public void OneWayAnovaConstructorTest()
{
// The following is the same example given in Wikipedia's page for the
// F-Test [1]. Suppose one would like to test the effect of three levels
// of a fertilizer on plant growth.
// To achieve this goal, an experimenter has divided a set of 18 plants on
// three groups, 6 plants each. Each group has received different levels of
// the fertilizer under question.
// After some months, the experimenter registers the growth for each plant.
double[][] samples =
{
new double[] { 6, 8, 4, 5, 3, 4 }, // records for the first group
new double[] { 8, 12, 9, 11, 6, 8 }, // records for the second group
new double[] { 13, 9, 11, 8, 7, 12 }, // records for the third group
};
// Now, he would like to test whether the different fertilizer levels has
// indeed caused any effect in plant growth. In other words, he would like
// to test if the three groups are indeed significantly different.
// To do it, he runs an ANOVA test:
OneWayAnova anova = new OneWayAnova(samples);
// After the Anova object has been created, one can display its findings
// in the form of a standard ANOVA table by binding anova.Table to a
// DataGridView or any other display object supporting data binding. To
// illustrate, we could use Accord.NET's DataGridBox to inspect the
// table's contents.
// Accord.Controls.DataGridBox.Show(anova.Table);
// The p-level for the analysis is about 0.002, meaning the test is
// significant at the 5% significance level. The experimenter would
// thus reject the null hypothesis, concluding there is a strong
// evidence that the three groups are indeed different. Assuming the
// experiment was correctly controlled, this would be an indication
// that the fertilizer does indeed affect plant growth.
// [1] http://en.wikipedia.org/wiki/F_test
Assert.AreEqual(anova.Table.Count, 3);
Assert.AreEqual("Between-Groups", anova.Table[0].Source);
Assert.AreEqual(84, anova.Table[0].SumOfSquares); // Sb
Assert.AreEqual(2, anova.Table[0].DegreesOfFreedom); // df
Assert.AreEqual(42, anova.Table[0].MeanSquares); // MSb
Assert.AreEqual(9.264705882352942, anova.Table[0].Statistic);
Assert.AreEqual(0.0023987773293928649, anova.Table[0].Significance.PValue, 1e-16);
Assert.IsFalse(double.IsNaN(anova.Table[0].Significance.PValue));
Assert.AreEqual("Within-Groups", anova.Table[1].Source);
Assert.AreEqual(68, anova.Table[1].SumOfSquares); // Sw
Assert.AreEqual(15, anova.Table[1].DegreesOfFreedom); // df
Assert.AreEqual(4.5333333333333332, anova.Table[1].MeanSquares); // MSw
Assert.IsNull(anova.Table[1].Statistic);
Assert.IsNull(anova.Table[1].Significance);
Assert.AreEqual("Total", anova.Table[2].Source);
Assert.AreEqual(152, anova.Table[2].SumOfSquares); // Sw
Assert.AreEqual(17, anova.Table[2].DegreesOfFreedom); // df
Assert.IsNull(anova.Table[2].Statistic);
Assert.IsNull(anova.Table[2].Significance);
}
