Ch. 10 Hypothesis Testing

I. Introduction

Experimental example





2.Logic of Hypothesis Testing



a. Hypotheses















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

H1: 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?

H1?



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



B. Non-Directional

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

Statistics