public void TTestPowerAnalysisConstructorTest7()
{
// When creating a power analysis, we have three things we can
// change. We can always freely configure two of those things
// and then ask the analysis to give us the third.
var analysis = new TTestPowerAnalysis(OneSampleHypothesis.ValueIsDifferentFromHypothesis);
// Those are:
double e = analysis.Effect; // the test's minimum detectable effect size
double n = analysis.Samples; // the number of samples in the test
double p = analysis.Power; // the probability of committing a type-2 error
// Let's set the desired effect size and the
// number of samples so we can get the power
analysis.Effect = 0.2; // we would like to detect at least 0.2 std. dev. apart
analysis.Samples = 60; // we would like to use at most 60 samples
analysis.ComputePower(); // what will be the power of this test?
double power = analysis.Power; // The power is going to be 0.33 (or 33%)
// Let's set the desired power and the number
// of samples so we can get the effect size
analysis.Power = 0.8; // we would like to create a test with 80% power
analysis.Samples = 60; // we would like to use at most 60 samples
analysis.ComputeEffect(); // what would be the minimum effect size we can detect?
double effect = analysis.Effect; // The effect will be 0.36 standard deviations.
// Let's set the desired power and the effect
// size so we can get the number of samples
analysis.Power = 0.8; // we would like to create a test with 80% power
analysis.Effect = 0.2; // we would like to detect at least 0.2 std. dev. apart
analysis.ComputeSamples();
double samples = analysis.Samples; // We would need around 199 samples.
Assert.AreEqual(198.15082094251142, samples, 1e-10);
Assert.AreEqual(0.36770431608203374, effect);
Assert.AreEqual(0.33167864622935495, power);
}
public void PowerTest()
{
int samples = 5;
double stdDev = 1;
double mean = 0.2;
{
TTest test = new TTest(mean, stdDev: stdDev, samples: samples,
alternate: OneSampleHypothesis.ValueIsSmallerThanHypothesis);
Assert.AreEqual(4, test.StatisticDistribution.DegreesOfFreedom);
Assert.AreEqual(0.02138791, test.Analysis.Power, 1e-6);
Assert.AreEqual(0.2, test.Analysis.Effect);
Assert.AreEqual(5, test.Analysis.Samples);
TTestPowerAnalysis target = (TTestPowerAnalysis)test.Analysis;
target.Power = 0.6;
target.ComputeSamples();
Assert.IsTrue(Double.IsNaN(target.Samples));
Assert.AreEqual(0.6, target.Power, 1e-6);
Assert.AreEqual(0.2, target.Effect);
}
{
TTest test = new TTest(mean, stdDev: stdDev, samples: samples,
alternate: OneSampleHypothesis.ValueIsGreaterThanHypothesis);
Assert.AreEqual(4, test.StatisticDistribution.DegreesOfFreedom);
Assert.AreEqual(0.2, test.Analysis.Effect);
Assert.AreEqual(0.102444276600, test.Analysis.Power, 1e-6);
Assert.AreEqual(5, test.Analysis.Samples, 1e-4);
TTestPowerAnalysis target = (TTestPowerAnalysis)test.Analysis;
target.Power = 0.6;
target.ComputeSamples();
Assert.AreEqual(91.444828012, target.Samples, 1e-6);
Assert.AreEqual(0.6, target.Power, 1e-6);
Assert.AreEqual(0.2, target.Effect);
}
{
TTest test = new TTest(mean, stdDev: stdDev, samples: samples,
alternate: OneSampleHypothesis.ValueIsDifferentFromHypothesis);
Assert.AreEqual(4, test.StatisticDistribution.DegreesOfFreedom);
Assert.AreEqual(0.2, test.Analysis.Effect);
Assert.AreEqual(0.06426957, test.Analysis.Power, 1e-6);
Assert.AreEqual(5, test.Analysis.Samples, 1e-4);
TTestPowerAnalysis target = (TTestPowerAnalysis)test.Analysis;
target.Power = 0.6;
target.ComputeSamples();
Assert.AreEqual(124.3957558, target.Samples, 1e-6);
Assert.AreEqual(0.6, target.Power, 1e-6);
Assert.AreEqual(0.2, target.Effect);
}
}