Uses the same sample of subjects measured on two different // occasions double diffSum = 0.0; double diffMean = 0.0; int size = Math.min(data1.length, data2.length); double[] diff = new double[size]; for(int i=0; i<size; i++) { diff[i] = data2[i] -data1[i]; diffSum += data2[i] -data1[i]; } diffMean = diffSum / size; diffSum = 0.0; for(int i=0; i<size; i++) { diffSum += Math.pow((diff[i] -diffMean), 2); } double diffSD = Math.sqrt(diffSum / (size - 1.0)); double diffSE = diffSD / Math.sqrt(size); tValue = diffMean / diffSE; } else { double means1 = 0; double means2 = 0; double sum1 = 0; double sum2 = 0; // calcuate means for (int i = 0; i < data1.length; i++) { sum1 += data1[i]; } for (int i = 0; i < data2.length; i++) { sum2 += data2[i]; } means1 = sum1 / data1.length; means2 = sum2 / data2.length; // calculate SD (Standard Deviation) sum1 = 0.0; sum2 = 0.0; for (int i = 0; i < data1.length; i++) { sum1 += Math.pow((means1 - data1[i]), 2); } for (int i = 0; i < data2.length; i++) { sum2 += Math.pow((means2 - data2[i]), 2); } double sd1 = Math.sqrt(sum1 / (data1.length - 1.0)); double sd2 = Math.sqrt(sum2 / (data2.length - 1.0)); // calculate SE (Standard Error) double se1 = sd1 / Math.sqrt(data1.length); double se2 = sd2 / Math.sqrt(data2.length); System.out.println("Data Sample one - > Means :" + means1 + " SD : " + sd1 + " SE : " + se1); System.out.println("Data Sample two - > Means :" + means2 + " SD : " + sd2 + " SE : " + se2); // degree of freedom double df1 = data1.length - 1; double df2 = data2.length - 1; // Calculate the estimated standard error of the difference double spooled2 = (sd1 * sd1 * df1 + sd2 * sd2 * df2) / (df1 + df2); double Sm12 = Math.sqrt((spooled2 / df1 + spooled2 / df2)); tValue = (means1 - means2) / Sm12; } System.out.println("t-test value : " + tValue); return tValue; } public static void main(String[] args) { int size = 10; System.out.println(Math.sqrt(size)); } }
测试程序：
package com.gloomyfish.dataming.study; import com.gloomyfish.data.mining.analysis.TTestAnalysisAlg; public class TTestDemo { public static double[] data1 = new double[]{ 35, 40, 12, 15, 21, 14, 46, 10, 28, 48, 16, 30, 32, 48, 31, 22, 12, 39, 19, 25 }; public static double[] data2 = new double[]{ 2, 27, 38, 31, 1, 19, 1, 34, 3, 1, 2, 3, 2, 1, 2, 1, 3, 29, 37, 2 }; public static void main(String[] args) { TTestAnalysisAlg tTest = new TTestAnalysisAlg(); tTest.analysis(data1, data2); tTest.setDependency(true); double[] d1 = new double[]{2, 0, 4, 2, 3}; double[] d2 = new double[]{8, 4, 11, 5, 8}; // The critical value for a one-tailed t-test with // df=4 and α=.05 is 2.132 double t = tTest.analysis(d1, d2); if(t > 2.132 || t < -2.132) { System.err.println("Very Bad!!!!"); } } }
