Standard Score - Applications

Applications

The z-score is often used in the z-test in standardized testing – the analog of the Student's t-test for a population whose parameters are known, rather than estimated. As it is very unusual to know the entire population, the t-test is much more widely used.

Also, standard score can be used in the calculation of prediction intervals. A prediction interval, consisting of a lower endpoint designated L and an upper endpoint designated U, is an interval such that a future observation X will lie in the interval with high probability, i.e.

for example γ = 0.95 (95%). For the standard score Z of X it gives:

By determining the quantile z such that

it follows: