Download presentation

Presentation is loading. Please wait.

Published byZackary Hatcher Modified about 1 year ago

1
1 more on Hypothesis Testing

2
2 Hypothesis Testing Hypothesis Testing Trial by jury

3
3 Individual on trial. Is he/she innocent? Evidence Trial Hypothesis Testing & Trial by jury

4
4 Individual on trial. Is he/she innocent? Evidence Trial Person InnocentGuilty Hypothesis Testing & Trial by jury

5
5 Individual on trial. Is he/she innocent? Evidence Trial Jury Person InnocentGuilty Not Guilty Guilty Hypothesis Testing & Trial by jury

6
6 Individual on trial. Is he/she innocent? Evidence Trial Jury Person InnocentGuilty Not Guilty Guilty Hypothesis Testing & Trial by jury

7
7 Individual on trial. Is he/she innocent? Evidence Trial Jury Person InnocentGuilty Not Guilty x Guiltyx Hypothesis Testing & Trial by jury

8
8 Evidence Trial Jury Person InnocentGuilty Not Guilty x Guiltyx Test of Hypothesis that = 0 ? EvidenceTrial Hypothesis Testing

9
9 Trial Jury Person InnocentGuilty Not Guilty x Guiltyx Test of Hypothesis that = 0 ? SampleTrial Hypothesis Testing

10
10 Jury Person InnocentGuilty Not Guilty x Guiltyx Test of Hypothesis that = 0 ? Sample Analysis Hypothesis Testing

11
11 Jury Population InnocentGuilty Not Guilty x Guiltyx Test of Hypothesis that = 0 ? Sample Analysis Hypothesis Testing

12
12 Jury Population = 0 Guilty Not Guilty x Guiltyx Test of Hypothesis that = 0 ? Sample Analysis Hypothesis Testing

13
13 Jury Population = 0 0 0 Not Guilty x Guiltyx Test of Hypothesis that = 0 ? Sample Analysis Hypothesis Testing

14
14 Us Population = 0 0 0 Not Guilty x Guiltyx Test of Hypothesis that = 0 ? Sample Analysis Hypothesis Testing

15
15 Us Population = 0 0 0 Not reject x Guiltyx Test of Hypothesis that = 0 ? Sample Analysis Hypothesis Testing

16
16 Us Population = 0 0 0 Not reject x Rejectx Test of Hypothesis that = 0 ? Sample Analysis Hypothesis Testing

17
17 Us Population = 0 0 0 Not reject Type II RejectType I Test of Hypothesis that = 0 ? Sample Analysis Hypothesis Testing

18
18 Probability of Type I error is i.e. the probability of rejecting the null hypothesis when it is true. Probability of Type II error is i.e the probability of not rejecting the null hypothesis when it is false. 1- is the power of the test. Possible errors in analysis results

19
19 1o1o Hypothesize a value ( 0 ) 2o2o Take a random sample (n). 3o3o Is it likely that the sample came from a population with mean 0 ( = 0.05) ? Hypothesis testing about :

20
20 We know that cholesterol levels in US men yrs are normally distributed with σ X 46 mg/100ml and μ = 211. We obtain a random sample of 12 hypertensive smokers and obtain a sample mean of 217 mg/100ml. We want to test whether their population mean is the same as that of the general population? 2 sided hypothesis test - Illustration H 0 : = 211 H A : 211

21
21 H 0 : = 211 H A : 211 = 46 mg/100ml 12 hypertensive smokers have: 2 sided hypothesis test - Illustration

22
22 Some prefer to quote the p-value. The p-value answers the question, “What is the probability of get- ting as large, or larger, a Discrepancy given the null hypothesis is true?” P-value Question: Do hypertensive smokers have the same mean as the general population?

23
23 Rejecting the null hypothesis Assume a specific threshold of Type I error, α –Typically α = 0.05 If p value < α Reject null

24
24 Some prefer to quote the p-value. The p-value answers the question, “What is the probability of get- ting as large, or larger, a Discrepancy given the null hypothesis is true?” P-value Answer: Do not reject the null hypothesis. No evidence that hypertensive smokers have a different mean than general population

25
25 Decide on statistic: Determine which values of consonant with the hypothesis that = 0 and which ones are not. are Look atand decide. Summary

26
26 Need to set up 2 hypotheses to cover all possibilities for . Choice of 3 possibilities: 1. Two-sided H 0 : = 0 H A : 0 Alternative hypothesis

27
27 Blood glucose level of healthy persons has = 9.7 mmol/L and = 2.0 mmol/L H 0 : 9.7 H A : > 9.7 Sample of 64 diabetics yields Example - One-sided alternative Do diabetics have blood glucose levels that are higher on average when compared to the general population?

28
28 Blood glucose level of healthy persons has = 9.7 mmol/L and = 2.0 mmol/L H 0 : 9.7 H A : > 9.7 n = 64 p-value << Example - One-sided alternative Answer: Reject the null hypothesis. Significant evidence that diabetics have a higher mean level of glucose when compared to the general population

29
29 Need to set up 2 hypotheses to cover all possibilities for . Choice of 3 possibilities: Two-sided H 0 : = 0 H A : 0 One-sided H 0 : 0 H A : < 0 One-sided H 0 : 0 H A : > 0 Alternative hypothesis

30
30 Summary Hypothesis testing: –Type I and II errors –Power Two sided hypothesis test One sided hypothesis test

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google