When I framed it to myself as “that’s a doubling of the tails!” it did sound impressive, but I remembered how easy it is to make modest changes in a distribution’s mean and/or variance sound extreme by focusing attention on the tails, where such changes have an outsized impact.
My reaction was to roughly translate that tail doubling into the corresponding change in the whole distribution’s standard deviation, and I got about 30%. Expressed like that, the change was clearly substantial, but it didn’t strike me as radical. Opinions may differ!
(For this reply, I thought I’d try estimating a standard deviation for each distribution in a more systematic way. From Pew’s appendix I worked out the mid-interval value for each of the 5 ideological-consistency bins, then calculated the standard deviations using those mid-interval bin values. This is still inexact, but hopefully less so than my original back-of-the-envelope guesstimate. For 1994 I got 3.90; for 2004, 3.91; and for 2014, 4.80. That gives a 23% increase in standard deviation from 2004 to 2014.)
When I framed it to myself as “that’s a doubling of the tails!” it did sound impressive, but I remembered how easy it is to make modest changes in a distribution’s mean and/or variance sound extreme by focusing attention on the tails, where such changes have an outsized impact.
My reaction was to roughly translate that tail doubling into the corresponding change in the whole distribution’s standard deviation, and I got about 30%. Expressed like that, the change was clearly substantial, but it didn’t strike me as radical. Opinions may differ!
(For this reply, I thought I’d try estimating a standard deviation for each distribution in a more systematic way. From Pew’s appendix I worked out the mid-interval value for each of the 5 ideological-consistency bins, then calculated the standard deviations using those mid-interval bin values. This is still inexact, but hopefully less so than my original back-of-the-envelope guesstimate. For 1994 I got 3.90; for 2004, 3.91; and for 2014, 4.80. That gives a 23% increase in standard deviation from 2004 to 2014.)