Decision Theory

**Null Hypotheses**- H
_{0}- no difference, zero effect **Alternative hypotheses**- H
_{1}- hypothesis that differs from H_{0}

**Significance level test [1]**

The way to reject the null hypothesis, based on the significant evidence against the hypothesis.

In practice, a significance level of 0.05 or 0.01 are chosen. For example, α=0.05 means that we are 95% confident that we have made the right decision.

Reject the hypothesis if the normalized z score lies outside the critical interval in the following table:

Level of significance, α | 0.1 | 0.05 | 0.01 | 0.005 |

Critical interval, one-tailed | z<1.28 | z<1.645 | z<2.33 | z<2.58 |

Critical interval, two-tailed | |z|<1.645 | |z|<1.96 | |z|<2.58 | |z|<2.81 |

Accept the hypothesis otherwise (or, if desired, make no decision at all).

Bibliography

1. M.R. Spiegel, D.P. Lindstrom, "Schaum's Easy Outline: Statistics," McGraw-Hill, 1999. http://www.amazon.com/Schaums-Easy-Outline-Murray-Spiegel/dp/0070527121/ref=sr_1_6?s=books&ie=UTF8&qid=1308482725&sr=1-6

page revision: 4, last edited: 19 Jun 2011 14:23