What Does Statistically Significant Mean?

Hilda Bastian writes an important and well written blog on this topic in a recent Scientific American blog .

I don’t think I have much else to add other than read this blog. There are some great links inside her blog to further understand this topic.

I think we are too focused on p <0.05. What if the p value is 0.051? Does that mean we should ignore the finding? Is it really any different than p value of 0.0499?

Confidence intervals give information on both statistical significance and clinical significance but I worry about how they are interpreted also. (Disclaimer: the interpretation and use of the confidence interval that follows is not statistically correct but is how we use them clinically.) Lets say a treatment improves a bad outcome with a relative risk (RR) of 0.94 with 95% CI of 0.66-1.12. So the treatment isn’t “statistically significant” (the CI includes 1.0) but there is potential for a relatively significant clinical benefit [ the lower bound of the CI suggests a potential 34% reduction in the bad outcome (1- RR = relative risk reduction so 1-0.66 = 0.34 or 34%)]. There is also potential for a clinically significant increase in risk of 12%. So which is more important? Somewhat depends on whether you believe in this treatment or not. If you believe in it you focus on the potential 34% reduction in outcomes. If you don’t believe in the treatment you focus on the 12% increased risk. So that’s the problem with confidence intervals but they give much more information than p-values do.