Question

The t test is an exact test but requires stronger assumptions about the data. (T/F)
Please give a brief explanation.

Answer 1

The t-test is an exact test but requires stronger assumptions about the data. : -FALSE

The T-test is not an exact test.

what is an exact test

In statistics, an exact (significance) test is a test where if the null hypothesis is true then all assumptions, upon which the derivation of the distribution of the test statistic is based, are met. Using an exact test provides a significance test that keeps the Type I error rate of the test ({\displaystyle \alpha }) at the desired significance level of the test.

For example, an exact test at the significance level of , when repeating the test over many samples where the null hypotheses is true, will reject at most of the time. This is opposed to an approximate test in which the desired type I error rate is only approximately kept (i.e.: the test might reject more than 5% of the time), while this approximation may be made as close to as desired by making the sample size big enough.

Exact tests that are based on discrete test statistic may be conservative tests, i.e. that its actual rejection rate is below the nominal significance level . For example, this is the case for Fisher's exact test. If the test statistic is continuous, it will reach the significance level exactly

Most of the p-values we calculate are based on an assumption that our test statistic meets some distribution. These distributions are generally a good way to calculate p-values as long as assumptions are met.

But it’s not the only way to calculate a p-value.

Rather than come up with a theoretical probability based on a distribution, exact tests calculate a p-value empirically.

Sot-test is not an exact test