karl_lembke (karl_lembke) wrote,
karl_lembke
karl_lembke

More playing with statistics

I went back to votesmart.com and looked at some of the other rating systems that were available. National Journal has a set of ratings where congresscritters are rated on the basis of how conservative they are, economically, socially, and in terms of foreign policy. Just as a test, I decided to look at the comparison of one set of ratings which ought to be diametrically opposed: liberal vs. conservative in terms of economic policy.
The correlation coefficient between these two ratings is -0.9980. That should be very close to a straight line, and by golly, it is.

Note also that here we have a nice, uniform distribution along the line. There are no clusters.
Part of this, though, has to do with how National Journal rates congresscritters. The NJ ratings are basically a ranking system – each congresscritter is rated on the percentage of congresscritters are more liberal or conservative. Therefore, you wouldn't expect any gaps in the line.

Now, in the last post, I speculated that the 50/50 point might represent some sort of political center. One comment noted that if this was the political center, then most people are poorly represented in Congress.
Interestingly enough, a graph with a nice, smooth line also means most people are poorly represented in Congress. No matter where you fall on that line, most congresscritters are someplace else.

The previous chart shows that the ADA is well-represented by one cluster of congresscritters, and the ACU is well-represented by another. Most Americans may not care about the issues those two interest groups care about.

And to make matters worse, we have no idea whether the item we're trying to measure is linear or uniform. We don't really know the shape of the ruler in either case.

We need to be careful of the assumptions we make.
Tags: politics
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