7.4:
Confidence Coefficient
The confidence interval for a population parameter is calculated based on a specific percent level of confidence.
This percentage—which can be 90%, 95%, or 99%—is arbitrarily decided for a given population parameter or sampling distribution.
The level at which the confidence interval is calculated is called the confidence coefficient, degree of confidence, or confidence level.
It is calculated simply by 1-ɑ, where ɑ; is the area under the curve distributed equally on both tails of the curve. This area also indicates the level of statistical significance.
In other words, the confidence level is the probability 1−α that the calculated confidence intervals would contain the population parameter. Here, it is assumed that the parameter values are obtained through unbiased sampling conducted a sufficient number of times.
If the confidence level is decided to be at 0.95—where α is 0.05—we are confident that 95% of all the calculated confidence intervals would contain the true population parameter value.
An appropriate confidence coefficient is crucial, without which, the confidence limits cannot be calculated or interpreted.
7.4:
Confidence Coefficient
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