Testnorm

testnorm is a function commonly found in statistical software and libraries designed to calculate the cumulative distribution function (CDF) of the standard normal distribution. The standard normal distribution is a specific case of the normal distribution with a mean of 0 and a standard deviation of 1. The CDF of a random variable gives the probability that the variable takes on a value less than or equal to a specified value.

In practical terms, testnorm(x) returns the area under the standard normal curve to the left of the value x. This value is crucial for many statistical procedures, including hypothesis testing, confidence interval construction, and probability calculations related to normally distributed data. For example, when performing a z-test, the p-value is often derived by calculating the probability of observing a test statistic as extreme or more extreme than the one obtained, which involves using the CDF of the standard normal distribution.

The input to testnorm is typically a numerical value representing the z-score. The output is a probability, a number between 0 and 1. Many programming languages and statistical packages provide implementations of this function, often under names like pnorm, cdfnorm, or simply norm.cdf. Understanding the behavior and application of testnorm is fundamental for anyone working with statistical analysis and interpretation.