Topic 5 Hypothesis testing

Here our goal is to use inferential statistics. We want to know something about the population just by using the information in our sample.

To do so, we will test some hypothesis. A hypothesis is simply a guess. There are two types of guesses.

  • \(x = something\)

  • \(x\neq something\)

  • We call null hypothesis guesses of the form: \(x = something\)

  • We call alternative hypothesis guesses of the form: \(x\neq something\)

For example, let us test the hypothesis that the mean of some population is 10. We usually refer to this guess as a null hypothesis.

Hypothesis testing relies on a simple idea: we check the information in our sample to see if we can reject or not reject our hypothesis. We never claim that a hypothesis is true!

We ask ourselves: based on the information in our sample, what are some values which we can claim ARE NOT representatives of the population? Is our hypothesis one of these values?

5.1 Types of erros

Important:There exists a true value for the population mean, even though we do not know it. Therefore, we want to check the chance of your guess being equal to what is true.

  • “true null” means that our guess is correct (guess = true population mean).
  • “false null” means that our guess is not correct (guess is not equal to the true population mean).

Given this terminology, we can make two types of mistakes in our tests:

  • Type I error: probability of rejecting a true null hypothesis.
  • Type II error: probability of not rejecting a false null hypothesis.

Academic convention states that researchers should minimize Type I error. Usually to a 5% chance of it happening.

The value we set for the probability of type I error is called \(\alpha\), or the maximum level of type I error we can tolerate.