# Confidence interval calculator

If you don't know the population's standard deviation, just leave it empty
Enter raw data directly
Enter summarized data
It is not recommended to exclude outliers unless you know the reasons

## Enter sample data

When entering data, press Enter or comma , after each value, or paste data from excel. The tool ignores empty cells or non-numeric cells.

Shapiro Wilk test
Outliers count: ,based on the Tukey's fences method, k=1.5

Information

Calculates the confidence interval of the mean and the standard deviation using the Normal distribution or the Student's t distribution for the mean and the Chi-Squared distribution for the standard deviation.
When using the sample data we know the sample's statistics but we don't know the true value of the population's measures. Instead, we may treat the population's measures as random variables and calculate the confidence interval.
First, we need to define the confidence level which is the required certainty level that the true value will be in the confidence interval. Researchers commonly use a confidence level of 0.95.

Mean confidence interval
When we know the population's standard deviation (σ), we will use the normal distribution. The average's (X) distribution is Normal (Mean, SD/√n) Otherwise, we will use the sample size standard deviation with the t distribution with n-1 degrees of freedom. The (X-Mean)/(S/√n) distribution is T.

Standard deviation confidence interval
(n-1)S22 distributed Chi-squared with n-1 degrees of freedom.

n - sample size.
S - sample standard deviation.
SD - population standard deviation.

## R Code

The following R code should produce the same results. unless you filled the population standard deviation as the R code use only the t distribution based on the sample standard deviation.
The sigma.test produce the confidence interval of the variance instead of the standard deviation