Step 2: Direction of Effect

Statistical significance only shows whether we can be confident that the coefficient is non-zero. However, we also have information about the direction of the effect, i.e. whether it is likely that the coefficient is positive or negative.

	% shift to Trump, 2012-2016
median income ($1,000s)	-0.158*
	(0.006)
Constant	8.337*
	(0.351)
Observations	3,111
Adjusted R2	0.203
Note:	* p<0.05

• Due to technicalities regarding “one-sided” versus “two-sided” confidence intervals, a p-value of \(0.05\) produces a 95% confidence that the coefficient is non-zero, and a 90% confidence that the coefficient’s sign is correct.
• There is a negative relationship between income and shifting to Trump. Because it is starred with \(p<0.05\), we think, with 90% confidence, this negative sign is not due to chance alone.
• This value of the coefficient, \(-0.158\), is called the estimated effect size of county median income on shifting to Trump between 2012 and 2016.
• We cannot be confident in the exact value of this coefficient. We can only be confident that the direction is negative.
• In technical terms, we have rejected the null hypothesis that the coefficient is zero, and accept the alternate hypothesis that the coefficient is negative.