SilasBarta comments on 2011 Survey Results - Less Wrong

94 Post author: Yvain 05 December 2011 10:49AM

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Comment author: SilasBarta 05 December 2011 07:13:27PM *  5 points [-]

Percentage point difference in belief probability isn't all that meaningful. 50% to 51% is a lot smaller confidence difference than 98% to 99%.

69.4% probability means 3.27 odds; 41.2% probability means 1.70 odds.

That means that, in the aggregate, survey takers find (3.27/1.70) = 1.924 -> 0.944 more bits of evidence for life somewhere in the universe, compared to somewhere in the galaxy.

Is that unreasonably big or unreasonably small?

EDIT: Oops, I can't convert properly. That should be 2.27 odds and 0.70 odds, an odds ratio of 3.24, or 1.70 more bits.

Comment author: Unnamed 06 December 2011 10:42:27PM *  1 point [-]

If we take the odds ratio for each individual respondent (instead of the aggregate), the median odds ratio is 10.1 -> 3.3 more bits of evidence for life in the universe, compared to somewhere in the galaxy. 25th percentile odds ratio: 2.7 -> 1.4 more bits; 75th percentile odds ratio: 75.7 -> 6.2 more bits. (This is all using the publicly available data set; looking at the aggregate in that data set I'm getting an odds ratio of 3.6 -> 1.8 more bits.)

People who believe in God/religion/the supernatural tend to give a lower odds ratio, but other than that the odds ratio doesn't seem to be associated with any of the other variables on the survey.

Comment author: gwern 05 December 2011 07:27:38PM *  0 points [-]

I'm not comfortable with bit odds, especially in this context, so I dunno. How would you frame that in the opposite terms, for lack of existence?

Comment author: SilasBarta 05 December 2011 08:26:18PM *  2 points [-]

That gives .44 odds non-existence in universe, 1.43 odds non-existence in galaxy, a ratio of 3.24, or 1.70 more bits of evidence for no (non-human) life in the galaxy compared to the universe in general.

And I forget why those two answers are allowed to be different...

EDIT: I made an error in the first calculation; as I suspected, the values are symmetric.