ANOVAFactorial Example 1

Example 1: Two-way Analysis of Variance

A two-way analysis of variance is performed with balanced data discussed by Snedecor and Cochran (1967, Table 12.5.1, p. 347). The responses are the weight gains (in grams) of rats that were fed diets varying in the source (A) and level (B) of protein. The model is

$y_{ijk} = \mu + \alpha _i + \beta _j + \gamma_{ij} + \varepsilon_{ijk} \,\,\,\,\, i = 1,\;2;\;j = 1,\;2,\;3;\;k = 1,\;2,\;...\,,\;10$

where

$\sum\limits_{i = 1}^2 {\alpha _i } = 0;\sum\limits_{j = 1}^3 {\beta _j } = 0;\sum\limits_{i = 1}^2 {\gamma _{ij} } = 0 \,\,\,\, {\rm{for}}\;j = 1,\;2,\;3;\;$

and

$\sum\limits_{j = 1}^3 {\gamma _{ij} } = 0 \,\,\,\, {\rm{for}}\;j = 1,\;2$

The first responses in each cell in the two-way layout are given in the following table:

	Protein Source (A)
Protein Level (B)	Beef	Cereal	Pork
High	73, 102, 118, 104, 81, 107, 100, 87, 117, 111	98, 74, 56, 111, 95, 88, 82, 77, 86, 92	94, 79, 96, 98, 102, 102, 108, 91, 120, 105
Low	90, 76, 90, 64, 86, 51, 72, 90, 95, 78	107, 95, 97, 80, 98, 74, 74, 67, 89, 58	49, 82, 73, 86, 81, 97, 106, 70, 61, 82


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

public class ANOVAFactorialEx1 {

    public static void main(String args[]) {
        int nSubscripts = 3;
        int[] nLevels = {3, 2, 10};
        double[] y = {
            73.0, 102.0, 118.0, 104.0, 81.0, 107.0, 100.0, 87.0, 117.0, 111.0,
            90.0, 76.0, 90.0, 64.0, 86.0, 51.0, 72.0, 90.0, 95.0, 78.0,
            98.0, 74.0, 56.0, 111.0, 95.0, 88.0, 82.0, 77.0, 86.0, 92.0,
            107.0, 95.0, 97.0, 80.0, 98.0, 74.0, 74.0, 67.0, 89.0, 58.0,
            94.0, 79.0, 96.0, 98.0, 102.0, 102.0, 108.0, 91.0, 120.0, 105.0,
            49.0, 82.0, 73.0, 86.0, 81.0, 97.0, 106.0, 70.0, 61.0, 82.0
        };
        NumberFormat nf = NumberFormat.getInstance();
        nf.setMaximumFractionDigits(6);
        ANOVAFactorial af = new ANOVAFactorial(nSubscripts, nLevels, y);

        System.out.println("P-value = " + nf.format(af.compute()));
    }
}

Output

P-value = 0.002299

Link to Java source.