package com.imsl.test.example.stat;

import com.imsl.stat.ANCOVA;

/**
 * <p>
 * Performs one-way analysis of covariance and tests for parallelism. </p>
 *
 * <p>
 * This example fits a one-way analysis of covariance model and performs a test
 * for parallelism using data discussed by Snedecor and Cochran (1967, Table
 * 14.8.1, pages 438-443). The responses are weight gains (in pounds per day) of
 * 40 pigs for four groups of pigs under varying treatments. Two
 * covariates-initial age (in days) and initial weight (in pounds) are used. For
 * each treatment, there are 10 pigs. Only the first 5 pigs from each treatment
 * are shown here.</p>
 *
 * <table align="center" border="1" width="540">
 * <tr>
 * <th colspan="3">Treatment 1</th>
 * <th colspan="3">Treatment 2</th>
 * <th colspan="3">Treatment 3</th>
 * <th colspan="3">Treatment 4</th>
 * </tr>
 * <tr>
 * <th>Age</th>
 * <th>Wt.</th>
 * <th>Gain</th>
 * <th>Age</th>
 * <th>Wt.</th>
 * <th>Gain</th>
 * <th>Age</th>
 * <th>Wt.</th>
 * <th>Gain</th>
 * <th>Age</th>
 * <th>Wt.</th>
 * <th>Gain</th>
 * </tr>
 * <tr align="center">
 * <td>78</td>
 * <td>61</td>
 * <td>1.4</td>
 * <td>78</td>
 * <td>74</td>
 * <td>1.61</td>
 * <td>78</td>
 * <td>80</td>
 * <td>1.67</td>
 * <td>77</td>
 * <td>62</td>
 * <td>1.4</td>
 * </tr>
 * <tr align="center">
 * <td>90</td>
 * <td>59</td>
 * <td>1.79</td>
 * <td>99</td>
 * <td>75</td>
 * <td>1.31</td>
 * <td>83</td>
 * <td>61</td>
 * <td>1.41</td>
 * <td>71</td>
 * <td>55</td>
 * <td>1.47</td>
 * </tr>
 * <tr align="center">
 * <td>94</td>
 * <td>76</td>
 * <td>1.72</td>
 * <td>80</td>
 * <td>64</td>
 * <td>1.12</td>
 * <td>79</td>
 * <td>62</td>
 * <td>1.73</td>
 * <td>78</td>
 * <td>62</td>
 * <td>1.37</td>
 * </tr>
 * <tr align="center">
 * <td>71</td>
 * <td>50</td>
 * <td>1.47</td>
 * <td>75</td>
 * <td>48</td>
 * <td>1.35</td>
 * <td>70</td>
 * <td>47</td>
 * <td>1.23</td>
 * <td>70</td>
 * <td>43</td>
 * <td>1.15</td>
 * </tr>
 * <tr align="center">
 * <td>99</td>
 * <td>61</td>
 * <td>1.26</td>
 * <td>94</td>
 * <td>62</td>
 * <td>1.29</td>
 * <td>85</td>
 * <td>59</td>
 * <td>1.49</td>
 * <td>95</td>
 * <td>57</td>
 * <td>1.22</td>
 * </tr>
 * </table>
 * <p>
 * For these data, the test for non-parallelism is not statistically significant
 * (p = 0.901). The one-way analysis of covariance test for the treatment means
 * adjusted for the covariates, assuming parallel slopes, is statistically
 * significant at a stated significance level of
 * \(\alpha = 0.05\), (p = 0.04931). Multiple comparisons can
 * be done using the least significant difference approach of comparing each
 * pair of treatment groups with the two-sample student-t test. Since the
 * adjusted means in the one-way analysis of covariance are correlated, the
 * standard error for these comparisons must be computed using the variances and
 * covariances in covm. The standard errors for these comparisons are fairly
 * similar ranging from 0.0630 to 0.0638. The Student's t comparisons identify
 * differences between groups 1 and 2, and 1 and 4 as being statistically
 * significant with p-values of 0.01225 and 0.03854 respectively.</p>
 *
 * @see <a href="ANCOVAEx2.java">Code</a>
 * @see <a href="doc-files/ANCOVAEx2.out">Output</a>
 */
public class ANCOVAEx2 {

    public static void main(String[] args) {
        int j;
        int ngroup = 4;
        double x1[][] = {
            {78.0, 90.0, 94.0, 71.0, 99.0, 80.0, 83.0, 75.0, 62.0, 67.0},
            {78.0, 99.0, 80.0, 75.0, 94.0, 91.0, 75.0, 63.0, 62.0, 67.0},
            {78.0, 83.0, 79.0, 70.0, 85.0, 83.0, 71.0, 66.0, 67.0, 67.0},
            {77.0, 71.0, 78.0, 70.0, 95.0, 96.0, 71.0, 63.0, 62.0, 67.0}
        };
        double x2[][] = {
            {61.0, 59.0, 76.0, 50.0, 61.0, 54.0, 57.0, 45.0, 41.0, 40.0},
            {74.0, 75.0, 64.0, 48.0, 62.0, 42.0, 52.0, 43.0, 50.0, 40.0},
            {80.0, 61.0, 62.0, 47.0, 59.0, 42.0, 47.0, 42.0, 40.0, 40.0},
            {62.0, 55.0, 62.0, 43.0, 57.0, 51.0, 41.0, 40.0, 45.0, 39.0}
        };
        double y[][] = {
            {1.40, 1.79, 1.72, 1.47, 1.26, 1.28, 1.34, 1.55, 1.57, 1.26},
            {1.61, 1.31, 1.12, 1.35, 1.29, 1.24, 1.29, 1.43, 1.29, 1.26},
            {1.67, 1.41, 1.73, 1.23, 1.49, 1.22, 1.39, 1.39, 1.56, 1.36},
            {1.40, 1.47, 1.37, 1.15, 1.22, 1.48, 1.31, 1.27, 1.22, 1.36}
        };
        double x[][][] = {x1, x2};
        /* setup covariate input matrix */

        ANCOVA awc = new ANCOVA(y, x);

        double testpl[] = awc.compute();
        double aov[] = awc.getANCOVA();
        double adjAov[] = awc.getAdjustedANOVA();
        double xymean[][] = awc.getMeans();
        double covm[][] = awc.getVarCovAdjustedMeans();

        System.out.println("\n           * * * 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   "
                + "%5.3f\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]);
        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      %f     %f    %f    %5.4f\n",
                aov[0], aov[3], aov[6], aov[8], aov[9]);
        System.out.printf("Error   %3.0f      %f     %f      \n", aov[1],
                aov[4], aov[7]);
        System.out.printf("Total   %3.0f      %f  \n\n\n", aov[2], aov[5]);
        System.out.println("         * * * Adjusted Analysis of Variance  * "
                + "* *\n");
        System.out.println("                                Sum of        "
                + "F     Prob of");
        System.out.println("Source                    DF    Squares      "
                + "Test   Larger F");
        System.out.printf("Groups after Covariates %3.0f   %10.2f    %5.2f   "
                + " %7.5f\n", adjAov[0], adjAov[2], adjAov[4], adjAov[6]);
        System.out.printf("Covariates after Groups %3.0f   %10.2f    %5.2f   "
                + " %7.5f\n\n\n", adjAov[1], adjAov[3], adjAov[5], adjAov[7]);
        System.out.println("           * * * Group Means * * *\n");
        System.out.println("GROUP  | Unadjusted   |  Adjusted |  Std. Error");
        for (int i = 0; i < ngroup; i++) {
            double se = Math.sqrt(covm[i][i]);
            System.out.printf("  %d    |   %5.4f     |   %5.4f  |   %7.4f\n",
                    i + 1, xymean[i][ngroup - 1], xymean[i][ngroup], se);
        }
        System.out.println("\n\n      * * * Student-t Multiple Comparisons * "
                + "* *\n");
        System.out.println(" Groups  |    Diff   | Std. Error | Student-t | "
                + "P-Value");
        for (int i = 0; i < ngroup - 1; i++) {
            for (j = i + 1; j < ngroup; j++) {
                double delta = xymean[i][ngroup] - xymean[j][ngroup];
                double se = Math.sqrt(covm[i][i] + covm[j][j] - 2.0
                        * covm[i][j]);
                double t = delta / se;
                double df = xymean[i][0] + xymean[j][0] - 2;
                double pvalue = 1.0 - com.imsl.stat.Cdf.studentsT(t, df);
                System.out.printf(" %d vs %d  |  %7.4f  |  %7.4f   | %7.3f   "
                        + "| %7.5f\n", i + 1, j + 1, delta, se, t, pvalue);
            }
        }
    }
}