/// <summary>
/// Estimates the number of samples necessary to attain the
/// required power level for the given effect size.
/// </summary>
///
/// <param name="sampleSize">The number of observations in the sample.</param>
/// <param name="power">The desired power level. Default is 0.8.</param>
/// <param name="alpha">The desired significance level. Default is 0.05.</param>
/// <param name="hypothesis">The alternative hypothesis (research hypothesis) to be tested.</param>
///
/// <returns>The required number of samples.</returns>
///
public static ZTestPowerAnalysis GetEffectSize(int sampleSize, double power = 0.8, double alpha = 0.05,
OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsDifferentFromHypothesis)
{
var analysis = new ZTestPowerAnalysis(hypothesis)
{
Samples = sampleSize,
Size = alpha,
Power = power,
};
analysis.ComputeEffect();
return(analysis);
}
/// <summary>
/// Estimates the number of samples necessary to attain the
/// required power level for the given effect size.
/// </summary>
///
/// <param name="delta">The minimum detectable difference.</param>
/// <param name="standardDeviation">The difference standard deviation.</param>
/// <param name="power">The desired power level. Default is 0.8.</param>
/// <param name="alpha">The desired significance level. Default is 0.05.</param>
/// <param name="hypothesis">The alternative hypothesis (research hypothesis) to be tested.</param>
///
/// <returns>The required number of samples.</returns>
///
public static ZTestPowerAnalysis GetSampleSize(double delta,
double standardDeviation = 1, double power = 0.8, double alpha = 0.05,
OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsDifferentFromHypothesis)
{
ZTestPowerAnalysis analysis = new ZTestPowerAnalysis(hypothesis)
{
Effect = (delta) / standardDeviation,
Size = alpha,
Power = power,
};
analysis.ComputeSamples();
return(analysis);
}
public void ZTestPowerAnalysisConstructorTest1()
{
ZTestPowerAnalysis target;
double actual, expected;
target = new ZTestPowerAnalysis(OneSampleHypothesis.ValueIsDifferentFromHypothesis)
{
Effect = 0.2,
Samples = 60,
Size = 0.10,
};
target.ComputePower();
expected = 0.4618951;
actual = target.Power;
Assert.AreEqual(expected, actual, 1e-5);
target = new ZTestPowerAnalysis(OneSampleHypothesis.ValueIsSmallerThanHypothesis)
{
Effect = 0.2,
Samples = 60,
Size = 0.10,
};
target.ComputePower();
expected = 0.00232198;
actual = target.Power;
Assert.AreEqual(expected, actual, 1e-5);
target = new ZTestPowerAnalysis(OneSampleHypothesis.ValueIsGreaterThanHypothesis)
{
Effect = 0.2,
Samples = 60,
Size = 0.10,
};
target.ComputePower();
expected = 0.6055124;
actual = target.Power;
Assert.AreEqual(expected, actual, 1e-5);
}
/// <summary>
/// Estimates the number of samples necessary to attain the
/// required power level for the given effect size.
/// </summary>
///
/// <param name="sampleSize">The number of observations in the sample.</param>
/// <param name="power">The desired power level. Default is 0.8.</param>
/// <param name="alpha">The desired significance level. Default is 0.05.</param>
/// <param name="hypothesis">The alternative hypothesis (research hypothesis) to be tested.</param>
///
/// <returns>The required number of samples.</returns>
///
public static ZTestPowerAnalysis GetEffectSize(int sampleSize, double power = 0.8, double alpha = 0.05,
OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsDifferentFromHypothesis)
{
var analysis = new ZTestPowerAnalysis(hypothesis)
{
Samples = sampleSize,
Size = alpha,
Power = power,
};
analysis.ComputeEffect();
return analysis;
}
/// <summary>
/// Estimates the number of samples necessary to attain the
/// required power level for the given effect size.
/// </summary>
///
/// <param name="delta">The minimum detectable difference.</param>
/// <param name="standardDeviation">The difference standard deviation.</param>
/// <param name="power">The desired power level. Default is 0.8.</param>
/// <param name="alpha">The desired significance level. Default is 0.05.</param>
/// <param name="hypothesis">The alternative hypothesis (research hypothesis) to be tested.</param>
///
/// <returns>The required number of samples.</returns>
///
public static ZTestPowerAnalysis GetSampleSize(double delta,
double standardDeviation = 1, double power = 0.8, double alpha = 0.05,
OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsDifferentFromHypothesis)
{
ZTestPowerAnalysis analysis = new ZTestPowerAnalysis(hypothesis)
{
Effect = (delta) / standardDeviation,
Size = alpha,
Power = power,
};
analysis.ComputeSamples();
return analysis;
}
public void ZTestPowerAnalysisConstructorTest2()
{
// 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 ZTestPowerAnalysis(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 0.34 (or 34%)
// 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 197 samples.
Assert.AreEqual(196.22199335872716, samples); // 196.22199335872716
Assert.AreEqual(0.36168309642441332, effect);
Assert.AreEqual(0.34062035960875625, power);
}