Pair comparing method

• When studying how a response variable depends on an explanatory variable itis convenient to create pairs of matched observations, i.e. pairs consistingof two observations that are homogenous, except for the studied explanatoryvariables and the response variable. So, the matching procedure is a methodwith the purpose to control for different nuisance variables. Normally theanalysis of such studies is straightforward, but it is possible to complicateit. Usually an expert that is not necessarily a statistician creates thematched pairs. In that case it is also customary that this expert finds onepair member suitable in several pairs, which means trouble for the analysingstatistician. The expert understanding for the statistical problems ishowever limited in most cases. Therefore it has been necessary to develop astatistical method for analysing the results from a study with matched pairs,where it is allowed for an observation unit to be member of several pairs. Anobvious consequence of that is that results from pairs with one common pairmember will be dependent. It is therefore necessary to formulate an analysingmethod that is applicable when there are dependencies between differentpairs. Another consequence from allowing the same object to occur in severalpairs is that it may lead to a data set with redundancy. This would be thesituation if objects a and b form one pair, a and c another and finally b andc a third pair. The third pair is just the difference between the two firsts.Then it is necessary to find a method that remove redundant pair like b and cas well.

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