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Is there any lookup table for UK which translates the MSOA(middle layer super output area) codes into the Postcodes division (i.e. EI2 XXX, where XXX can be anything else).

I have found lookup tables which match every postcode to MSOA but grouping the postcodes in greater divisions seems to be a real headache as they are not clear enough(for instance Scottish postcode and English may be belong to the same MSOA but their postcode totally differ since one may start with "S" and the other one with "E").

P.S. if it is LSOA or other geography domains please do not be discouraged to include.

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The UK Data Service has files containing every single postcode and the broader geographical boundaries to which it belongs, including the MSOA (and LSOA) you are looking for. They include plenty of other geographical units - perhaps the most comprehensive set of units available.

More details can be found in the User Guides (for example here for February 2015 edition).

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You already have the most useful lookup table that is possible given the design of super output areas and postcodes.

The problem is that postcodes are not designed for the convenience of census or geographic analysis: they are purely for the convenience of the people who deliver mail. So there is no simple relationship between groups of postcodes and MSOAs or LSOAs (which are designed for convenient analysis of statistical geography. The boundaries grouping postcodes together into higher areas simply don't bear any meaningful relationship to sensible ways of grouping geographic areas like MSOAs.

If you want to analyse variation by geography, stick to LSOA or MSOA: postcodes, however grouped, are bad for this sort of analysis.

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