Next, re: the last graph.... I'm thinking that claiming an R2 significant to four digits with a sample size of what, 15 (?) is just silly. Is there something else? IANAS.
So, under what auspices was this study done? Are they serious? Because it's hard for me to imagine that any serious researcher or academic would suggest generalizing from a single case.
Finally, I would actually be interested in seeing your scatterplot, just to satisfy my curiosity....
That's certainly one thing that should provoke amusement. There are a couple of other silly things, given here in no particular order:
In the room example, using the median would make far more sense, and in the same fashion there are measures of goodness-of-fit that are less sensitive to outliers than r-squared. But of course those are more complicated to compute (and they are not included in any standard Office suite I know).
So, under what auspices was this study done?
It's hard to say anything definitive about this point, since I did not get the original context, if any, of this study. I suspect, however, that it was simply a case of someone seeing something he thought said something he liked to hear.
The references in the study indicate that the data was culled from some propaganda leaflet coming out of some office in Luxembourg with the aim of attracting investments to Luxembourg. I don't know what they did to the data in the first place, but given the choice of countries to include, I suspect that I wouldn't like it.
Are they serious? Because it's hard for me to imagine that any serious researcher or academic would suggest generalizing from a single case.
I am very much afraid that they are serious. While you're right about how a serious academic researcher would handle things, you must remember that these guys aren't serious researchers, much less academics. They are an employer's union, and they have a political agenda.
This kind of hack job isn't designed to convince anybody who actually takes the time to read it and has the minimal numerical literacy to understand what's going on. It's designed to provide political cover for people who already support its conclusions.
The chain of events goes something like this:
Think tank writes study -> political operative pitches study to friendly newsie, exaggerating a bit in the process -> newsie reports study, exaggerating and simplifying in the process -> other newsies interview politician about study -> politician uses study as justification for policy/protection against criticism/blunt instrument to bash opponents.
The maddening thing about this is that if you attempt to criticize the exaggerations and simplifications, the politicians/political operatives/newsies will respond by saying that it's complicated, technical stuff and they have to simplify matters for the end-users to understand. And it's not like a thorough debunking of the original study will ever make it to the papers of your local newspaper - it is, after all, "too technical" for readers to understand.
Even if you do get to challenge the study publicly, the authors will cling to the weasel words they used in the text of the study, bring out the fourth hand of the Deck of Cards and generally try to muddy the waters.
This works, because if you can muddy the waters badly enough, and few enough people can understand the technical issues, then the side that shouts louder has the better chance of 'winning' the argument.
The fact that we can't shout our opponents down (and the fact that even if we could it would be an intellectually dishonest way of doing business) means that we have to educate people - starting with the newsies - instead.
OK, here goes. Remember that the claim in the report was that inequality correlated with wealth? Well, if we want to test that, we should plot their chosen measures of wealth - disposible income and growth - against their chosen measure of inequality - the GINI.
To make the graphs below I had to extract the numbers from their figures, which of course involves a certain uncertainty. Furthermore, the figures didn't come with any error-bars, precluding a straightforward statistical analysis (besides, even if they had, I must admit to being too lazy to roll out the big guns for a hack study like this). Fortunately, as you'll see, it wasn't necessary to go beyond chi-by-eye.
(Recall that a correlation would show up by clustering the data points around a line from the lower left to upper right - an anti-correlation would show up as a clustering of points around a line from upper left to lower right.)
GINI vs. disposible income for poorest quintile.
GINI vs. disposible income for middle three-fifths.
GINI vs. disposible income for richest quintile.
GINI vs. growth.
As you can see, the three first figures do not exactly show impressive correlation. The casual reader could be tempted to say that there is even a slight anti-correlation in the first two, but the reader is warned to be careful in the extreme - if there is any such trend in the data, it is slight and the sampling methods used in this study are suspect anyway, so any conclusions drawn on the basis of this data set should be viewed with the utmost caution.
The growth over GINI plot is what physicists call a "shotgun plot" - for reasons that should be obvious...
- Jake If you only spend 20 minutes of the rest of your life on economics, go spend them here.
