public void TTestConstructorTest()
{
// mean = 0.5, var = 1
double[] sample =
{
-0.849886940156521, 3.53492346633185, 1.22540422494611, 0.436945126810344, 1.21474290382610,
0.295033941700225, 0.375855651783688, 1.98969760778547, 1.90903448980048, 1.91719241342961
};
// Null Hypothesis: Values are equal
// Alternative : Values are different
double hypothesizedMean = 0;
OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsDifferentFromHypothesis;
TTest target = new TTest(sample, hypothesizedMean, hypothesis);
Assert.AreEqual(3.1254485381338246, target.Statistic);
Assert.AreEqual(OneSampleHypothesis.ValueIsDifferentFromHypothesis, target.Hypothesis);
Assert.AreEqual(DistributionTail.TwoTail, target.Tail);
Assert.AreEqual(0.012210924322697769, target.PValue);
Assert.IsTrue(target.Significant);
// Null hypothesis: value is smaller than hypothesis
// Alternative : value is greater than hypothesis
// If the null hypothesis states that the population parameter is less
// than zero (or a constant), the z-score that rejects the null is always
// positive and greater than the score set for the rejection condition.
hypothesis = OneSampleHypothesis.ValueIsGreaterThanHypothesis;
target = new TTest(sample, hypothesizedMean, hypothesis);
// z-score is positive:
Assert.AreEqual(3.1254485381338246, target.Statistic);
Assert.AreEqual(OneSampleHypothesis.ValueIsGreaterThanHypothesis, target.Hypothesis); // right tail
Assert.AreEqual(DistributionTail.OneUpper, target.Tail); // right tail
Assert.AreEqual(0.0061054621613488846, target.PValue);
Assert.IsTrue(target.Significant); // null should be rejected
// Null hypothesis: value is greater than hypothesis
// Alternative: value is smaller than hypothesis
// If the null hypothesis states that the population parameter is
// greater than zero (or a constant), the z-score that rejects the
// null is always negative and less than the score set for the
// rejection condition.
hypothesis = OneSampleHypothesis.ValueIsSmallerThanHypothesis;
target = new TTest(sample, hypothesizedMean, hypothesis);
// z-score is positive:
Assert.AreEqual(3.1254485381338246, target.Statistic);
Assert.AreEqual(OneSampleHypothesis.ValueIsSmallerThanHypothesis, target.Hypothesis); // left tail
Assert.AreEqual(DistributionTail.OneLower, target.Tail); // left tail
Assert.AreEqual(0.99389453783865112, target.PValue);
Assert.IsFalse(target.Significant); // null cannot be rejected
}
public void PValueToStatisticTest()
{
double df = 2.6;
double p = 0.05;
double t = 0;
{
TTest target = new TTest(t, df, OneSampleHypothesis.ValueIsDifferentFromHypothesis);
Assert.AreEqual(DistributionTail.TwoTail, target.Tail);
double actual = target.PValueToStatistic(p);
double expected = 3.4782;
Assert.AreEqual(expected, actual, 1e-4);
}
{
TTest target = new TTest(t, df, OneSampleHypothesis.ValueIsSmallerThanHypothesis);
Assert.AreEqual(DistributionTail.OneLower, target.Tail);
double actual = target.PValueToStatistic(p);
double expected = -2.5086;
Assert.AreEqual(expected, actual, 1e-4);
}
{
TTest target = new TTest(t, df, OneSampleHypothesis.ValueIsGreaterThanHypothesis);
Assert.AreEqual(DistributionTail.OneUpper, target.Tail);
double actual = target.PValueToStatistic(p);
double expected = 2.5086;
Assert.AreEqual(expected, actual, 1e-4);
}
p = 0.95;
{
TTest target = new TTest(t, df, OneSampleHypothesis.ValueIsDifferentFromHypothesis);
Assert.AreEqual(DistributionTail.TwoTail, target.Tail);
double actual = target.PValueToStatistic(p);
double expected = 0.0689;
Assert.AreEqual(expected, actual, 1e-4);
}
{
TTest target = new TTest(t, df, OneSampleHypothesis.ValueIsSmallerThanHypothesis);
Assert.AreEqual(DistributionTail.OneLower, target.Tail);
double actual = target.PValueToStatistic(p);
double expected = 2.5086;
Assert.AreEqual(expected, actual, 1e-4);
}
{
TTest target = new TTest(t, df, OneSampleHypothesis.ValueIsGreaterThanHypothesis);
Assert.AreEqual(DistributionTail.OneUpper, target.Tail);
double actual = target.PValueToStatistic(p);
double expected = -2.5086;
Assert.AreEqual(expected, actual, 1e-4);
}
}
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);
}
}
public void StatisticToPValueTest()
{
double df = 2.2;
double t = 1.96;
{
TTest target = new TTest(t, df, OneSampleHypothesis.ValueIsDifferentFromHypothesis);
Assert.AreEqual(DistributionTail.TwoTail, target.Tail);
double actual = target.StatisticToPValue(t);
double expected = 0.1773;
Assert.AreEqual(expected, actual, 1e-4);
}
{
TTest target = new TTest(t, df, OneSampleHypothesis.ValueIsSmallerThanHypothesis);
Assert.AreEqual(DistributionTail.OneLower, target.Tail);
double actual = target.StatisticToPValue(t);
double expected = 0.9113;
Assert.AreEqual(expected, actual, 1e-4);
}
{
TTest target = new TTest(t, df, OneSampleHypothesis.ValueIsGreaterThanHypothesis);
Assert.AreEqual(DistributionTail.OneUpper, target.Tail);
double actual = target.StatisticToPValue(t);
double expected = 0.0887;
Assert.AreEqual(expected, actual, 1e-4);
}
t = -1.96;
{
TTest target = new TTest(t, df, OneSampleHypothesis.ValueIsDifferentFromHypothesis);
Assert.AreEqual(DistributionTail.TwoTail, target.Tail);
double actual = target.StatisticToPValue(t);
double expected = 0.1773;
Assert.AreEqual(expected, actual, 1e-4);
}
{
TTest target = new TTest(t, df, OneSampleHypothesis.ValueIsSmallerThanHypothesis);
Assert.AreEqual(DistributionTail.OneLower, target.Tail);
double actual = target.StatisticToPValue(t);
double expected = 0.0887;
Assert.AreEqual(expected, actual, 1e-4);
}
{
TTest target = new TTest(t, df, OneSampleHypothesis.ValueIsGreaterThanHypothesis);
Assert.AreEqual(DistributionTail.OneUpper, target.Tail);
double actual = target.StatisticToPValue(t);
double expected = 0.9113;
Assert.AreEqual(expected, actual, 1e-4);
}
}
public void TTestConstructorTest2()
{
// Consider a sample generated from a Gaussian
// distribution with mean 0.5 and unit variance.
double[] sample =
{
-0.849886940156521, 3.53492346633185, 1.22540422494611, 0.436945126810344, 1.21474290382610,
0.295033941700225, 0.375855651783688, 1.98969760778547, 1.90903448980048, 1.91719241342961
};
// One may rise the hypothesis that the mean of the sample is not
// significantly different from zero. In other words, the fact that
// this particular sample has mean 0.5 may be attributed to chance.
double hypothesizedMean = 0;
// Create a T-Test to check this hypothesis
TTest test = new TTest(sample, hypothesizedMean,
OneSampleHypothesis.ValueIsDifferentFromHypothesis);
// Check if the mean is significantly different
Assert.AreEqual(true, test.Significant);
// Now, we would like to test if the sample mean is
// significantly greater than the hypothesized zero.
// Create a T-Test to check this hypothesis
TTest greater = new TTest(sample, hypothesizedMean,
OneSampleHypothesis.ValueIsGreaterThanHypothesis);
// Check if the mean is significantly larger
Assert.AreEqual(true, greater.Significant);
// Now, we would like to test if the sample mean is
// significantly smaller than the hypothesized zero.
// Create a T-Test to check this hypothesis
TTest smaller = new TTest(sample, hypothesizedMean,
OneSampleHypothesis.ValueIsSmallerThanHypothesis);
// Check if the mean is significantly smaller
Assert.AreEqual(false, smaller.Significant);
}
/// <summary>
/// Converts a given test statistic to a p-value.
/// </summary>
///
/// <param name="x">The value of the test statistic.</param>
///
/// <returns>The p-value for the given statistic.</returns>
///
public override double StatisticToPValue(double x)
{
return(TTest.StatisticToPValue(x, StatisticDistribution, Tail));
}
/// <summary>
/// Converts a given p-value to a test statistic.
/// </summary>
///
/// <param name="p">The p-value.</param>
///
/// <returns>The test statistic which would generate the given p-value.</returns>
///
public override double PValueToStatistic(double p)
{
return(TTest.PValueToStatistic(p, StatisticDistribution, Tail));
}
public void TTestConstructorTest()
{
// mean = 0.5, var = 1
double[] sample =
{
-0.849886940156521, 3.53492346633185, 1.22540422494611, 0.436945126810344, 1.21474290382610,
0.295033941700225, 0.375855651783688, 1.98969760778547, 1.90903448980048, 1.91719241342961
};
double hypothesizedMean = 0;
TTestHypotesis hypothesis = TTestHypotesis.MeanIsDifferentThanHypothesis;
TTest target = new TTest(sample, hypothesizedMean, hypothesis);
Assert.AreEqual(3.1254485381338246, target.Statistic);
Assert.AreEqual(Hypothesis.TwoTail, target.Hypothesis);
Assert.AreEqual(0.012210924322697769, target.PValue);
hypothesis = TTestHypotesis.MeanIsGreaterThanHypothesis;
target = new TTest(sample, hypothesizedMean, hypothesis);
Assert.AreEqual(3.1254485381338246, target.Statistic);
Assert.AreEqual(Hypothesis.OneUpper, target.Hypothesis); // right tail
Assert.AreEqual(0.0061054621613488846, target.PValue);
hypothesis = TTestHypotesis.MeanIsSmallerThanHypothesis;
target = new TTest(sample, hypothesizedMean, hypothesis);
Assert.AreEqual(3.1254485381338246, target.Statistic);
Assert.AreEqual(Hypothesis.OneLower, target.Hypothesis); // left tail
Assert.AreEqual(0.99389453783865112, target.PValue);
}