/// <summary>
/// confidence level is alpha
/// </summary>
/// <param name="alpha"></param>
/// <returns></returns>
public ClosedNeighborhood <double> meanDifferenceConfidenceInterval(int levelA, int levelB, double confidenceLevel)
{
return(new ClosedNeighborhood <double>(
observationsAverageByLevel(levelA) - observationsAverageByLevel(levelB),
TDistribution.UpperDividePoint((1 - confidenceLevel) / 2, this.degreesOfFreedomError)
*
((errorSquareAverage
* (1.0 / observationsCountByLevel(levelA) + 1.0 / observationsCountByLevel(levelB))
).Power(.5))
));
}