Family of $t$ Tests
$t$-tests is a family of Statistical tests that use $t$-statistics
- critical values come from the $t$-distribution - used for calculating $p$-values
$t$ Tests
The following tests are $t$-tests:
Assumptions
Assumptions for $t$ tests are similar to the assumptions of the $z$-tests
- Observations are independent (if less than 10% of population is sampled, then we can make sure it's satisfied)
- Sample size is sufficiently large so C.L.T. holds
- Moderate skew, few outliers (not too extreme)
Sample Size
- the sample size can be smaller than for $z$-tests
- so it can be smaller than 30 - after 30 we can safely use $z$-tests with almost the same outcomes
$t$-distribution:
- the tails are thicker than for $N(0,1)$ and observations are more likely to fall within 2$\sigma$ from the mean
- this is exactly the correction we need to account for poorly estimated Standard Error when the sample size is not big
Alternatives to $t$-Tests
Sources