Example 2: Wilcoxon Rank Sum Test

The following example uses the same data as in example 1. Here, all the statistics are displayed.

import java.text.*;
import com.imsl.*;
import com.imsl.stat.*;

public class WilcoxonRankSumEx2 {

    public static void main(String args[]) {
        double[] x = {7.3, 6.9, 7.2, 7.8, 7.2};
        double[] y = {7.4, 6.8, 6.9, 6.7, 7.1};
        String[] labels = {
            "Wilcoxon W statistic ........................",
            "2*E(W) - W ..................................",
            "p-value ..................................... ",
            "Adjusted Wilcoxon statistic .................",
            "Adjusted 2*E(W) - W .........................",
            "Adjusted p-value ............................ ",
            "W statistics for averaged ranks..............",
            "Standard error of W (averaged ranks) ........ ",
            "Standard normal score of W (averaged ranks) . ",
            "Approximate Two-sided p-value of W .......... "
        };

        WilcoxonRankSum wilcoxon = new WilcoxonRankSum(x, y);
        NumberFormat nf = NumberFormat.getInstance();
        nf.setMinimumFractionDigits(3);

        // Turn off printing of warning messages.
        Warning.setOut(null);
        double[] exact = wilcoxon.computeExactPValues();
        double[] stat = wilcoxon.getStatistics();

        for (int i = 0; i < 7; i++) {
            System.out.println(labels[i] + " " + nf.format(stat[i]));
        }

        System.out.println("Mann-Whitney statistic ............"
                + ".......... " + nf.format(wilcoxon.getMannWhitney()));

        for (int i = 7; i < 10; i++) {
            System.out.println(labels[i] + " " + nf.format(stat[i]));
        }

        System.out.println("Exact Left-Tailed p-value ............"
                + ".......  " + nf.format(exact[0]));
        System.out.println("Exact Right-Tailed p-value ..........."
                + ".......  " + nf.format(exact[1]));
        System.out.println("Exact Two-sided p-value .............."
                + ".......  " + nf.format(exact[2]));
    }
}

Output

Wilcoxon W statistic ........................ 34.000
2*E(W) - W .................................. 21.000
p-value .....................................  0.110
Adjusted Wilcoxon statistic ................. 35.000
Adjusted 2*E(W) - W ......................... 20.000
Adjusted p-value ............................  0.075
W statistics for averaged ranks.............. 34.500
Mann-Whitney statistic ...................... 19.500
Standard error of W (averaged ranks) ........  4.758
Standard normal score of W (averaged ranks) .  1.471
Approximate Two-sided p-value of W ..........  0.141
Exact Left-Tailed p-value ...................  0.937
Exact Right-Tailed p-value ..................  0.079
Exact Two-sided p-value .....................  0.159