Fundamental Analysis

# confidence interval

## What is a confidence interval?

A confidence interval in statistics refers to the probability that a population parameter falls between a set of values ​​for a certain percentage of time.

### key takeaways

• Confidence intervals show the probability that a parameter falls between a pair of values ​​near the mean.
• Confidence intervals measure the degree of uncertainty or certainty in the sampling method.
• They are usually constructed with a 95% or 99% confidence level.

Confidence intervals measure the degree of uncertainty or certainty in the sampling method. They can take any number of probability limits, the most common being a 95% or 99% confidence level. Confidence intervals are made using statistical methods, such as t-tests.

Statisticians use confidence intervals to measure uncertainty in a sample variable. For example, a researcher randomly selects different samples from the same population and calculates a confidence interval for each sample to see how it represents the true value of a population variable. The resulting datasets are all different; some intervals include the true population parameter, while others do not.

confidence interval is a range of values, above and below the mean of the statistic, that may contain an unknown population parameter. The confidence level is the probability or percentage of certainty that the confidence interval will contain the true population parameter when you draw a random sample multiple times. Or, in the vernacular, “We are 99% sure (confidence level) that most of these samples (confidence intervals) contain true population parameters.”

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

## Calculate confidence intervals

Suppose a group of researchers is studying the height of high school basketball players. The researchers took a random sample from the population and determined the average height to be 74 inches.

The 74-inch mean is a point estimate of the population mean. The point estimate by itself is of limited use because it cannot reveal the uncertainty associated with the estimate; you don’t quite know how far this 74-inch sample mean might be from the population mean. What’s missing is the level of uncertainty in this single sample.

Confidence intervals provide more information than point estimates. By establishing a 95% confidence interval using the mean and standard deviation of the sample, and assuming a normal distribution represented by a bell curve, the researchers derived upper and lower bounds that contained the true mean 95% of the time.

Assume the spacing is between 72 inches and 76 inches. If researchers randomly selected 100 samples from the entire population of high school basketball players, the mean of 95 of those samples should be between 72 and 76 inches.

If researchers want greater confidence, they can widen the interval to 99% confidence. Doing this will always create a wider range because it makes room for more sample means. If they determined the 99% confidence interval to be between 70 inches and 78 inches, they could expect 99 out of 100 samples to be evaluated to contain the mean between these numbers.

On the other hand, a 90% confidence level means that we expect 90% of the interval estimates to contain the population parameters, and so on.

## What do the confidence intervals reveal?

A confidence interval is a range of values, above and below the mean of a statistic, that may contain unknown population parameters. The confidence level is the probability or percentage of certainty that the confidence interval will contain the true population parameter when you draw a random sample multiple times.

## How to use confidence intervals?

Statisticians use confidence intervals to measure uncertainty in a sample variable. For example, a researcher randomly selects different samples from the same population and calculates a confidence interval for each sample to see how it represents the true value of a population variable. The resulting datasets are all different, with some intervals containing the true population parameters and others not.

## What are common misconceptions about confidence intervals?

The biggest misconception about confidence intervals is that they represent the percentage of data from a given sample that fall between the upper and lower bounds. In other words, it is incorrect to assume that a 99% confidence interval means that 99% of the data in a random sample falls between these bounds. It effectively means that you can be 99% sure that the range will contain the population mean.

## What is a T-test?

Confidence intervals are made using statistical methods, such as t-tests. The t-test is an inferential statistic used to determine whether there is a significant difference between the means of two groups, which may be related to certain characteristics. Three key data values ​​are required to calculate the t-test. They include the difference between the means of each dataset (called the mean difference), the standard deviation for each group, and the number of data values ​​for each group.

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