What happens to Pat's perceptions of climate change risks as his/her science literacy score goes up?
A curious and thoughtful correspondent asks:
A while ago, I had read your chart with two lines in red and blue, showing the association between scientific literacy and opinion on climate change separately for liberals and conservatives. [A colleague] gave it favorable mention again in her excellent presentation at the * * * seminar today.The subsequent conversation reminded me that I had always wanted to see in addition the simple line chart showing the association between scientific literacy and opinion on climate change for all respondents (without breakdown for liberals and conservatives). Have you ever published or shared that? Please share chart, or, if you haven't ever run that one, please share the data?Much thanks!
The line that plots the relationship for the sample as a whole will be exactly in between the other 2 lines. The "right/left" measure is a composite Likert scale formed by summing the (standardized) responses to 5-point left-right ideology & 7-point party-identification measure. In the figures you are referring to, the relationship between science literacy and partisan identity is plotted separately for subjects based on their score in relation to the mean on that scale.
I've added a line plotting "sample mean" relationship between global warming risk perceptions (measured on the "Industrial Strength Risk Perception Measure") to figures for two data sets, one in which subjects' science comprehension was measured with "Ordinary Science Intelligence 1.0" (used in the CCP Nature Climate Change study) & other in which the same was measured with OSI_2.0.
I'm sure you can see the significance (practical, as well as "statistical") of this display for the question you proposed, viz., "What's the impact of science literacy in general, for the population as a whole, controlling for partisanship, etc?"
It's that the question has no meaningful answer.
The main effect is just a simple average of the opposing effects that science comprehension has on climate change risk perceptions (beliefs, etc) conditional on one's cultural identity (for which right-left political outlooks are only 1 measure of many).
If the effect is "positive" or "negative," that just tells you something about the distribution of cultural-affinities, the relative impact of such affinities on risk perceptions, &/or differences in the correlation between science comprehension and cultural outlooks (which turn out to be trivially small, too) in that particular sample.
Maybe this scatterplot can get this point across visually:
In sum, because science comprehension interacts with cultural identity and b/c everyone identifies more or less with one or another cultural group, talking about the "main" effect is not a meaningful thing to do. All one can say is, "the effect of science comprehension on perceptions of climate change risk depends on who one is."
Or put it this way: the question, "What's the effect of science comprehension in general, for the population as a whole?" amounts to asking what happens to Pat as he/she becomes more science comprehending. Pssssst . . . Pat doesn’t exist!
Again, I'm sure you get this now that you've seen the data, but it's quite remarkable how many people don't. How many want to seize on the (trivially small) "main effect" & if it happens to be sloped toward their group's position, say "See! Smart people agree with our group! Ha ha! Nah, nah, boo, boo!"
They end up looking stupid.
Not just because anyone who thinks about this can figure out what I've explained about the meaninglessness of "main effect" when the data display this relationship.
But also because when we see his relationship and when the "main effect" is this small, that effect is likely to shift direction the next time someone collects data, something that could happen for any of myriad non-consequential reasons (proportion of cultural types in the sample, random variation in the size of the interaction effect, slight modifications in the measure of science literacy). At that point, those who proclaimed themselves the "winners" of the last round of the "whose is bigger" game look like fools (they are, aren't they?).
But how about some more information about Pat? And about his/her cultural worldview & ideology & their effect on his/her beliefs about climate change? Why not-- we all love Pat!