The Z statistic Where

The Z statistic Where

The Z statistic Where

The Z statistic Where

The t Statistic(s) Using an estimated, which we’ll call we can create an estimate of which we’ll call where

The t Statistic(s) Using, instead of we get a statistic that isn’t from a normal (Z) distribution - it is from a family of distributions called t

The t Statistic(s) What’s the difference between t and Z?

The t Statistic(s) What’s the difference between t and Z? Nothing if n is really large (approaching infinity) –because n-1 and n are almost the same number!

The t Statistic(s) With small values of n, the shape of the t distribution depends on the degrees of freedom (n-1)

The t Statistic(s) With small values of n, the shape of the t distribution depends on the degrees of freedom (n-1) –specifically it is flatter but still symmetric with small n

The t Statistic(s) Since the shape of the t distribution depends on the d.f., the fraction of t scores falling within any given range also depends on d. f.

The t Statistic(s) The Z table isn’t useful (unless n is huge) instead we use a t-table which gives tcrit for different degrees of freedom (and usually both one- and two-tailed tests)

The t Statistic(s) There is a t table on page 142 of your book Look it over - notice how t crit changes with the d.f. and the alpha level

The t Statistic(s) The logic of using this table to test alternative hypothesis against null hypothesis is precisely as with Z scores - in fact, the values in the bottom row are given by the Z table and the familiar +/ appears for alpha =.05 (two- tailed)

Next Time: More about t tests