No Evidence that Economic Growth Differs Based on Who is President

If you divide the last 40 years into the six respective presidencies since 1977 (Carter, Reagan, Bush Sr, Clinton, W. Bush, Obama) and treat Real GDP Growth as a normally distributed random variable which produced 40 independent observations, is there a statistically significant difference in the mean GDP growth parameter (μ) between the six presidencies?

Below is the list of years analyzed, from 1977 to 2015 (actually only 39 observations, not 40, because the full year GDP growth for 2016 is not yet determined).

The one-way ANOVA test for equality of means essentially compares inter-group variation to intra-group variation to determine whether the difference in group means is statistically significant.

The assumption that economic growth for the 39 past years is approximately normal holds true, as seen from the histogram of GDP Growth.

GDP Growth by Year and President (Source: US Bureau of Economic Analysis)

Obs	President	Party	Year	Real Annual GDP Growth (%)
1	Carter	Democrat	1977	4.90
2	Carter	Democrat	1978	6.68
3	Carter	Democrat	1979	1.30
4	Carter	Democrat	1980	0.00
5	Reagan	Republican	1981	1.29
6	Reagan	Republican	1982	-1.40
7	Reagan	Republican	1983	7.83
8	Reagan	Republican	1984	5.63
9	Reagan	Republican	1985	4.28
10	Reagan	Republican	1986	2.94
11	Reagan	Republican	1987	4.45
12	Reagan	Republican	1988	3.84
13	Bush	Republican	1989	2.78
14	Bush	Republican	1990	0.65
15	Bush	Republican	1991	1.22
16	Bush	Republican	1992	4.33
17	Clinton	Democrat	1993	2.63
18	Clinton	Democrat	1994	4.13
19	Clinton	Democrat	1995	2.28
20	Clinton	Democrat	1996	3.80
21	Clinton	Democrat	1997	4.45
22	Clinton	Democrat	1998	5.00
23	Clinton	Democrat	1999	4.69
24	Clinton	Democrat	2000	2.89
25	W. Bush	Republican	2001	0.21
26	W. Bush	Republican	2002	2.04
27	W. Bush	Republican	2003	4.36
28	W. Bush	Republican	2004	3.12
29	W. Bush	Republican	2005	3.03
30	W. Bush	Republican	2006	2.39
31	W. Bush	Republican	2007	1.87
32	W. Bush	Republican	2008	-2.70
33	Obama	Democrat	2009	-0.20
34	Obama	Democrat	2010	2.73
35	Obama	Democrat	2011	1.68
36	Obama	Democrat	2012	1.28
37	Obama	Democrat	2013	2.66
38	Obama	Democrat	2014	2.49
39	Obama	Democrat	2015	1.88

Conclusion: 

The F-Value from the ANOVA test indicates that there is not enough evidence (at the 5% significance level) to conclude that the different presidencies had inherently different mean real GDP growth parameters.

In other words, we cannot conclude that the observed yearly historical differences in economic growth level by presidency are anything other than the expected level of variation caused by other factors completely separate from the identity of the sitting president.

Why this is true, in my perspective:

1) The Federal Reserve has a more direct and immediate role than the President of the United States in influencing GDP growth through monetary policy. For example, by sharply increasing interest rates, the Fed can curb economic growth and even cause a recession (as happened in the early 1980's).

2) Policies of the current presidential administration may not have an impact until many years (and many presidencies) later. Just as investments in infrastructure, education, and the like will boost economic growth somewhere down the road, bad economic policies can cause financial disasters many years after they are implemented.

3) The business cycle is inherent to a capitalist economy, and periods of growth and contraction are influenced by a wide variety of factors that are out of the president's immediate control - these include consumer spending and confidence, business confidence and uncertainty, world political events, oil shocks, etc.

What the one-way ANOVA test cleverly captures is that GDP growth has on average varied enough within presidencies, no doubt in large part due to the natural boom-and-bust cycles, that we cannot reliably conclude that variance between presidencies is significant.