Adventures in probability

Michael Veall cautions against reading too much into sudden poll changes.

So even if a party is up say 3.5 percentage points comparing a new poll with a previous poll, if each poll had a margin of error of 3.1 percentage points, the 3.5 percentage point increase should be compared to a margin for error of about 4.4 percentage points. There is a reasonable chance that the party’s vote intention share in the total population did not change at all: all that happened was that the pollsters randomly happened to choose more of the party’s supporters in the second poll.

The margins of errors for changes in leads can be twice as large again. If a party is leading by 5 percentage points in one poll and then by 9 percentage points in the next poll, the margin of error around that 4 percentage point gain could be over 8 percentage points. While probably the lead increased, there is still a significant chance that the lead decreased.