🚀 go-pugleaf

Jon Dodd wrote:

 > I wonder if any of you could help me with what might be a 
 > trivial problem and might not be. I am not a mathematician 
 > so don't have a clue where to start.
--snip--
 > I use a non-parametric statistic based on signal detection 
 > theory (ROC analysis) to give a measure of the 
 > distinctivness(overlap) of 2 distributions of numbers.
 > The method is really straightforward and I provide a 
 > simple example below.
--snip--
 > The problem I have is in assessing a significance level 
 > for the value I obtain from the above type analysis given 
 > nd1 and nd2 can be of any length and unequal.
--snip--

Calculation of standard errors for non-parametric ROC-area index
estimates was discussed in:

  Bamber D.  The area above the ordinal dominance graph and the area
below the receiver operating graph.  Journal of Mathemaical Psychology
1975; 12: 387.

and later in:

  Hanley JA, McNeil BJ.  The meaning and use of the area under a
receiver operating characteristic (ROC) curve.  Radiology 1982; 143: 29.


An approach for testing the statistical significance of differences
between independent index estimates was described in the paper by Hanley
and McNeil listed above, whereas techniques for testing differences
between correlated index estimates can be found in:

  Hanley JA, McNeil BJ.  A method of comparing the areas under receiver
operating characteristic curves derived from the same cases.  Radiology
1983; 148: 839.

and in:

  DeLong ER, DeLong DM, Clarke-Pearson DL.  Comparing the areas under
two or more correlated receiver operating characteristic curves: a
nonparametric approach.  Biometrics 1988; 44: 837.


   Charles Metz