calculating degrees of freedom for 95% confidence

When calculating confidence intervals about an effect (eg. But the wide 95% CI shows the estimate of the effect of beer vs vodka on pain is very imprecise. Since the 95% CI crosses zero, there is no difference between beer and vodka. Here, on average, subjects who drank beer would experience as low as 0 points less pain to as high as 9 points less pain 95% of the time. If we had only tested 5 instead of 30 subjects, we might have found beer reduced pain response by 4 points (95% CI 0-8 points) compared to vodka. So confidence intervals indicate how precise an estimate is. If the study was repeated many times, on average, subjects who drank beer would experience as low as 2 points less pain to as high as 6 points less pain 95% of the time. For example, if we found that beer was better than vodka at reducing pain response by 4 points (95% CI 2-6 points) on a 10 point scale, this means subjects who drank beer experience 4 points less pain on average compared to those who drank vodka. The confidence interval about an effect indicates how the effect varies if the study is repeated many times.

How do degrees of freedom influence t values when calculating confidence intervals? In a previous post we saw that t distributions with more degrees of freedom approximate the Normal distribution more closely, and degrees of freedom are increased by testing more subjects.

Calculating degrees of freedom for 95% confidence