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Please recommend a better test strategy??

  • To: mathgroup at
  • Subject: [mg24974] Please recommend a better test strategy??
  • From: Richard Palmer <mapsinc at>
  • Date: Mon, 28 Aug 2000 08:27:31 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

I'm examining some binary response data using a non parametric approach.  I
want to test the parametric approach.  For each observation in the data, I
estimated a probability of response: call it

I have the observed response for the data, call it

I created a new table with 10 cells and three columns.  The first column
counts the # of observations where the estimated
Pr[response][observation(i)] is in the interval [0,0.1}, the second column
of the new table is the sum of the probabilities in this category, and the
third column is the count of the number of observations where a response
occurred.   If I divide the second and the third column by the first column,
I have an average probability for the range, and an an average frequency of
response for the range.  The other 9 cells of the table are constructed
similarly.  There are more than 20 observations in each cell in the new
table.   I want to test the hypothesis that average frequency=average
probability.  A regression model

   average frequency=c+k * average probability +error

does not reject c being 0 and k being 1.  Is there a better test strategy?
Would some Chi Square variant work here?

Richard Palmer 

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