Ch. 10 Hypothesis Testing

I. Introduction

Experimental example

- a. hypothesis generated

- b. manipulate independent variable, measure dependent variable

- c. analyze data

2.Logic of Hypothesis Testing

a. Hypotheses

- 1. Alternative hypothesis (H
_{1})

- 2. Null hypothesis (Ho)

b. Testing the Null

i. compute probability that differences are due to chance

ii. if the probability that the difference is due to chance is low enough, we can reject the null,
accept the alternative; if the probability that the difference is due to chance is high we must fail to
reject the null

iii. "How low" depends on our "decision rule"

Example, using the sign test

DIRECTIONAL HYPOTHESIS, TESTING ONE-TAILED PROBABILITY

H_{1}: Tests cause increases in anxiety ie., anxiety is higher on test days than on others

Ho: Tests do not increase anxiety

11 students selected randomly from stat 241 class

During test | During Class |

17 | 15 |

12 | 10 |

16 | 17 |

20 | 13 |

18 | 10 |

21 | 20 |

19 | 14 |

18 | 17 |

14 | 11 |

19 | 21 |

22 | 12 |

An investigator wants to measure the effectiveness of an advertisement that promotes a brand of
toothpaste. He/she randomly selects people from the population and shows one group that
advertisement , but not the other group. Then he/she measures the number of tubes of toothpaste
they bought. Did the ad work i.e, did it increase sales?

H_{1}?

Ho?

AD GROUP | NO-AD GROUP |

4 | 1 |

4 | 2 |

3 | 0 |

1 | 2 |

2 | 0 |

0 | 1 |

1 | 0 |

0 | 1 |

3. Type I, Type II Error

4. Influences on setting alpha

5. Directional (one-tailed) vs. Non-directional (two-tailed) Hypothesis Testing

A. Directional: Differences is expressed in a particular direction

- i. test probability that results are due to chance in one direction only

- ii. If p < .05, in that direction, reject null

- iii. If p < .05 in the other direction, retain null

B. Non-Directional

- i. test probability that results are due to chance in both directions
- ii. If p < .05 in either direction, reject null

AIDS INFO | NO-AIDS INFO |

19 | 22 |

12 | 20 |

17 | 19 |

21 | 24 |

15 | 18 |

23 | 19 |

21 | 25 |

10 | 18 |

20 | 23 |

10 | 15 |

14 | 17 |

6. Deciding on directional vs. Nondirectional

1. When there is good theoretical reason

2. Must be decided in advance