# Confidence Interval

## What is a 'Confidence Interval'

A confidence interval measures the probability that a population parameter will fall between two set values. The confidence interval can take any number of probabilities, with the most common being 95% or 99%.

A confidence interval is the probability that a value will fall between an upper and lower bound of a probability distribution. For example, given a 99% confidence interval, stock XYZ's return will fall between -6.7% and +8.3% over the next year. In layman's terms, you are 99% confident that the returns of holding XYZ stock over the next year will fall between -6.7% and +8.3%.

## BREAKING DOWN 'Confidence Interval'

Statisticians use confidence intervals to measure uncertainty. A higher probability associated with the confidence interval means that there is a greater degree of certainty that the parameter falls within the bounds of the interval. Therefore, a higher the confidence level indicates that the parameters must be broader to ensure that level of confidence.

For example, 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. What they are missing at this point is the degree of uncertainty in this single sample.

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 72 inches to 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 70 inches to 78 inches, they can expect 99 of 100 samples evaluated to contain a mean value between these numbers.

## Common Misconceptions

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.