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« How many talks did I give last yr? And how about yr before that, & yr before that ... | Main | More evidence of AOT's failure to counteract politically motivated reasoning »

#scicomm question: what communicates essential information more effectively--unfilled overlapping pdd's or filled/transparency ones?

Been having more fun with Stata 15's new transparency feature but was wondering if maybe I'm neglecting communication effectiveness in favor of some other aesthetic consideration.

So tell me: Which looks better--this

 or this?


Both convey the same info on how "high numeracy" & "low numeracy" study subjects do on a covariance problem, the numbers of which are manipulated to make the right answers either identity-affirming or identity-threatening.  What they are both illustrating, then, is that high numeracy subjects lose nearly all their accuracy edge when they analyze covariance data that contradicts their political presuppositions and thus threatens their cultural identity.

So assume an attentive reader comes across this point in the text and is directed to look at the Figures to make the point even more vivid.  Does one of these graphic reporting methods work better than the other?

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Reader Comments (9)

The eye is very drawn to the darker green in the filled overlap case. This gives the initial impression that the precise shape of that dark green overlap is what one should focus on, when really it is not. In short, it's over emphatic. So I prefer the unfilled, simply because that minor distraction doesn't occur with the initial impression.

October 31, 2017 | Unregistered CommenterAndy West

I agree with Andy - don't shade regions unless the shading has some meaning. Also, shaded regions just enrich the ink-jet refill cartel (not as inherently evil as the science article paywall cartel, but close).

October 31, 2017 | Unregistered CommenterJonathan

@Jonathan & @Andy-- the overlap is conceptually important: the area under both curves is a measure of the likelihood that the two values are statistically equivalent. But that likely is clear enough with the unfilled PDDs, too.

November 2, 2017 | Registered CommenterDan Kahan

I agree with the others re the overlap, and because it's shaded darkest, it suggests that is where the most meaningful information is. But there are a couple other issues with presenting in this way - filled or un. If you are presenting the findings to people very familiar with statistics, you'll probably be fine either way.

But for folks who aren't, the filled PDDs signal that there's something important about the shaded area. That's a bonus. In both cases, however, the tendency is to focus on the top of the curve, and compare height. But the focus should be on the difference in probability score - the horizontal placement of the curves. If you changed the x-axis numbers to percents, that would help.

But something else here is interesting, and is a bit lost. Your data seem to say that the identity affirmation condition boosted probability of correct answer over the control - if skin rash can ever be thought of as control. :)
Isn't that an interesting finding, too, when talking about motivated reasoning? It's true for both low- and high- numeracy conditions.

Finally - If you really want to draw people's attention to the high-numeracy group differences between identity affirmation and threat, then I would graph those together, not side by side. Or at least call attention, with a label, to the mean probability for each group.

This data would be great for Andy Kreibel's #MakeoverMonday - He's at @VizWizBI on the Twitter.

November 2, 2017 | Unregistered CommenterLynn Davey

Count me in for preferring the bottom graphics, actually. When I see an unfilled line, I think of it as a time series trace and I try to identify the peak location. When the bottom is shaded in, I think more immediately of a probability distribution and I look for cross-entropy.

November 3, 2017 | Unregistered Commenterdypoon

Also, I'd probably be interested in seeing linear regression coefficients on the logit-transformed response and an ANOVA table. The distribution plots are good for diagnostic purposes, but ultimately more informative would be to know how the log odds lie, given that the diagnostics are good.

So that ends up being another reason to prefer the shaded graphs - they make it easier to evaluate skew.

November 3, 2017 | Unregistered Commenterdypoon

@Lynn-- good observation. I'm pondering it

November 4, 2017 | Registered CommenterDan Kahan

For what it's worth, I didn't find either version any clearer or more intuitive than the other, although I did find the shaded versions more attractive.

For helping to make the comparisons Lynn mentions, I'd have stacked the graphs vertically rather than horizontally, so the x axes all match and you can see how they line up or change. Also, add dotted lines or other markers to emphasise the means of each distribution - what you want the audience to pay attention to.

Also, unless the binary 'low numeracy'/'high numeracy' classification really was binary, I'd consider doing probability and numeracy on the two axes, and do a scatter plot colour-coded by trial. You might even be able to do them all on the same plot.

November 5, 2017 | Unregistered CommenterNiV

For me the hardest aspect of understanding the study was why the results were translated into probability distributions. I'd like a graph that would help to understand why distributions instead of discrete data points are shown.

As with others, in order to better choose, I'd like to see
a) a chart that shows two or all three of the 'high numeracy' distributions on one graph
b) charts stacked vertically -- perhaps with a light vertical line thru the center point of each

November 12, 2017 | Unregistered CommenterCortlandt

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