How is the significance level (α) calculated from the confidence coefficient?

The significance level (α) is intrinsically linked to the confidence coefficient in statistical hypothesis testing. The confidence coefficient represents the proportion of times that a confidence interval will capture the true parameter if the same sampling method is repeated numerous times. It typically ranges from 0 to 1 (or 0% to 100%).

To understand the relationship, consider that the confidence coefficient indicates how confident we are in our estimate. For example, a 95% confidence interval means that there is a 95% probability that the true parameter lies within that interval. The remaining percentage, which adds up to 100%, represents the uncertainty or the area outside the confidence interval where the true parameter may lie. Therefore, the significance level (α), which represents this uncertainty, is calculated as the complement of the confidence coefficient.

Specifically, if the confidence coefficient is C, then the significance level can be derived as follows:

• α = 1 - C

This shows that for a confidence coefficient of 0.95 (or 95%), the significance level would be:

• α = 1 - 0.95 = 0.05 (or 5%).

This relationship is fundamental in hypothesis testing, linking the confidence intervals to the risk of making a