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首頁(yè)精彩閱讀數(shù)據(jù)分析之獨(dú)立樣本的T-Test分析_數(shù)據(jù)分析師
數(shù)據(jù)分析之獨(dú)立樣本的T-Test分析_數(shù)據(jù)分析師
2014-11-04
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數(shù)據(jù)分析之獨(dú)立樣本的T-Test分析

比較兩個(gè)獨(dú)立樣本數(shù)據(jù)之間是否有顯著性差異，將實(shí)驗(yàn)數(shù)據(jù)與標(biāo)準(zhǔn)數(shù)據(jù)對(duì)比，查看

實(shí)驗(yàn)結(jié)果是否符合預(yù)期。T-Test在生物數(shù)據(jù)分析，實(shí)驗(yàn)數(shù)據(jù)效果驗(yàn)證中很常見(jiàn)的數(shù)

據(jù)處理方法。- T-table查找表

獨(dú)立樣本T-test條件：

1.      每個(gè)樣本相互獨(dú)立沒(méi)有影響

2.      樣本大致符合正態(tài)分布曲線

3.      具有同方差異性

單側(cè)檢驗(yàn)(one-tail Test)與雙側(cè)檢驗(yàn)(Two-Tail Test)

20140420223257859

基本步驟：

1.雙側(cè)檢驗(yàn), 條件聲明  alpha值設(shè)置為0.05

根據(jù)t-table, alpha = 0.05, df = 38時(shí), 對(duì)于t-table的值為2.0244

20140420223336734

2. 計(jì)算自由度(Degree of Freedom)

Df = （樣本1的總數(shù) + 樣本2的總數(shù)）- 2

3. 聲明決策規(guī)則

如果計(jì)算出來(lái)的結(jié)果t-value的結(jié)果大于2.0244或者小于-2.0244則拒絕

4. 計(jì)算T-test統(tǒng)計(jì)值

20140420223400687

5. 得出結(jié)論

如果計(jì)算結(jié)果在雙側(cè)區(qū)間之內(nèi)，說(shuō)明兩組樣本之間沒(méi)有顯著差異。

可重復(fù)樣本的T-Test計(jì)算

同樣一組數(shù)據(jù)在不同的條件下得到結(jié)果進(jìn)行比對(duì)，發(fā)現(xiàn)是否有顯著性差異，最常見(jiàn)

的對(duì)一個(gè)人在飲酒與不飲酒條件下駕駛車(chē)輛測(cè)試，很容易得出酒精對(duì)駕駛員有顯著

影響

算法實(shí)現(xiàn)：

對(duì)獨(dú)立樣本的T-Test計(jì)算最重要的是計(jì)算各自的方差與自由度df1與df2

20140420223438750

對(duì)可重復(fù)樣本的對(duì)比t-test計(jì)算

20140420223457937

程序?qū)崿F(xiàn)：

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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
            {
                diff[i] = data2[i] -data1[i];
                diffSum += data2[i] -data1[i];
            }
            diffMean = diffSum / size;
            diffSum = 0.0;
            for(int i=0; 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);
         

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