The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under both the tails of the curve. Further, this area indicates the levels of statistical significance. Mathematically, α + CL = 1.
The confidence coefficient is essential for the interpretation of the confidence interval. Three commonly used confidence coefficients are 0.90, 0.95, and 0.99. For these three confidence coefficients, the value of α is 0.1, 0.05, and 0.01, respectively. These coefficients can also be expressed as a percentage – 90%, 95%, and 99%, respectively.
For example, using a confidence level of 95%, where α is 0.05, a researcher can confidently say that 95% of all of the calculated confidence intervals will contain the true population parameter value.
This text is adapted from Openstax, Introductory Statistics, Section 8, Confidence Interval
