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Using the logit transformation for probabilities,that is the basic quantitative model for a single query j they propose is logit [[theta]]j 1 [[alpha]]j [[Delta]]j logit [[theta]]j 2 [[alpha]]j [[Delta]]j Here [[theta]]j 1 and [[theta]]j 2 are probabilities corresponding to recall and fallout respectively as defined in the previous section
...[[alpha]]j measures the specificity of the query formulation;[[Delta]]j measures the separation of relevant and non relevant documents
...For a given query j if the query i has been formulated in a more specific way than j,one would expect the recall and fallout to decrease,i
...[[theta]]i 1 <[[theta]]j 1 and [[theta]]i 2 <[[theta]]j 2 Also,if for query i the system is better at separating the non relevant from the relevant documents than it is for query j one would expect the recall to increase and the fallout to decrease,i
...[[theta]]i 1 >[[theta]]j 1 and [[theta]]i 2 <[[theta]]j 2 Given that logit is a monotonic transformation,these interpretations are consistent with the simple quantitative model defined above
...To arrive at an estimation procedure for [[alpha]]j and [[Delta]]j is a difficult technical problem and the interested reader should consult Robertson s thesis [19]...logit [[theta]]j 1 [[alpha]]j 1 [[Delta]]logit [[theta]]j 2 [[alpha]]j 2 [[Delta]]From them it would appear that [[Delta]]could be a candidate for a single number measure of effectiveness
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