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WSMD? JA! "Confidence intervals" for "Political Polarization Literacy" test

Winning entry. Verified by "Virgin Mary on your French toast, you say?"™ miracle certifiersFormer Freud expert & current stats legend  Andrew Gelman and Josh " 'Hot Hand Fallay' Fallacy" Miller have announced publicly that they scored perfect 14.75's (higher, actually) on the CCP/APPC "Political Polarization Literacy" test.  

They have now demanded that they be awared the "Gelman Cup." That request actually made their "political polarization literacy" scores a bit more credibile, since obviously they are too busy measuring public opinion to stay current with CCP contests and their respective prizes (I've sent them an authentic "Worrship the Industrial Strength Risk Perception Measure!" Virgin Mary Frenchtoast slice" for their performances).

But speaking of CCP games ... you guessed it: Time for another installment of

 the insanely popular CCP series, "Wanna see more data? Just ask!," the game in which commentators compete for world-wide recognition and fame by proposing amazingly clever hypotheses that can be tested by re-analyzing data collected in one or another CCP study. For "WSMD?, JA!" rules and conditions (including the mandatory release from defamation claims), click here.

Statistical Modeling, Causal Inference, and Social Science commentator@Rahul wondered what it would look like if the plots in the "Political Polarization Literacy" test figure had confidence intervals.

Here's the answer: 

(If you forgot what the policy items are, you can either go back to the original post or just click here.)

Actually, I'm not sure CIs add interesting information here.

Once one knows that the N = 1200 & the sample is representative, it's pretty easy to know what the CIs will look like (around 0.04 at pr = 0.50; smaller as one approaches pr = 0 & pr = 1.0).

The intersting information here is in the covariances of positions and left_right. The CIs don't make that any clearer; if anything, they make that a bit harder to see!  So I'd say for the purposes of the game, the lowess plots, sans CIs, were all the "statistics" & "modeling" needed for us to start learning something (about WEKS) from the data.

But that's my view. Others might disagree.

Who knows-- they might even disagree with me that "spike plots" rather than, say, colored confidence bands are a prettier way to denote 0.95 CI zones if one thinks there is something to be gained by fitting a model to data like these!

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