  # SCIP

Solving Constraint Integer Programs

Statistical tests

## Detailed Description

public methods for statistical tests

Below are the public methods for statistical tests inside of SCIP

## Functions

SCIP_EXPORT SCIP_Real SCIPstudentTGetCriticalValue (SCIP_CONFIDENCELEVEL clevel, int df)

SCIP_EXPORT SCIP_Real SCIPcomputeTwoSampleTTestValue (SCIP_Real meanx, SCIP_Real meany, SCIP_Real variancex, SCIP_Real variancey, SCIP_Real countx, SCIP_Real county)

SCIP_EXPORT SCIP_Real SCIPerf (SCIP_Real x)

SCIP_EXPORT SCIP_Real SCIPnormalGetCriticalValue (SCIP_CONFIDENCELEVEL clevel)

SCIP_EXPORT SCIP_Real SCIPnormalCDF (SCIP_Real mean, SCIP_Real variance, SCIP_Real value)

## ◆ SCIPstudentTGetCriticalValue()

 SCIP_EXPORT SCIP_Real SCIPstudentTGetCriticalValue ( SCIP_CONFIDENCELEVEL clevel, int df )

get critical value of a Student-T distribution for a given number of degrees of freedom at a confidence level

Parameters
 clevel (one-sided) confidence level df degrees of freedom

Definition at line 94 of file misc.c.

References studentt_maxdf, studentt_quartiles, and studentt_quartilesabove.

Referenced by SCIPvarCalcPscostConfidenceBound(), and SCIPvarSignificantPscostDifference().

## ◆ SCIPcomputeTwoSampleTTestValue()

 SCIP_EXPORT SCIP_Real SCIPcomputeTwoSampleTTestValue ( SCIP_Real meanx, SCIP_Real meany, SCIP_Real variancex, SCIP_Real variancey, SCIP_Real countx, SCIP_Real county )

compute a t-value for the hypothesis that x and y are from the same population; Assuming that x and y represent normally distributed random samples with equal variance, the returned value comes from a Student-T distribution with countx + county - 2 degrees of freedom; this value can be compared with a critical value (see also SCIPstudentTGetCriticalValue()) at a predefined confidence level for checking if x and y significantly differ in location

Parameters
 meanx the mean of the first distribution meany the mean of the second distribution variancex the variance of the x-distribution variancey the variance of the y-distribution countx number of samples of x county number of samples of y

Definition at line 111 of file misc.c.

References MAX, SCIP_INVALID, SCIP_Real, and SQRT.

Referenced by SCIPvarSignificantPscostDifference().

## ◆ SCIPerf()

 SCIP_EXPORT SCIP_Real SCIPerf ( SCIP_Real x )

returns the value of the Gauss error function evaluated at a given point

Parameters
 x value to evaluate

Definition at line 144 of file misc.c.

References exp(), REALABS, SCIP_Real, sign(), x, and y.

Referenced by SCIPcalcCumulativeDistribution(), and SCIPnormalCDF().

## ◆ SCIPnormalGetCriticalValue()

 SCIP_EXPORT SCIP_Real SCIPnormalGetCriticalValue ( SCIP_CONFIDENCELEVEL clevel )

get critical value of a standard normal distribution at a given confidence level

Parameters
 clevel (one-sided) confidence level

Definition at line 171 of file misc.c.

References studentt_quartilesabove.

## ◆ SCIPnormalCDF()

 SCIP_EXPORT SCIP_Real SCIPnormalCDF ( SCIP_Real mean, SCIP_Real variance, SCIP_Real value )

calculates the cumulative distribution P(-infinity <= x <= value) that a normally distributed random variable x takes a value between -infinity and parameter value.

The distribution is given by the respective mean and deviation. This implementation uses the error function erf().

calculates the cumulative distribution P(-infinity <= x <= value) that a normally distributed random variable x takes a value between -infinity and parameter value.

The distribution is given by the respective mean and deviation. This implementation uses the error function SCIPerf().

Parameters
 mean the mean value of the distribution variance the square of the deviation of the distribution value the upper limit of the calculated distribution integral

Definition at line 184 of file misc.c.

References SCIP_Real, SCIPdebugMessage, SCIPerf(), sqrt(), and SQRTOFTWO.

Referenced by SCIPvarPscostThresholdProbabilityTest().