Hypothesis Testing

I've often wondered if the changes in the size of government could really be attributable to the party in power. Said another way: Could an outside observer use data over our history to accurately discern which party was in power by looking at the changes in the size of government?

To test this, we need a hypothesis. I submit the null hypothesis:

There is no statistical difference between the growth in government dependent upon the party in power.

Mathematically, if we sum the changes in government size and compute the averages when the Republicans are in power, and the average when the Democrats are in power, we have:

Average Republican Growth – Average Democratic Growth = 0.

I gathered the following information: Yearly GDP, Yearly Federal Government Outlays, and who holds the office of the President, and the majority of each house of Congress, all for the past 40 years.

For purposes of government size, I divided Yearly Fed Gov Outlays by Yearly GDP. This normalizes the size and removes changes due to inflation (and presumable, population growth). Interestingly, The size of our Federal government has been relatively constant, moving between 18.84% in 1970, 22.86% in 1983, 19.78% in 2000, and back to 20.66% in 2008.

For Party in power, I decided that it would be two out of three: Whichever party held at least two of: Majority of Senate, Majority of House, and Presidency, would be tagged as the party in power.
Also, since budgets (hence Federal outlays) are done for the following year, I imposed a one year lag between when a party rises to power and when they effect the size of government. So, we have the following:
1970 – 1981: Democratic
1982 – 1987: Republican
1988 – 1995: Democratic
1996 – 2007: Republican
2008 – on: Democratic

What we are going to do then is compute the averages, the standard deviations, and run a standard double tailed hypothesis test, to see if we can reject the null hypothesis (i.e., that instead Average Republican Growth – Average Democratic Growth is NOT equal to zero.) We'll use a 95% confidence interval, which will answer the question: Can we say with 95% certainty that the difference is not zero?

Computed Data:
Republican: Average – 99.62%; Median – 99.32%, Standard Deviation: .0307
Democratic: Average – 101.86%; Median – 99.92%, Standard Deviation: .0557

(Interestingly, more than half the time, government decreases under either party, hence the medians below 100%. For the Republicans, 11 of 18, for the Democrats, 12 of 22)

To reject the null hypothesis at 95% confidence, the normal distribution table says we need a value of greater than 1.96 after we compute the answer to the equation:

Ave D – Ave R / SQRT((R stddev squared / 18) + (D stddev squared / 22))

And we get?

1.61.

Since 1.61 < 1.96, we cannot reject the null hypothesis at 95% confidence that the two are indeed different. So, my hypothesis withstands statistical analysis. An outside observer cannot discern the party in power by looking at changes in the size of the Federal government, because there is not enough evidence that the underlying distributions are different.

What about relaxing the statistical standards? For instance, could we reject the null hypothesis at 90%?

No. Although it is really close – we would need a value greater than 1.64.

So – What does this say? Basically, we cannot determine, with certainty, that the difference between the averages reveals an actual underlying difference between the two distributions. The two overlap almost entirely – and that there is a slight difference today between the averages may very well be an aberration. Or maybe not. We would need more data covering the time frame in question. However, there is no more data – we've got all 40 years. Data from previous to 40 years ago may help answer the question: In the past, was there a difference, that is gone today? But it doesn't directly help us today.

There is something interesting here, too. The computed value doesn't meet the requirements for a 90% confidence, but it is really close. You might be tempted to think that there is an actual difference – and that perhaps the inclusion of state government data would push it over. And that may be true. But what I find intriguing is that it was an outcome of a very similar nature that had everyone saying that the Global Warming hypothesis was null. If you recall, one of the scientists revealed that the near-term data (last 15 years), just missed the mark for the 95% confidence interval, and so he couldn't reject the null hypothesis on that data alone.

Perhaps you agree. Perhaps you'd like to declare Global Warming dead. But understand this: There is statistically more evidence for Global Warming than there is that Republicans and Democrats influence the overall size of government differently.


Footnote: I did not expect this outcome. Like almost everyone I know, I really expected that the data would damn the Democrats, and that our conventional wisdom would be upheld. I had started to suspect that it may not be fully true during the last decade, and especially recently. I will have to gather more data – I suspect now that the source of our conventional wisdom was planted during the 1930's – that government did grow, but its size appears to have stabilized.
I was tempted too to not include the past two years. 2009 was the only year during the 40 I looked at were GDP fell – which if used as a yardstick imposes an enormous growth on government even if it maintains the same dollar outlays – which it didn't, due to the stimulus bills. But that reveals even more that differences in size are more likely due to other causes than the party in power: 2009's 19% growth goes against the Democrats, and if the underlying distribution can absorb a value that far off the average without pushing it past the 90% confidence interval, then the null hypothesis is very, very solid.