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2.3.1.2 Definitions

Definition 15   Given a Model for a set of observations, a Hypothesis Test (HT) involves:
  1. The null hypothesis $ H_0$. This is the hypothesis under which we will evaluate the data. $ H_0$ is a statement about the distribution underlying the data.
  2. The alternative hypothesis $ H_a$. This is an alternative statement about the data distribution. The goal of a hypothesis test is to choose between $ H_0$ and $ H_a$.
  3. The test statistic $ S$. This is a function of the data (a random variable) with the following two properties:
    • Under $ H_0$ we know something about the distribution of $ S$.
    • $ S$ is relevant to the choice $ H_0$ vs. $ H_a$
  4. The critical region $ C$. A set of values that are used to reject the null hypothesis. In other words, the null hypothesis is rejected whenever the value we observe for $ S$ is in $ C$.

In the toxic fish example we have:


next up previous contents
Next: 2.3.1.3 Critical region and Up: 2.3.1 Basic elements of Previous: 2.3.1.1 Main idea
Eran Borenstein
2007-05-04