Confidence Interval in Statistics

Table of Contents

What is Confidence Interval?

The confidence interval, in statistics, represents an estimate of an interval that may consist of a population parameter. In other words, it refers to the probability of a population parameter falling between a set of values for a particular proportion of times. A confidence level is a term often associated with sampling because it helps calculate the degree of uncertainty or certainty in a specific sampling method.

There are two limits to the interval which define it. The confidence interval comes in the form of a percentage, which has an upper and lower bound. These percentages reflect the confidence level.

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What is Confidence Level?

Confidence level refers to the percentage of probability or certainty that the confidence interval consists of the true population parameter when a random sample gets drawn many times. A confidence level of 0% shows that there is no certainty that the sample includes a true population parameter and, therefore, will draw a different sample each time. A confidence level of 100%, on the other hand, shows that no matter how many times the simple get drawn again, it will result in the same selection.

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How to calculate the Confidence Interval?

It is necessary to determine the criteria for testing first to calculate the confidence interval. The confidence interval varies based on the chosen criteria. Next, it is crucial to select a sample from a given population. The sample helps in testing or performing the hypothesis. Next, it is necessary to determine the mean and standard deviation for the sample chosen.

From the given data, it is straightforward to calculate a confidence level. It may range from 90% up to 99%. After calculating the confidence interval, it is also possible to calculate the confidence coefficient for the confidence interval chosen. The calculation of the confidence coefficient is straightforward using z-tables. Finally, it is also possible to determine the margin of error for the estimation.

By using the above information, the confidence interval for the chosen sample with the confidence level becomes determinable. The formula to calculate the confidence interval is as below.

Confidence level = Mean of sample ± Critical Factor x Standard deviation of the sample

How to interpret the Confidence Interval?

Most users of the confidence interval often misinterpret or misuse it. Even most professionals or scientists don’t interpret it correctly. For example, a 99% confidence level does not imply that for a given realized interval, the probability that the population parameter lies within the interval is 99%. In fact, for any confidence level, users tend to misinterpret it as the probability of population parameter lying within the interval.

It is one of the most common misconceptions involving confidence level. After calculating the confidence interval, there is no longer a probability of covering the confidence level. It either includes the parameter value, or it doesn’t. That is why the confidence interval varies for various samples while the true population parameter doesn’t, regardless of the selected sample.

Conclusion

Confidence interval is a term used to represent the estimate of an interval that consists of a population parameter. It is a term closely related to the confidence level, which refers to the percentage of probability or certainty that the confidence interval consists of the true population parameter.