1. Hypothesis Testing By Boon Xuan, Mei Ying and Fatin
Reading: Salsburg, David (2001). The Lady Tasting Tea: How Statistics
Revolutionized Science in the Twentieth Century, W.H. Freeman (Chapter 11, Hypothesis testing)

2. Overview: What is hypothesis testing? What is hypothesis?
How to test the hypothesis?
Application to real life
Conclusion

3. What is Hypothesis Testing?
The administrator at your local hospital states that on weekends the average wait time for emergency room visits is 10 minutes.  Based on discussions you have had with friends who have complained on how long they waited to be see in in the ER over a weekend, you dispute the administrator's claim.  You decide to test the hypothesis.

4. Significant results, reject H0 P > 0.05
Step 1
H0: µ = 10
HA: µ > 10
Step 2
Step 2
Level of significance = 0.05
Step 3
Step 3
Step 4
Step 4
Find Probability
i.e. “p-value”
P < 0.05
Significant results, reject H0
P > 0.05
Insignificant results, accept H0

5. What is Hypothesis? Consists of: Null Hypothesis
Alternative Hypothesis – Have to be narrowly defined!
Statisticians Egon Pearson and Jerzy Neyman wen through a few cases where hypothesis testing resulted in rejecting of a hypothesis that was obviously true
Neyman-Pearson formulation of hypothesis testing
Simple
Taught to be a rigid concept
Wrong emphasis
Emphasis on hypotheses are dampened

6. “Neyman's major discovery was that significance testing made no sense unless there were at least two possible hypotheses.”

7. How to Test the Hypothesis?
Jerzy
Neyman
Find Probability!
What is probability?
Allow us to apply statistical methods to scientific problems
Used to show that the hypothesis is not true
A theoretical probability under circumstances that are most likely to be flawed

8. Find Probability! How to Test the Hypothesis? John Venn
(British Philosopher)
Find Probability!
Frequentist Definition of Probability
Law of large probabilities
If we throw a dice repeatedly, the proportion of times we get a 1 will draw closer and closer to the probability

9. Real Life Application
Use of hypothesis have gone beyond science journals
Used in:
Courts of law to show employment discrimination
Drug regulatory authorities in the U.S. and Canada

10. A book example 1.Gilbert Conclusion: 3.HER STATE Divorced
Mother of 2 young children
Have been dating
Stable job with high pay
1.Gilbert
Good nurse
Looked up to
Particularly good in a crisis
4. IS SHE A MURDERER?
Hypothesis testing was carried out
Was it true that there were more deaths when Gilbert was on duty?
i.e. not just 1 or 2 more (coincidence)
2. HOWEVER
Too many crises when Gilbert was on duty
Certain patients died
Accused of murder
Conclusion:
The judge ruled that such statistical evidence should not be allowed for this trial due to certain incorrect methods used. However, it was concluded that a small p-value does allow you to reasonably say that event is not due to chance.

11. Conclusion:
Hypothesis testing is a means to determine if suggested hypothesis should be rejected or not
Hypotheses (Null and Alternative) are important for hypothesis testing to be accurate
Focus on finding probability is secondary but is important as well
Examples of real life applications for hypothesis testing

12. References:
Salsburg, David (2001). The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century, W.H. Freeman (Chapter 11, Hypothesis testing)
Cobb, Gehlbach. Statistics in the Courtroom