probability is estimated based only on the presence of query terms within a document or the presence 

and absence of terms. 

 Ordering principle  O1: That probable relevance is based on the presence of search terms in 

documents  

 Ordering principle  O2: That probable relevance is based both on the presence of search terms in 

documents and their absence from documents  

Four weighting schemes, F

1

 F

4

, can be derived from the combination of the two variants of the 

independence assumption and the ordering principle, Table 1.   

 Independence 

Independence 

assumption I1 

assumption I2 

Ordering principle O1 

F1 

F2 

Ordering principle O2 

F3 

F4 

Table 1: Term weighting functions derived from the combination of independence 

assumptions and ordering principles  

In [RSJ76] each of these possible strategies was instantiated to give an actual method for weighting a 

query term, summarised in Figure 5. The weighting methods themselves are based on a contingency 

table, Table 2, which converts the probability values into values that can be calculated from term 

occurrence information. 

rel  

rel  

x

i

= 1 

r n r n 

x

i

= 0  

R r N n R+r N n 

R N R   

Table 2: Contingency table to calculate term weights 

where  r = the number of relevant documents containing term x

i

n = the number of documents containing term x

i

R = the number of relevant documents for query q 

N = the number of documents in the collection 

Each of the four term weighting functions is a ratio of two proportions

8

: 

F

1

 is the ratio of the proportion of relevant documents in which the query term t occurs (ordering 

principle O1) to the proportion of all documents in which t occurs (independence assumption I1).  

F

2

 is the ratio of the proportion of relevant documents in which the query term t occurs (ordering 

principle O1)) to the proportion of all non relevant documents in which t occurs (independence 

assumption I2).  

F

3

 and F

4

 both use odds 

F

3

, the ratio of `relevance odds' (the ratio of relevant documents containing term t and relevant 

documents not containing t   ordering principle O2) and `collection odds' (the ratio of documents 

containing t and documents not containing t   independence assumption I1). 

  F

4

 is the ratio of  relevance odds    ordering principle O2 and `non relevance odds' (the ratio of 

non relevant documents containing t and the non relevant documents not containing  t   

independence assumption I2). 

8

It may be the case, especially when using small samples, that some of the values in the weights could be zero, 

resulting in error when taking logs. The solution is to add 0.5 to each cell in the numerator and denominator of 

each function. 

 10