Posts tagged statistics

From kohenari:

As many of my friends who left the Republican party in the past decade can attest, George Bush Lost an Entire Generation for the Republican Party:

[F]or the past 40 years voting patterns haven’t differed much by age. In fact, there’s virtually no difference between generations at all until you get to the George Bush era. At that point, young voters suddenly leave the Republican Party en masse. Millennials may be far less likely than older generations to say there’s a big difference between Republicans and Democrats, but their actual voting record belies that.
Whatever it was that Karl Rove and George Bush did—and there are plenty of possibilities, ranging from Iraq to gays to religion—they massively alienated an entire generation of voters. Sure, they managed to squeak out a couple of presidential victories, but they did it at the cost of losing millions of voters who will probably never fully return. This chart is their legacy in a nutshell.


I’d be cautious about this conclusion. There’s a noticeable drop between 2008 and 2012, which could mean the 2008 election was merely a “spike” or “outlier” in the larger trend. Making a sweeping generalization based on three data points (and 2004 looks to be within the margin of normal error) isn’t a good idea.
Also, we don’t know (based on only six years of data) whether the young people who voted Democratic in 2008 and 2012 won’t eventually vote Republican 20 or 30 years from now. Stranger things have happened (e.g. the “solid South” went from strongly Democratic in the 1940s to strongly Republican after the 1970s). Besides, notice that the 2012 and 1972 gaps (+16%) are identical. The gap has narrowed before. Projecting that it will never narrow again is odd.

From kohenari:

As many of my friends who left the Republican party in the past decade can attest, George Bush Lost an Entire Generation for the Republican Party:

[F]or the past 40 years voting patterns haven’t differed much by age. In fact, there’s virtually no difference between generations at all until you get to the George Bush era. At that point, young voters suddenly leave the Republican Party en masse. Millennials may be far less likely than older generations to say there’s a big difference between Republicans and Democrats, but their actual voting record belies that.

Whatever it was that Karl Rove and George Bush did—and there are plenty of possibilities, ranging from Iraq to gays to religion—they massively alienated an entire generation of voters. Sure, they managed to squeak out a couple of presidential victories, but they did it at the cost of losing millions of voters who will probably never fully return. This chart is their legacy in a nutshell.

I’d be cautious about this conclusion. There’s a noticeable drop between 2008 and 2012, which could mean the 2008 election was merely a “spike” or “outlier” in the larger trend. Making a sweeping generalization based on three data points (and 2004 looks to be within the margin of normal error) isn’t a good idea.

Also, we don’t know (based on only six years of data) whether the young people who voted Democratic in 2008 and 2012 won’t eventually vote Republican 20 or 30 years from now. Stranger things have happened (e.g. the “solid South” went from strongly Democratic in the 1940s to strongly Republican after the 1970s). Besides, notice that the 2012 and 1972 gaps (+16%) are identical. The gap has narrowed before. Projecting that it will never narrow again is odd.

Via theatlantic:

Countries With Higher Math Scores Have Unhappier Kids

Um. No. Even just an eye-ball scan shows this can’t possibly be a statistically significant finding. Too much “noise” in the data with far too many outliers.
Besides, look at the Pearson correlation coefficient: -0.32 is well below the +/- 0.7 typically used as a minimal threshold of statistical significance on its own. And the p-value of 0.011 would not be accepted as statistically significant in a multiple regression model (and this is a simple bivariate model).
Basically, there’s only an 89% chance that the Pearson coefficient (-0.32) is correct. And that Pearson correlation coefficient (r) basically translates to an R-squared of 0.1024. In other words, math scores (PISA) can only account for about 10% 1% of the variation in happiness (and vice versa) across countries.
Addendum: In fact, just looking at the names by the dots, I notice that most of the low-math/high-happiness countries are developing countries and most of the high-math/low-happiness countries are post-communist countries. I suspect that dropping all non-OECD countries might find a correlation going in the opposite direction (though probably not a strong one then, either).
Addendum 2: A reader pointed out that I misread the p-value and thought it was lower than it really was. I was blinded because the graph clearly shows a non-relationship and so my mind pushed the decimal over. I’m still convinced this is a non-finding, however.

Via theatlantic:

Countries With Higher Math Scores Have Unhappier Kids

Um. No. Even just an eye-ball scan shows this can’t possibly be a statistically significant finding. Too much “noise” in the data with far too many outliers.

Besides, look at the Pearson correlation coefficient: -0.32 is well below the +/- 0.7 typically used as a minimal threshold of statistical significance on its own. And the p-value of 0.011 would not be accepted as statistically significant in a multiple regression model (and this is a simple bivariate model).

Basically, there’s only an 89% chance that the Pearson coefficient (-0.32) is correct. And that Pearson correlation coefficient (r) basically translates to an R-squared of 0.1024. In other words, math scores (PISA) can only account for about 10% 1% of the variation in happiness (and vice versa) across countries.

Addendum: In fact, just looking at the names by the dots, I notice that most of the low-math/high-happiness countries are developing countries and most of the high-math/low-happiness countries are post-communist countries. I suspect that dropping all non-OECD countries might find a correlation going in the opposite direction (though probably not a strong one then, either).

Addendum 2: A reader pointed out that I misread the p-value and thought it was lower than it really was. I was blinded because the graph clearly shows a non-relationship and so my mind pushed the decimal over. I’m still convinced this is a non-finding, however.

theyuniversity:

Coincidence?

A good reminder not to confuse correlation and causation.

theyuniversity:

Coincidence?

A good reminder not to confuse correlation and causation.

"Pixar's Sad Decline—in 1 Chart" | The Atlantic

This is a great example of a terrible use of a linear regression model. Please don’t ever do this. It’s (at best) A passing C (and only because the graph looks like a good graph).

Yesterday I posted an observation about the relationship between democracy & taxes. But when compiling that data, I also pulled some data on “size of government” (as measured by the conservative Fraser Institute). Their Economic Freedom index includes a component for “size of government,” which gives a score of 10 to “small” governments and zero to “big” governments.
That relationship is even more interesting.
Again, pulling from The Economist Democracy Index (2011), I plotted country scores along the two variables: Democracy Index score and “Size of Government” score. The Fraser Institute data has fewer countries, so instead of 161 countries, this time I was only able to plot 138 countries.
Notice that the line is virtually flat. It’s slightly leaning towards the “wrong” end (democracy scores increase as size of government increases). But, statistically speaking, there is no relationship (Pearson’s r = -0.1086; p = 0.2048).
What does this mean? Well, basically, it means that there’s no reason to suggest that “size of government” has any relationship to whether a country is democratic or not. Like w/ yesterday’s data, this has no bearing on whether “big” government is “good” or not (those are ideological/philosophical debates you’re welcome to have). But, empirically, the evidence doesn’t support the assertion that “big” governments are bad for democracy.
For example, which countries scored the “best” according to the Fraser Institute in terms of “size of government”? Here’s the list of countries that scored a 9 (no country scored a 10):
Togo
El Salvador
Madagascar
Jamaica
Haiti
And here’s the countries that scored the “worst” in terms of the “size of government,” according to the Fraser Institute:
Sweden (3)
The Netherlands (3)
For comparison, the United States scored a 7.
(I should note that the Fraser Institute did not give scores to a number of countries, including North Korea and Cuba. But the list of excluded countries also includes “small” states like Afghanistan, Libya, Somalia, and Yemen.)

Yesterday I posted an observation about the relationship between democracy & taxes. But when compiling that data, I also pulled some data on “size of government” (as measured by the conservative Fraser Institute). Their Economic Freedom index includes a component for “size of government,” which gives a score of 10 to “small” governments and zero to “big” governments.

That relationship is even more interesting.

Again, pulling from The Economist Democracy Index (2011), I plotted country scores along the two variables: Democracy Index score and “Size of Government” score. The Fraser Institute data has fewer countries, so instead of 161 countries, this time I was only able to plot 138 countries.

Notice that the line is virtually flat. It’s slightly leaning towards the “wrong” end (democracy scores increase as size of government increases). But, statistically speaking, there is no relationship (Pearson’s r = -0.1086; p = 0.2048).

What does this mean? Well, basically, it means that there’s no reason to suggest that “size of government” has any relationship to whether a country is democratic or not. Like w/ yesterday’s data, this has no bearing on whether “big” government is “good” or not (those are ideological/philosophical debates you’re welcome to have). But, empirically, the evidence doesn’t support the assertion that “big” governments are bad for democracy.

For example, which countries scored the “best” according to the Fraser Institute in terms of “size of government”? Here’s the list of countries that scored a 9 (no country scored a 10):

  • Togo
  • El Salvador
  • Madagascar
  • Jamaica
  • Haiti

And here’s the countries that scored the “worst” in terms of the “size of government,” according to the Fraser Institute:

  • Sweden (3)
  • The Netherlands (3)

For comparison, the United States scored a 7.

(I should note that the Fraser Institute did not give scores to a number of countries, including North Korea and Cuba. But the list of excluded countries also includes “small” states like Afghanistan, Libya, Somalia, and Yemen.)

I was compiling some data for some class exercises and lecture presentations for next semester, and wanted to make a small observation. This stems from the difficulty I find in explaining to my students why states (or “governments”—although there’s obviously an important conceptual distinction between state and government) are important. Many of my students have a fairly strong anti-government bias, which is reinforced by their biases against taxes.
Whether strong states (or “central governments”) are a good thing or not is a question for moral or political philosophy. Certainly, strong states can be authoritarian (although, ironically, many authoritarian regimes actually have weak states). 
Similarly, whether taxes are useful or not is also a question for moral or political philosophy. And certainly many countries (including our own) spend tax dollars wastefully and/or on things we’d rather they didn’t (e.g. pacifists still pay taxes that go to military spending).
But the question of whether high taxes erode, weaken, or otherwise undermine democracy is an empirical question. That is, we can test it with existing data. To compare taxes across the world, I used tax burden as percent of GDP (this is better than using tax rates, since it looks at the share of taxes as the share of the total economy). I used data from the conservative Heritage Foundation. I wanted to see if there was any relationship between taxes and democracy. I used the 2011 Democracy Index measure developed by The Economist (the higher the score, the higher the quality of democracy). 
Turns out, there is a relationship between taxes and democracy. But it’s not what some of you might expect. The figure below plots 161 countries on both dimensions; the red line is the statistically estimated relationship (or “trendline”) between the two variables. The quality of democracy increases as tax burden as percent of GDP increases. The relationship is fairly strong (Pearson’s r = 0.6553; p < 0.000). 
There are outliers, obviously. But for the most part, countries w/ high democracy scores have high tax burdens. In contrast, countries w/ the low democracy scores tend to have low tax burdens.
How low? The ten countries with the lowest tax burdens as percent of GDP are:
United Arab Emirates (1.4% of GDP)
Kuwait (1.5% of GDP)
Equatorial Guinea (1.7% of GDP)
Oman (2.0% of GDP)
Qatar (2.2% of GDP)
Libya (2.7% of GDP)
Chad (4.2% of GDP)
Bahrain (4.8% of GDP)
Burma (4.9% of GDP)
Saudi Arabia (5.3% of GDP)
The United States comes in w/ a respectable tax burden of 26.9% of GDP. That ranks as the 57th highest in the world. That puts us just below Bolivia (27% of GDP), tied w/ South Africa, and just above South Korea (26.8% of GDP). Among the 34 wealthy OECD countries, the average tax burden is 36.2% of GDP. Other than South Korea, only Chile (among OECD countries) has a lower tax burden (18.6% of GDP).
Of course, this doesn’t answer the question of whether we should or shouldn’t have higher taxes. But it’s pretty clear that high taxes are not necessarily going to undermine our democracy.

I was compiling some data for some class exercises and lecture presentations for next semester, and wanted to make a small observation. This stems from the difficulty I find in explaining to my students why states (or “governments”—although there’s obviously an important conceptual distinction between state and government) are important. Many of my students have a fairly strong anti-government bias, which is reinforced by their biases against taxes.

Whether strong states (or “central governments”) are a good thing or not is a question for moral or political philosophy. Certainly, strong states can be authoritarian (although, ironically, many authoritarian regimes actually have weak states). 

Similarly, whether taxes are useful or not is also a question for moral or political philosophy. And certainly many countries (including our own) spend tax dollars wastefully and/or on things we’d rather they didn’t (e.g. pacifists still pay taxes that go to military spending).

But the question of whether high taxes erode, weaken, or otherwise undermine democracy is an empirical question. That is, we can test it with existing data. To compare taxes across the world, I used tax burden as percent of GDP (this is better than using tax rates, since it looks at the share of taxes as the share of the total economy). I used data from the conservative Heritage Foundation. I wanted to see if there was any relationship between taxes and democracy. I used the 2011 Democracy Index measure developed by The Economist (the higher the score, the higher the quality of democracy). 

Turns out, there is a relationship between taxes and democracy. But it’s not what some of you might expect. The figure below plots 161 countries on both dimensions; the red line is the statistically estimated relationship (or “trendline”) between the two variables. The quality of democracy increases as tax burden as percent of GDP increases. The relationship is fairly strong (Pearson’s r = 0.6553; p < 0.000). 

There are outliers, obviously. But for the most part, countries w/ high democracy scores have high tax burdens. In contrast, countries w/ the low democracy scores tend to have low tax burdens.

How low? The ten countries with the lowest tax burdens as percent of GDP are:

  1. United Arab Emirates (1.4% of GDP)
  2. Kuwait (1.5% of GDP)
  3. Equatorial Guinea (1.7% of GDP)
  4. Oman (2.0% of GDP)
  5. Qatar (2.2% of GDP)
  6. Libya (2.7% of GDP)
  7. Chad (4.2% of GDP)
  8. Bahrain (4.8% of GDP)
  9. Burma (4.9% of GDP)
  10. Saudi Arabia (5.3% of GDP)

The United States comes in w/ a respectable tax burden of 26.9% of GDP. That ranks as the 57th highest in the world. That puts us just below Bolivia (27% of GDP), tied w/ South Africa, and just above South Korea (26.8% of GDP). Among the 34 wealthy OECD countries, the average tax burden is 36.2% of GDP. Other than South Korea, only Chile (among OECD countries) has a lower tax burden (18.6% of GDP).

Of course, this doesn’t answer the question of whether we should or shouldn’t have higher taxes. But it’s pretty clear that high taxes are not necessarily going to undermine our democracy.

My friend Matt Shugart commented on my previous post on this subject that I should&#8217;ve used a logarithmic scale and forced the regression through the origin (since zero guns should equal zero gun deaths). He&#8217;s right of course, but I didn&#8217;t want to complicate things.
I hadn&#8217;t wanted to complicate things methodologically, but I went ahead and adjusted the simple bivariate regression making those changes. The picture is, perhaps, a little clearer. But it does (as expected) drop the R-squared slightly (so the model now explains only about 18 percent of the variation in the data). But the overall relationship stands: more guns, more gun-related homicides deaths.
And don&#8217;t forget: that red dot is the US.

My friend Matt Shugart commented on my previous post on this subject that I should’ve used a logarithmic scale and forced the regression through the origin (since zero guns should equal zero gun deaths). He’s right of course, but I didn’t want to complicate things.

I hadn’t wanted to complicate things methodologically, but I went ahead and adjusted the simple bivariate regression making those changes. The picture is, perhaps, a little clearer. But it does (as expected) drop the R-squared slightly (so the model now explains only about 18 percent of the variation in the data). But the overall relationship stands: more guns, more gun-related homicides deaths.

And don’t forget: that red dot is the US.

UNDP Data Explorer

Talking about development & underdevelopment in POL 102 today. In addition to showing them the amazing Hans Rosling, I also want to show the students some UNDP (United Nations Development Program) data on development. The UNDP’s site recently added some really neat interactive tools to display much of their data (borrowing a page from Hans Rosling’s Gapminder project).

The problem is that anecdotal evidence often seems much more compelling than dry statistics. Man seems to have a tendency to impart information in the form of a story. … Official data are often flawed and need to be revised; we should always be on the lookout for rogue items that stand out from the general trend. But economic statistics are (generally) honest attempts to make sense of vast, complex systems. They offer a more robust view of the world than your brother-in-law or the story your neighbour heard at work.
From “The dangers of anecdotal evidence" | The Economist
States &amp; Taxes
This week in POL 102, we&#8217;re discussing the state. As part of that discussion, students are looking at the 2012 Failed States Index.
One of the things I try to impress on my students is that the old adage &#8220;the government that governs least, governs best&#8221; is not necessarily true (ask a Somali refugee). The top ten &#8220;failed&#8221; states include a number of countries with little or no effective governance. One way to think about the positive attributes of states is to simply look at the relationship between state &#8220;strength&#8221; (operationalized by the Failed States Index) and &#8220;size of government&#8221; (operationalized as tax burden as a % of GDP, with data from the Heritage Foundation). The above graph shows that relationship.
The graph shows that states with smaller tax revenues tend to have higher Failed States Index scores. This simple statistical model explains about 36.5% of variation in the data (R2=0.36501), so the relationship is not particularly strong. The data reflects a representative sample of 62 countries. The orange dot represents the US.

States & Taxes

This week in POL 102, we’re discussing the state. As part of that discussion, students are looking at the 2012 Failed States Index.

One of the things I try to impress on my students is that the old adage “the government that governs least, governs best” is not necessarily true (ask a Somali refugee). The top ten “failed” states include a number of countries with little or no effective governance. One way to think about the positive attributes of states is to simply look at the relationship between state “strength” (operationalized by the Failed States Index) and “size of government” (operationalized as tax burden as a % of GDP, with data from the Heritage Foundation). The above graph shows that relationship.

The graph shows that states with smaller tax revenues tend to have higher Failed States Index scores. This simple statistical model explains about 36.5% of variation in the data (R2=0.36501), so the relationship is not particularly strong. The data reflects a representative sample of 62 countries. The orange dot represents the US.