/// <summary>
/// Computes the power for a test with givens values of
/// <see cref="IPowerAnalysis.Effect">effect size</see> and <see cref="IPowerAnalysis.Samples">
/// number of samples</see> under <see cref="IPowerAnalysis.Size"/>.
/// </summary>
///
/// <returns>
/// The power for the test under the given conditions.
/// </returns>
///
public override void ComputePower()
{
double samples = (Samples1 * Samples2) / (double)(Samples1 + Samples2);
double Za = ZTest.PValueToStatistic(Size, Tail);
double Zb = Za - Math.Sqrt(samples) * Effect;
Power = NormalDistribution.Standard.ComplementaryDistributionFunction(Zb);
}
/// <summary>
/// Gets the recommended sample size for the test to attain
/// the power indicating in <see cref="IPowerAnalysis.Power"/> considering
/// values of <see cref="IPowerAnalysis.Effect"/> and <see cref="IPowerAnalysis.Size"/>.
/// </summary>
///
/// <returns>
/// Recommended sample size for attaining the given
/// <see cref="IPowerAnalysis.Power"/> for size effect <see cref="IPowerAnalysis.Effect"/>
/// under the given <see cref="IPowerAnalysis.Size"/>.
/// </returns>
///
public override void ComputeSamples()
{
double Za = ZTest.PValueToStatistic(Size, Tail);
double Zb = NormalDistribution.Standard
.InverseDistributionFunction(Power);
double n = (Za + Zb) / Effect;
Samples = n * n;
}
/// <summary>
/// Computes the minimum detectable effect size for the test
/// considering the power given in <see cref="IPowerAnalysis.Power"/>, the
/// number of samples in <see cref="IPowerAnalysis.Samples"/> and the significance
/// level <see cref="IPowerAnalysis.Size"/>.
/// </summary>
///
/// <returns>
/// The minimum detectable <see cref="IPowerAnalysis.Effect">effect
/// size</see> for the test under the given conditions.
/// </returns>
///
public override void ComputeEffect()
{
double Za = ZTest.PValueToStatistic(Size, Tail);
double Zb = NormalDistribution.Standard
.InverseDistributionFunction(Power);
double n = Math.Sqrt(Samples1 + Samples2);
double d = (Za + Zb) / n;
Effect = d;
}
public void PValueToStatisticTest()
{
double p = 0.05;
double z = 0;
{
ZTest target = new ZTest(z, OneSampleHypothesis.ValueIsDifferentFromHypothesis);
Assert.AreEqual(DistributionTail.TwoTail, target.Tail);
double actual = target.PValueToStatistic(p);
double expected = 1.96;
Assert.AreEqual(expected, actual, 0.01);
}
{
ZTest target = new ZTest(z, OneSampleHypothesis.ValueIsSmallerThanHypothesis);
Assert.AreEqual(DistributionTail.OneLower, target.Tail);
double actual = target.PValueToStatistic(p);
double expected = -1.6449;
Assert.AreEqual(expected, actual, 1e-4);
}
{
ZTest target = new ZTest(z, OneSampleHypothesis.ValueIsGreaterThanHypothesis);
Assert.AreEqual(DistributionTail.OneUpper, target.Tail);
double actual = target.PValueToStatistic(p);
double expected = 1.6449;
Assert.AreEqual(expected, actual, 1e-4);
}
p = 0.95;
{
ZTest target = new ZTest(z, OneSampleHypothesis.ValueIsDifferentFromHypothesis);
Assert.AreEqual(DistributionTail.TwoTail, target.Tail);
double actual = target.PValueToStatistic(p);
double expected = 0.0627;
Assert.AreEqual(expected, actual, 1e-5);
}
{
ZTest target = new ZTest(z, OneSampleHypothesis.ValueIsSmallerThanHypothesis);
Assert.AreEqual(DistributionTail.OneLower, target.Tail);
double actual = target.PValueToStatistic(p);
double expected = 1.6449;
Assert.AreEqual(expected, actual, 1e-4);
}
{
ZTest target = new ZTest(z, OneSampleHypothesis.ValueIsGreaterThanHypothesis);
Assert.AreEqual(DistributionTail.OneUpper, target.Tail);
double actual = target.PValueToStatistic(p);
double expected = -1.6449;
Assert.AreEqual(expected, actual, 1e-4);
}
}