
 ELS Model Level 1 


Determining The Test Statistic
We will generate 10,000 ELS sets satisfying the Null hypothesis and 10,000 ELSs satisfying the Alternative
hypothesis. Each ELS set has 10 ELSs for each of the two key words. Thus there is a total of
at most 20 distances. Some pair of ELSs may not be comparable because there is not cylinder size
resonant to both of them. In this case we omit the ELS pair from the calculation.
We will examine the arithmetic mean, the geometric mean, the harmonic mean, and a linear
function of the order statistics. The order statistics are computed by sorting the distances
from smallest to largest and omitting the first one since the first one and the second one in
the sorted list are guaranteed to be identical. The weights for the order statistics are set as
they would be for the Fisher Linear Discriminant analysis. For each test statistic we will
determine its misidentification rate for a significance level of 1%. And for each we will examine
its receiver operating curve.



