Lies, Damned Lies, and Statistics (15): Measuring Public Opinion But Leaving Out a Chunk of the Public

There seems to be no end to the number of battles in our war against the abuse of statistics. Take a look at this graph:

(source)

A poll of presidential approval ratings is a public opinion poll, so one expects to see the diverse opinions of the entire public represented in the results. That’s not the case here. As you can see, the numbers for the red and green lines don’t add up to 100%. Only the extreme opinions – strong approval and disapproval – are shown. Now, strictly speaking, there’s nothing to object: all necessary information is given, there’s no undue manipulation of the scales etc.

However, there’s approximately a third of public opinion that’s not included in this graph. At a minimum, this should have been made clear. I admit that my first, quick impression of this graph was that I was looking at a graph that shows the entirety of public opinion. Only after a few seconds of looking more closely did I realize that the graph doesn’t in fact offer a measurement of public opinion, but only of the opinion of the most outspoken parts of the public. Why not include a third and fourth line for “moderately (dis)approve”? Or, even better, include the moderates in the totals and just give the number for approval and disapproval, combining strong and moderate? What’s the added value of only showing the extremes? Or is this part of the current media culture?

I understand that it’s useful to know the strength of the groups who strongly approve and disapprove, but this is misleading. The graph as it is now clearly hints at a strong swing towards disapproval of Obama, but including the moderates could change that impression, and could, theoretically, show an increase in overall approval (moderate and strong). The difference between strong approval and strong disapproval is smaller than the total share of the moderates who are left out; if all or most of those moderates moderately approve (unlikely but possible), then the total approval ratings would be higher than the total disapproval ratings.

For example, the 2004 exit poll put George W. Bush’s strong approval at 33%, to strong disapproval of 34%. But his overall approval was 53% to disapproval at 46%, and he was re-elected 51%-48%. (source)

But maybe the point of this graph is precisely the creation of the impression that Obama is going down the drain. If that’s the case, then this is an example of statistical fraud. There’s no way to know this, however. One thing I know is that all this will strengthen the persistent criticism that Rasmussen, the author of the graph, has a republican bias.

I said before that strictly speaking, there’s nothing wrong with this graph, apart from the fact that it could have mentioned more explicitly that a large chunk of public opinion is left out. However, if we look at this graph against the background of contemporary politics, it becomes more problematic. Politics today is often a shouting match between extreme positions. Such a spectacle is, after all, more entertaining than intelligent discussions that look for a common ground and a real possibility of persuasion of the other side. Hence, cable TV and the internet promote this kind of “gladiator politics“. Graphs such as this one only drive people further down the cul-de-sac of us-against-them politics. I don’t believe democracy was intended to end up there.

• Gwyneth Paltrow