def. A Hypothesis test is a criteria to determine between two statements about an unknown parameter of a distribution:


  • is the Null hypothesis
  • is the Alternative hypothesis

def. Type I and II Errors, as well as size and power are defined as follows:

  1. Type I Error is the probability of a false positive: → the Size of the test = Level of the test
  2. Type II Error is the probability of a false negative: → the Power of the test

⇒ Constructing a -level test is to construct one that has a true negative rate of [= a false positive rate of ]


def. let . then the p-value is the minimum [= false positive rate = size] at which you would adopt .


Common Hypothesis Tests

Multiple Hypothesis Testing

Motivation. Assume 20 sets of sample data. Then the false positive rate of one sample:

What Is the Bonferroni Correction?

A good explaination of the bonferroni correction.

⇒ This is too high to be acceptable. This is p-hacking. Thus:

def. Bonferroni Correction. In -tests on a single dataset , level must be changed to in order to make a reasonable test.

More Types of Tests