package com.imsl.test.example.stat;

import com.imsl.stat.ANCOVA;
import com.imsl.math.PrintMatrix;

/**
 * <p>
 *  Performs a one-way analysis of covariance.  </p>
 * <p>
 * This example fits a one-way analysis of covariance model assuming parallelism
 * using data discussed by Snedecor and Cochran (Table 14.6.1, pages 432-436).
 * The responses are concentrations of cholesterol (in mg/100 ml) in the blood
 * of two groups of women: women from Iowa and women from Nebraska. The age of a
 * woman is the single covariate. The cholesterol concentrations and ages of the
 * women according to state are shown in the following table. (There are 11 Iowa
 * women and 19 Nebraska women in the study. Only the first 5 women from each
 * state are shown here.)</p>
 *
        <table align="center" border="1" width="40%">
 * <tr>
 * <th colspan="2">Iowa</th>
 * <th colspan="2">Nebraska</th>
 * </tr>
 * <tr>
 * <th>Age</th>
 * <th>Cholesterol</th>
 * <th>Age</th>
 * <th>Cholesterol</th>
 * </tr>
 * <tr align="center">
 * <td>46</td>
 * <td>181</td>
 * <td>18</td>
 * <td>137</td>
 * </tr>
 * <tr align="center">
 * <td>52</td>
 * <td>228</td>
 * <td>44</td>
 * <td>173</td>
 * </tr>
 * <tr align="center">
 * <td>39</td>
 * <td>182</td>
 * <td>33</td>
 * <td>177</td>
 * </tr>
 * <tr align="center">
 * <td>65</td>
 * <td>249</td>
 * <td>78</td>
 * <td>241</td>
 * </tr>
 * <tr align="center">
 * <td>54</td>
 * <td>259</td>
 * <td>51</td>
 * <td>225</td>
 * </tr>
 * </table>
 * <p>
 * There is no evidence from the data to indicate that the regression lines for
 * cholesterol concentration as a function of age are not parallel for Iowa and
 * Nebraska women (p-value is 0.5425). The parallel line model suggests that
 * Nebraska women may have higher cholesterol concentrations than Iowa women.
 * The cholesterol concentrations (adjusted for age) are 195.5 for Iowa women
 * versus 224.2 for Nebraska women. The difference is 28.7 with an estimated
 * standard error of</p>
 * $$\sqrt{170.4 + 97.4 - 2(2.9)} = 16.1$$
 *
 * @see <a href="ANCOVAEx1.java">Code</a>
 * @see <a href="doc-files/ANCOVAEx1.out">Output</a>
 */
public class ANCOVAEx1 {

    public static void main(String args[]) {

        double y[][] = {
            {181.0, 228.0, 182.0, 249.0, 259.0, 201.0, 121.0, 339.0, 224.0,
                112.0, 189.0},
            {137.0, 173.0, 177.0, 241.0, 225.0, 223.0, 190.0, 257.0, 337.0,
                189.0, 214.0, 140.0, 196.0, 262.0, 261.0, 356.0, 159.0, 191.0,
                197.0}};
        double x[][][] = new double[1][2][];
        x[0][0] = new double[]{46.0, 52.0, 39.0, 65.0, 54.0, 33.0, 49.0, 76.0,
            71.0, 41.0, 58.0};
        x[0][1] = new double[]{18.0, 44.0, 33.0, 78.0, 51.0, 43.0, 44.0, 58.0,
            63.0, 19.0, 42.0, 30.0, 47.0, 58.0, 70.0, 67.0, 31.0, 21.0,
            56.0};
        ANCOVA awc = new ANCOVA(y, x);

        double testpl[] = awc.compute();
        double aov[] = awc.getANCOVA();

        System.out.println("             * * * Analysis of Variance * * *\n");
        System.out.println("                  Sum of         "
                + "Mean                Prob of");
        System.out.println("Source   DF      Squares        Square    "
                + "Overall F  Larger F");
        System.out.printf("Model  %3.0f     %10.2f      %9.2f  %2.2f      "
                + "%8.6f\n", aov[0], aov[3], aov[6], aov[8], aov[9]);
        System.out.printf("Error   %3.0f    %10.2f     %9.2f \n", aov[1],
                aov[4], aov[7]);
        System.out.printf("Total   %3.0f     %10.2f \n\n\n", aov[2], aov[5]);
        System.out.println("           * * * Test for Parallelism  * * *\n");
        System.out.println("                       Sum of     Mean     F     "
                + " Prob of");
        System.out.println("Source           DF    Squares   Square   Test   "
                + " Larger F");
        System.out.println("Extra due to");
        System.out.printf("Nonparallelism %3.0f %10.2f   %7.2f   %7.5f %5.4f\n",
                testpl[0], testpl[3], testpl[6], testpl[8], testpl[9]);
        System.out.println("Extra Assuming");
        System.out.printf("Nonparallelism  %3.0f  %10.2f  %7.2f \n", testpl[1],
                testpl[4], testpl[7]);
        System.out.println("Error Assuming");
        System.out.printf("Parallelism     %3.0f  %10.2f \n\n\n", testpl[2],
                testpl[5]);
        new PrintMatrix("XY Mean Matrix\n").print(awc.getMeans());
        new PrintMatrix("\n\nVar./Covar. Matrix of Adjusted Group Means"
                + "\n").print(awc.getVarCovAdjustedMeans());
    }
}