Confidence level = 1 – Significance level (alpha)

Confidence level and significance level are two important concepts in statistical hypothesis testing. The confidence level measures how confident we are that our conclusions are correct. In contrast, the significance level (also called alpha value) is the probability of rejecting the null hypothesis when it is true (Type I error).

Significance Level

The significance level, also known as alpha, is a probability threshold used in statistical hypothesis testing. It is the probability of rejecting the null hypothesis when it is true.

The significance level is typically chosen by the researcher based on the study's requirements. Common significance levels include 0.05 and 0.01. 

Confidence Level

The confidence level is usually expressed as a percentage and is typically chosen by the researcher based on the desired precision level and the study's requirements. Common confidence levels include 90%, 95%, and 99%.

Relationship Between Significance Level and Confidence Level

 The relationship between the confidence level and the significance level is expressed as:

Confidence level = 1 - Significance level (alpha).

In other words, the confidence level equals one minus the significance level.

For example, if our significance level is 0.05, this means that there is a 5% probability of rejecting the null hypothesis when it is true. The corresponding confidence level would be 1 - 0.05 = 0.95 or 95%.