/**
* \brief Runs a one-sample Z test on a vector of numbers.
* \param[in] values The vector of numbers.
* \param[in] distributionMean The mean of the entire population.
* \param[in] distributionStandardDeviation the standard deviation of the entire population.
* \param[in] The confidence level (commonly used values: 0.95, 0.999)
* \param[in] testCase The test case containing the hypothesis and null hypothesis chosen in germanStudentsTest()
*/
void StatisticalTesting::oneSampleZTest(const std::vector<double>& values,
const double& distributionMean, const double& distributionStandardDeviation,
const double& confidenceLevel, const TestCase& testCase) {
/**
* TODO: Execute the Z test for the given vector of numbers and either
* reject the null hypothesis or state that you cannot reject the null hypothesis.
*/
/*
* Available methods:
* - lookupZTable(double Z): returns the cumulative density function
* of the standard normal distribution at Z (see slide 23 for examples).
* - testCase.getHypothesis(): returns the hypothesis (see germanStudentsTest() above)
* - testCase.getNullHypothesis(): returns the null hypothesis (see germanStudentsTest() above)
*
* For both the hypothesis and the null hypothesis, the following methods are available:
* - hypothesis.getDirection(): Returns one element from the following enumeration:
* LESS, GREATER, AT_LEAST, AT_MOST, EQUAL, or DIFFERENT.
* - hypothesis.reject(): Rejects the hypothesis.
* - hypothesis.cannotReject(): States that we cannot reject the hypothesis based on the data.
*/
double zscore = zScore(values,distributionMean,distributionStandardDeviation);
double zlookup = lookupZTable(zscore);
const Hypothesis& h1 = testCase.getHypothesis();
const Hypothesis& h0 = testCase.getNullHypothesis();
double zconfidence = 0;
normal s;
/* If greater or lesser the area of significance is on one side of curve. so we use quantile with same
* confidence level. Else we can divide alpha by 2 for two sided test
*
*/
if (h0.getDirection()==AT_MOST) {
zconfidence = confidenceLevel;
if (zlookup>zconfidence)
h0.reject();
else {
h0.cannotReject();
}
}
else {
if(h0.getDirection()==AT_LEAST)
{
zconfidence = (1-confidenceLevel);
if (zlookup<zconfidence)
h0.reject();
else {
h0.cannotReject();
}
}
else {
double left_boundry = (1-confidenceLevel);
double right_boundry = confidenceLevel;
if((zlookup<left_boundry)||(zlookup>right_boundry))
h0.reject();
else {
h0.cannotReject();
}
}
}
}
/**
* \brief Runs a one-sample t test on a vector of numbers.
* \param[in] values The vector of numbers.
* \param[in] distributionMean The mean of the entire population.
* \param[in] The confidence level (commonly used values: 0.95, 0.999)
* \param[in] testCase The test case containing the hypothesis and null hypothesis chosen in germanStudentsTest()
*/
void StatisticalTesting::oneSampleTTest(const std::vector<double>& values, const double& distributionMean,
const double& confidenceLevel, const TestCase& testCase) {
/**
* TODO: Execute the one sample T test for the given vector of numbers and either
* reject the null hypothesis or state that you cannot reject the null hypothesis.
*/
/*
* Available methods:
* - lookupTTable(size_t degreeOfFreedom, double confidenceLevel, TestType testType):
* returns the quantile function of the student's t distribution (see slide
* of the standard normal distribution at Z (see slide 29 for examples).
* testType can be either ONE_SIDED or TWO_SIDED.
* - testCase.getHypothesis(): returns the hypothesis (see germanStudentsTest() above)
* - testCase.getNullHypothesis(): returns the null hypothesis (see germanStudentsTest() above)
*
* For both the hypothesis and the null hypothesis, the following methods are available:
* - hypothesis.getDirection(): Returns one element from the following enumeration:
* LESS, GREATER, AT_LEAST, AT_MOST, EQUAL, or DIFFERENT.
* - hypothesis.reject(): Rejects the hypothesis.
* - hypothesis.cannotReject(): States that we cannot reject the hypothesis based on the data.
*/
size_t dof = values.size() -1;
double tscore = tValue(values,distributionMean);
double tlookup ;
const Hypothesis& h1 = testCase.getHypothesis();
const Hypothesis& h0 = testCase.getNullHypothesis();
/* If greater or lesser the area of significance is on one side of curve. so we use quantile with same
* confidence level. Else we can divide alpha by 2 for two sided test
*
*/
if (h0.getDirection()==AT_MOST) {
tlookup = lookupTTable(dof,confidenceLevel,StatisticalTesting::ONE_SIDED);
if (tscore >tlookup )
h0.reject();
else {
h0.cannotReject();
}
}
else {
if(h0.getDirection()==AT_LEAST)
{
tlookup = lookupTTable(dof,(1-confidenceLevel),StatisticalTesting::ONE_SIDED);
if (tscore < tlookup )
h0.reject();
else {
h0.cannotReject();
}
}
else {
double right_boundry = lookupTTable(dof,confidenceLevel,StatisticalTesting::ONE_SIDED);
double left_boundry = lookupTTable(dof,(1-confidenceLevel),StatisticalTesting::ONE_SIDED);
if((tscore<left_boundry)||(tscore>right_boundry))
h0.reject();
else {
h0.cannotReject();
}
}
}
}
