Margins of error. Hey, media, here's a multiple choice question for you: if Party A leads Party B by 4.99% in a poll whose margin of error (95% confidence interval - i.e. "nineteen times out of twenty") is 5%, what is the chance that Party A is, in fact, ahead of Party B?
a. 50%: because the poll difference is within the poll's margin of error, it's a statistical tie, so there is equal chance of either party being ahead.
b. a hair under 95%: because a difference of 5% gives a 95% certainty of Party A being in the lead, a difference of very slightly under 5% will give a certainty very slightly under 95%.
c. it's impossible to say
(The correct answer is in the comments section, though I like to think that my limited readership is smart enough that it won't need to check.)
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4 comments:
B
Steve, it's actually a hair under 97.5%, not 95% You have to account for the fact that that deviation is over a 95% range in both directions... one time out of 20 the variation will be more divergent than 5%, but half of that 5% will have understated the 4.99% lead by more than 5%
You'd be right, except that you're forgetting that if each party's support is off by 2.51% in appropriately divergent directions, that also places Party B ahead; neither party needs to be individually off by more than 4.99% for the lead to be incorrect.
At 2.5% then we'd be dealing with one standard deviation, not two, and there would be at least a 1/36 chance... in those instances where there were 2.5% deviation in either direction... but also, there's a high degree of negative correlation between voter intentions across parties. It's an inherently zero-sum game.
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