Download presentation

Presentation is loading. Please wait.

Published byColin McCann Modified over 3 years ago

1
STATISTICS HYPOTHESES TEST (II) One-sample tests on the mean and variance Professor Ke-Sheng Cheng Department of Bioenvironmental Systems Engineering National Taiwan University

2
Tests on Mean 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 2

3
(1) 2 is known 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 3

4
1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 4

5
(2) 2 is unknown 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 5

6
1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 6

7
(3) 2 is known 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 7

8
(4) 2 is unknown 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 8

9
Tests on Variance 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 9

10
(1) is known 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 10

11
1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 11

12
1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 12

13
(2) is unknown 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 13

14
1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 14

15
(3) is known 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 15

16
1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 16

17
(4) is unknown 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 17

18
1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 18

19
1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 19

20
1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 20

21
1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 21

22
t-test in R 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 22 For a two-tailed test, the p-value in R is twice of the exceedance probability shown in the above figure.

23
1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 23

24
1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 24

25
Paired t-test The paired t test provides a hypothesis test of the difference between population means for a pair of random samples whose differences are approximately normally distributed. 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 25

26
If the population from which paired differences to be analyzed by a paired t test were sampled violate one or more of the paired t test assumptions, the results of the analysis may be incorrect or misleading. For example, if the assumption of independence for the paired differences is violated, then the paired t test is simply not appropriate. 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 26

27
Note that the two values that make up each paired difference need not be independent, and in fact are expected to be correlated, such as before and after measurements. If you treat paired data as coming from two independent samples, such as doing an inappropriate two-sample unpaired t test instead of a paired t test, then you may sacrifice power. 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 27

28
If the assumption of normality is violated, or outliers are present, then the paired t test may not be the most powerful test available, and this could mean the difference between detecting a true difference or not. A nonparametric test or employing a transformation may result in a more powerful test. For example, if the distribution of the paired differences is not symmetric, a transformation may produce symmetry. 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 28

29
The test statistic is calculated as: 1/31/2014 Department of Bioenvironmental Systems Engineering National Taiwan University 29 Two-sided test One-sided test

Similar presentations

Presentation is loading. Please wait....

OK

PSSA Preparation.

PSSA Preparation.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google