public void ZTestConstructorTest()
{
// This example has been gathered from the Wikipedia's page about
// the Z-Test, available from: http://en.wikipedia.org/wiki/Z-test
// Suppose there is a text comprehension test being run across
// a given demographic region. The mean score of the population
// from this entire region are around 100 points, with a standard
// deviation of 12 points.
// There is a local school, however, whose 55 students attained
// an average score in the test of only about 96 points. Would
// their scores be surprisingly that low, or could this event
// have happened due to chance?
// So we would like to check that a sample of
// 55 students with a mean score of 96 points:
int sampleSize = 55;
double sampleMean = 96;
// Was expected to have happened by chance in a population with
// an hypothesized mean of 100 points and standard deviation of
// about 12 points:
double standardDeviation = 12;
double hypothesizedMean = 100;
// So we start by creating the test:
ZTest test = new ZTest(sampleMean, standardDeviation, sampleSize,
hypothesizedMean, OneSampleHypothesis.ValueIsSmallerThanHypothesis);
// Now, we can check whether this result would be
// unlikely under a standard significance level:
bool significant = test.Significant;
// We can also check the test statistic and its P-Value
double statistic = test.Statistic;
double pvalue = test.PValue;
Assert.AreEqual(statistic, -2.47, 0.01);
Assert.AreEqual(pvalue, 0.0068, 0.001);
/* This is the one-sided p-value for the null hypothesis that the 55 students
* are comparable to a simple random sample from the population of all test-takers.
* The two-sided p-value is approximately 0.014 (twice the one-sided p-value).
*/
test = new ZTest(sampleMean, standardDeviation, sampleSize, hypothesizedMean,
OneSampleHypothesis.ValueIsDifferentFromHypothesis);
Assert.AreEqual(test.Statistic, -2.47, 0.01);
Assert.AreEqual(test.PValue, 0.014, 0.005);
}
/// <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(ZTest.StatisticToPValue(x, 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(ZTest.PValueToStatistic(p, Tail));
}
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);
}
}
public void EffectSizeTest2()
{
// Example from http://wise.cgu.edu/powermod/computing.asp
double mean = 104;
double stdDev = 10;
int samples = 25;
double hypothesizedMean = 100;
OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsDifferentFromHypothesis;
ZTest target = new ZTest(mean, stdDev, samples, hypothesizedMean, hypothesis);
ZTestPowerAnalysis power = (ZTestPowerAnalysis)target.Analysis;
power.Size = 0.05;
power.Power = 0.80;
power.ComputeEffect();
Assert.AreEqual(0.56, power.Effect, 0.001);
}
public void PowerTest2()
{
// Example from http://www.cyclismo.org/tutorial/R/power.html
double mean = 6.5;
double stdDev = 2;
int samples = 20;
double hypothesizedMean = 5;
OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsDifferentFromHypothesis;
ZTest target = new ZTest(mean, stdDev, samples, hypothesizedMean, hypothesis);
IPowerAnalysis power = target.Analysis;
Assert.AreEqual(0.918362, power.Power, 1e-6);
}
public void StatisticToPValueTest()
{
double z = 1.96;
{
ZTest target = new ZTest(z, OneSampleHypothesis.ValueIsDifferentFromHypothesis);
Assert.AreEqual(DistributionTail.TwoTail, target.Tail);
double actual = target.StatisticToPValue(z);
double expected = 0.05;
Assert.AreEqual(expected, actual, 1e-5);
}
{
ZTest target = new ZTest(z, OneSampleHypothesis.ValueIsSmallerThanHypothesis);
Assert.AreEqual(DistributionTail.OneLower, target.Tail);
double actual = target.StatisticToPValue(z);
double expected = 0.975;
Assert.AreEqual(expected, actual, 1e-5);
}
{
ZTest target = new ZTest(z, OneSampleHypothesis.ValueIsGreaterThanHypothesis);
Assert.AreEqual(DistributionTail.OneUpper, target.Tail);
double actual = target.StatisticToPValue(z);
double expected = 0.025;
Assert.AreEqual(expected, actual, 1e-5);
}
z = -1.96;
{
ZTest target = new ZTest(z, OneSampleHypothesis.ValueIsDifferentFromHypothesis);
Assert.AreEqual(DistributionTail.TwoTail, target.Tail);
double actual = target.StatisticToPValue(z);
double expected = 0.05;
Assert.AreEqual(expected, actual, 1e-5);
}
{
ZTest target = new ZTest(z, OneSampleHypothesis.ValueIsSmallerThanHypothesis);
Assert.AreEqual(DistributionTail.OneLower, target.Tail);
double actual = target.StatisticToPValue(z);
double expected = 0.025;
Assert.AreEqual(expected, actual, 1e-5);
}
{
ZTest target = new ZTest(z, OneSampleHypothesis.ValueIsGreaterThanHypothesis);
Assert.AreEqual(DistributionTail.OneUpper, target.Tail);
double actual = target.StatisticToPValue(z);
double expected = 0.975;
Assert.AreEqual(expected, actual, 1e-5);
}
}
public void SampleSizeTest1()
{
// Example from http://wise.cgu.edu/powermod/computing.asp
double mean = 104;
double stdDev = 10;
int samples = 25;
double hypothesizedMean = 100;
OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsGreaterThanHypothesis;
ZTest target = new ZTest(mean, stdDev, samples, hypothesizedMean, hypothesis);
ZTestPowerAnalysis power = (ZTestPowerAnalysis)target.Analysis;
power.Size = 0.01;
power.Power = 0.90;
power.ComputeSamples();
double sampleSize = System.Math.Ceiling(power.Samples);
Assert.AreEqual(82, sampleSize, 1e-16);
}
public void PowerTest1()
{
// Example from http://wise.cgu.edu/powermod/computing.asp
double mean = 105;
double stdDev = 10;
int samples = 25;
double hypothesizedMean = 100;
OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsGreaterThanHypothesis;
ZTest target = new ZTest(mean, stdDev, samples, hypothesizedMean, hypothesis);
var power = target.Analysis;
Assert.AreEqual(0.804, power.Power, 1e-3);
mean = 90;
target = new ZTest(mean, stdDev, samples, hypothesizedMean, hypothesis);
power = target.Analysis;
Assert.AreEqual(0.0, power.Power, 1e-3);
}
public void ZTestConstructorTest4()
{
// Example from http://science.kennesaw.edu/~jdemaio/1107/hypothesis_testing.htm
double mean = 51.5;
double stdDev = 10;
int samples = 100;
double hypothesizedMean = 50;
// Null Hypothesis: mean = 58
// Alternative : mean != 58
OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsDifferentFromHypothesis;
ZTest target = new ZTest(mean, stdDev, samples, hypothesizedMean, hypothesis);
Assert.AreEqual(1.5, target.Statistic, 0.01);
Assert.AreEqual(OneSampleHypothesis.ValueIsDifferentFromHypothesis, target.Hypothesis);
Assert.AreEqual(DistributionTail.TwoTail, target.Tail);
Assert.IsFalse(target.Significant);
}
public void ZTestConstructorTest3()
{
// Example from http://science.kennesaw.edu/~jdemaio/1107/hypothesis_testing.htm
double mean = 53;
double stdDev = 8;
int samples = 49;
double hypothesizedMean = 58;
// Null Hypothesis: mean = 58
// Alternative : mean > 58
OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsGreaterThanHypothesis;
ZTest target = new ZTest(mean, stdDev, samples, hypothesizedMean, hypothesis);
Assert.AreEqual(-4.38, target.Statistic, 0.01);
Assert.AreEqual(OneSampleHypothesis.ValueIsGreaterThanHypothesis, target.Hypothesis);
Assert.AreEqual(DistributionTail.OneUpper, target.Tail);
Assert.IsFalse(target.Significant);
}
public void ZTestConstructorTest()
{
/* Suppose that in a particular geographic region, the mean and standard
* deviation of scores on a reading test are 100 points, and 12 points,
* respectively. Our interest is in the scores of 55 students in a particular
* school who received a mean score of 96. We can ask whether this mean score
* is significantly lower than the regional mean — that is, are the students
* in this school comparable to a simple random sample of 55 students from the
* region as a whole, or are their scores surprisingly low?
*/
ZTest target;
target = new ZTest(100, 12, 96, 55, Hypothesis.OneLower);
Assert.AreEqual(target.Statistic, -2.47, 0.01);
Assert.AreEqual(target.PValue, 0.0068, 0.001);
/* This is the one-sided p-value for the null hypothesis that the 55 students
* are comparable to a simple random sample from the population of all test-takers.
* The two-sided p-value is approximately 0.014 (twice the one-sided p-value).
*/
target = new ZTest(100, 12, 96, 55, Hypothesis.TwoTail);
Assert.AreEqual(target.PValue, 0.014, 0.005);
}
