I am new to statistics so this might be an easy question. I know that if a confidence interval includes 1.0 then the result is not statistically significant because it includes the null. But, what if the confidence interval starts at 1.0? Like 95% CI: 1.0 – 1.9? Is that still statistically significant? It includes the null, but it doesn't cross it. Thanks!
Solved – What if a confidence interval starts at 1.0
confidence intervalstatistical significance
Best Answer
It is incredibly unlikely that a confidence interval has the null value as an end point. But, let's assume that it did happen. This would mean that the p value for your associated test would be equal to $\alpha$, the false positive rate. In the case of a z test
$$ 0 = \bar{x} - z_{\alpha/2} \sigma/\sqrt{n} \implies z_{\alpha/2} = \bar{x}/\sigma/\sqrt{n} $$
and
$$ 2 \mathbf{\Phi}^{-1}(z_{\alpha/2}) = \alpha$$
by definition. Here, $\mathbf{\Phi}^{-1}$ is the standard normal quantile function. What the investigator would do at this point is not something I am prepared to discuss at the point. Though I will say this: If the CI you've been given (be it from software or otherwise) has only one digit of precision, ask for more. I guarantee you that a CI which includes the null is likely due to rounding.