zStatistik
zStatistik, often referred to as the z-statistic, is a standardized statistic used to measure how many standard deviations an observed value is from a specified reference value. It is based on the standard normal distribution and is widely employed in hypothesis testing, confidence interval construction, and cross-study comparison. A common form is z = (X − μ0) / σ for a single observation X with a known population mean μ0 and population standard deviation σ. For a sample mean X̄ from n observations, the standardized form is z = (X̄ − μ0) / (σ/√n) when σ is known. When σ is unknown and the sample size is small, the t-statistic is used instead of z.
Interpretation of z-statistics relies on the standard normal model. Under the null hypothesis and appropriate conditions,
Applications of zStatistik span several statistical practices. In hypothesis testing, it enables quick assessment of deviations
Limitations include the reliance on independence and, usually, a known σ or large sample size to justify