An Interactive Guide to the Z-Test for Trading
The Z-test is used for comparing means with large samples when population variance is known. This guide explains its types with interactive trading examples.
Purpose & Analogy
A Z-test, like a t-test, checks if differences in means are significant. However, it's used for large crowds (samples > 30) where you already have a map of the entire population's variability (known population standard deviation).
Key Assumptions
The main requirements are a large sample size (n > 30), approximately normally distributed data, and critically, a known population standard deviation. This last point makes it rarer in practice than the t-test.
Two-Sample Z-Test
This test compares the means of two large, independent stocks or assets. It's used when you have extensive historical data that provides the population standard deviations for both.
Example: A firm compares the average daily volatility of 'Stock A' vs. 'Stock B' over the past five years (~1260 data points each). With known population standard deviations for both stocks' volatility, they test if there is a significant difference between them.