## What Is Confidence Interval?

A confidence interval, in statistics, refers to the probability that a population parameter will fall between two set values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. A confidence interval can take any number of probabilities, with the most common being a 95% or 99% confidence level.

Confidence *interval* and confidence *level *are interrelated but are not exactly the same.

## Understanding Confidence Interval

Statisticians use confidence intervals to measure uncertainty. For example, a researcher selects different samples randomly from the same population and computes a confidence interval for each sample. The resulting datasets are all different; some intervals include the true population parameter and others do not.

A ** Confidence interval **is a range of values that likely would contain an unknown population parameter.

**refers to the percentage of probability, or certainty, that the confidence interval would contain the true population parameter when you draw a random sample many times. Or, in the vernacular, "We are 99% certain (**

*Confidence level**confidence level)*that most of these datasets

*(confidence intervals)*contain the true population parameter."

### Key Takeaways

- A confidence interval calculates the probability that a population parameter will fall between two set values.
- Confidence intervals measure the degree of uncertainty or certainty in a sampling method.
- Most often, confidence intervals reflect confidence levels of 95% or 99%.

## Calculating a Confidence Interval

Suppose a group of researchers is studying the heights of high school basketball players. The researchers take a random sample from the population and establish a mean height of 74 inches. The mean of 74 inches is a point estimate of the population mean. A point estimate by itself is of limited usefulness because it does not reveal the uncertainty associated with the estimate; you do not have a good sense of how far away this 74-inch sample mean might be from the population mean. What's missing is the degree of uncertainty in this single sample.

Confidence intervals provide more information than point estimates. By establishing a 95% confidence interval using the sample's mean and standard deviation, and assuming a normal distribution as represented by the bell curve, the researchers arrive at an upper and lower bound that contains the true mean 95% of the time. Assume the interval is between 72 inches and 76 inches. If the researchers take 100 random samples from the population of high school basketball players as a whole, the mean should fall between 72 and 76 inches in 95 of those samples.

If the researchers want even greater confidence, they can expand the interval to 99% confidence. Doing so invariably creates a broader range, as it makes room for a greater number of sample means. If they establish the 99% confidence interval as being between 70 inches and 78 inches, they can expect 99 of 100 samples evaluated to contain a mean value between these numbers. A 90% confidence level means that we would expect 90% of the interval estimates to include the population parameter. Likewise, a 99% confidence level means that 95% of the intervals would include the parameter.

## Common Misconceptions About Confidence Interval

The biggest misconception regarding confidence intervals is that they represent the percentage of data from a given sample that falls between the upper and lower bounds. For example, one might erroneously interpret the aforementioned 99% confidence interval of 70-to-78 inches as indicating that 99% of the data in a random sample falls between these numbers. This is incorrect, though a separate method of statistical analysis exists to make such a determination. Doing so involves identifying the sample's mean and standard deviation and plotting these figures on a bell curve.