What are the differences between z-distribution and t-distribution?

Question

What are the differences between z-distribution and t-distribution?

Answer 1

Point #1: If you ask a mathematical question it's imperative that you tell us what discipline in math you're asking about.

The best guess I can make would be two ways of examining a data set, one in which a flat plane is extended into 3D space (the z vector); and the other of which is a view of the flat space through time (the t vector). Although they both represent adding dimensions to the data, they represent different dimensions.

Answer 2

The Z distribution is just a special case of the normal distribution, with an idealized mean of 0 and standard deviation of 1. This allows us to create a compact and useful table for all normal distributions -- a very important property before the days of fancy calculators and computers.

The t distribution is similar to the Z distribution, but is sensitive to sample size and is used for small samples, or moderate size samples when the population standard deviation is unknown. It is little different from Z for large sample sizes.

Answer 3

In probability and statistics, Student's t-distribution (or simply the t-distribution) is a probability distribution that arises in the problem of estimating the mean of a normally distributed population when the sample size is small. It is the basis of the popular Student's t-tests for the statistical significance of the difference between two sample means, and for confidence intervals for the difference between two population means. The Student's t-distribution is a special case of the generalised hyperbolic distribution.

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. Normal distributions can be transformed to standard normal distributions by the formula: