Download Hypothesis Testing - Department of Statistics and Applied Probability

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)
Overview:
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What is hypothesis testing?
What is hypothesis?
How to test the hypothesis?
Application to real life
Conclusion
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.
Step 1
H0: µ = 10
HA: µ > 10
Step 2
Level of significance = 0.05
Step 3
Find Probability
i.e. “p-value”
Step 4
P < 0.05
Significant results, reject H0
P > 0.05
Insignificant results, accept H0
What is Hypothesis?
• Consists of:
1. Null Hypothesis
2. 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
“Neyman's major discovery was that significance testing
made no sense unless there were at least two possible
hypotheses.”
How to Test the Hypothesis?
Find Probability!
Jerzy
Neyman
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
How to Test the Hypothesis?
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
John Venn
(British Philosopher)
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
A book example
1.Gilbert
• Good nurse
• Looked up to
• Particularly
good in a crisis
2. HOWEVER
• Too many crises when
Gilbert was on duty
• Certain patients died
• Accused of murder
Conclusion:
3.HER STATE
• Divorced
• Mother of 2 young
children
• Have been dating
• Stable job with high pay
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)
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.
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
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