  Click through rates (CTR) offer useful user feedback that can be used to
infer the relevance of search results for queries. However it is not very
meaningful to look at the raw click through rate of a search result because the
likelihood of a result being clicked depends not only on its relevance but also
the position in which it is displayed. One model of the browsing behavior, the
{\em Examination Hypothesis} \cite{RDR07,Craswell08,DP08}, states that each
position has a certain probability of being examined and is then clicked based
on the relevance of the search snippets. This is based on eye tracking studies
\cite{Claypool01, GJG04} which suggest that users are less likely to view
results in lower positions. Such a position dependent variation in the
probability of examining a document is referred to as {\em position bias}. Our
main observation in this study is that the position bias tends to differ with
the kind of information the user is looking for. This makes the position bias
{\em query specific}. In this study, we present a model for analyzing a query
specific position bias from the click data and use these biases to derive
position independent relevance values of search results. Our model is based on
the assumption that for a given query, the positional click through rate of a
document is proportional to the product of its relevance and a {\em query
specific} position bias. We compare our model with the vanilla examination
hypothesis model (EH) on a set of queries obtained from search logs of a
commercial search engine. We also compare it with the User Browsing Model (UBM)
\cite{DP08} which extends the cascade model of Craswell et al\cite{Craswell08}
by incorporating multiple clicks in a query session. We show that the our
model, although much simpler to implement, consistently outperforms both EH and
UBM on well-used measures such as relative error and cross entropy.
