The first column shows the Oldham West and Royton results in the General Election (GE) when over 43000 votes were cast. In the By-election (B-E) there were just under 28000 votes, as shown in the fourth column. If these had been cast in exactly the same proportions as at the GE (ie the same reduction in turnout had applied uniformly*) the parties would have had votes as in the second column.
The Green and Monster Raving Loony (MRL) votes can be ignored. What is striking is the consistency of the Liberal Democrat vote between columns two and four and the “poor” showing of the Conservatives. Where did those 2600 Conservative votes go? It seems like about 2000 to Labour and only 800 to UKIP.
Perhaps it’s fair to conclude that quite a few of the voters who are interested enough in politics to turn out for a by-election will vote tactically for whatever is in their own party’s long-term best interest.
Data from Wikipedia.
ADDENDUM 6 DECEMBER
* This was not the only assumption as well as ignoring the Green and MRL. It is possible that some people who turned out for the by-election hadn’t voted in May. More significantly, voters who did turn out for both could have shifted their allegiances in seven months. This diagram indicates the possibilities:
I don't know if the data is available, but it would be very interesting to see the numbers of postal votes, GE and B-E, broken out by party.