Barack Obama Farewell Address

Chicago (CNN)

Popular but politically humbled, President Barack Obama said goodbye to the nation Tuesday night, declaring during his farewell address that he hasn't abandoned his vision of progressive change but warning that it now comes with a new set of caveats.

His voice at moments catching with emotion, Obama recounted a presidency that saw setbacks as well as successes. Admitting candidly that political discourse has soured under his watch, Obama demanded that Americans renew efforts at reconciliation.

"It falls to each of us to be those anxious, jealous guardians of our democracy," the President said. "To embrace the joyous task we've been given to continually try to improve this great nation of ours." Obama also stressed solidarity despite a presidency sometimes at odds with Congress.

"Democracy does not require uniformity," Obama said. "Our founders quarreled and compromised, and expected us to do the same. But they knew that democracy does require a basic sense of solidarity -- the idea that for all our outward differences, we are all in this together; that we rise or fall as one." Obama's farewell speech

In a concession that, for now, his brand of progressive politics is stalled in Washington, Obama admitted "for every two steps forward, it often feels we take one step back." He implored his backers to be vigilant in protecting basic American values he warned could come under siege.

"Democracy can buckle when we give in to fear," he said. "So just as we, as citizens, must remain vigilant against external aggression, we must guard against a weakening of the values that make us who we are."

Specific Hypothesis and Results

This is a sharply focused event, and rather than the 6 hours we typically analyse, we examine just two hours, from the beginning of the speech at 8 pm local Chicago time (02:00 to 04:00 UTC, on 11 Jan). The specified event includes much of the time Obama spent shaking hands and hugging supporters after his speech. The outcome is Chisquare 7217 on 7200 df, for p = 0.441 and Z = 0.147.

As you can see in the graph below, there is no "Obama effect" like that we saw early in his Presidency. I'd personally have liked to see a wildly convincing departure for this last hurrah, but it was not to be.

Interpretation

The following graph is a visual display of the statistical result. It shows the second-by-second accumulation of small deviations of the data from what’s expected. Our prediction is that deviations will tend to be positive, and if this is so, the jagged line will tend to go upward. If the endpoint is positive, this is evidence for the general hypothesis and adds to the bottom line. If the endpoint is outside the smooth curve showing 0.05 probability, the deviation is nominally significant. If the trend of the cumulative deviation is downward, this is evidence against the hypothesis, and is subtracted from the bottom line. For more detail on how to interpret the results, see The Science and related pages, as well as the standard caveat below.

Standard caveat

It is important to keep in mind that we have only a tiny statistical effect, so that it is always hard to distinguish signal from noise. This means that every success might be largely driven by chance, and every null might include a real signal overwhelmed by noise. In the long run, a real effect can be identified only by patiently accumulating replications of similar analyses.