OT Unless the percentages match, no such thing as a statistical dead
I've wondered about this off and on, and I once asked on another
newsgroup, but until today, I've never remembered to google it.
The more I think about this, the more things become clear. When the say
the difference is within the margin of error, is there a 95% chance the
guy who is ahead, is ahead? No. But I just realized that the chance
never goes below 50+%, because if it were lower than 50, the odds would
be that he is behind. And if his poll numbers exceed the other guy, the
odds are he's ahead, not behind.
On Wednesday, April 2, 2014 10:59:39 AM UTC-4, micky wrote:
Consider a poll on candidates Smith versus Jones. We poll one person who pi
cks Smith. Our poll indicates Smith with 100% of the vote, but we wouldn't
put much confidence in the result of that poll.
So we poll another person who picks Jones. Now, with a sample size of 2, we
have 50% Smith and 50% Jones but how reliable is a poll of two people when
there are thousands of people who will be voting?
We go out ringing doorbells again and end up with a hundred responses, 52 f
or Smith and 48 for Jones, a 4% difference between the two. Based on the sa
mple size and other parameters*, we might find that the results of this pol
l give us a 99% confidence that the results of the sample are within 5% of
the results had we polled the entire electorate.
You could think of it as meaning that Smith should end up with somewhere be
tween 57% (52% + 5%) and 47% (52% - 5%)of the vote and Jones should end up
with somewhere between 53% (48% + 5%) and 43% (48% - 5%)of the vote. Since
we're 99% confident that either candidate could end up with over 50% and wi
n, it's a "statistical dead heat."
* Here's a good reference on all that: http://en.wikipedia.org/wiki/Sample_
On Wednesday, April 2, 2014 5:08:26 AM UTC-4, micky wrote:
I do a lot of statistical analysis at work. Crunching the numbers is the ea
sy part; explaining the results in terms that non-statisticians will unders
tand is difficult. I agree that "statistical dead heat" is a misleading phr
ase but it gets the point across to people who don't understand standard de
viations, confidence intervals and sampling techniques.
If you want to get the point across without using fancy words, say
"Smith is probably ahead now, but because we didn't poll every person,
Jones might actually be ahead."
Using the example from your other post, you could say " There's an 80%**
chance that Smith is ahead now and a 20% chance that he's behind.
**Whatever the number really is. And maybe I should have included a
1% chance they were tied. I don't know what the chances are for that.
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