Hypothesis Testing By Boon Xuan Mei Ying and

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: • • • 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 H 0: µ = 10 HA: µ > 10 Step 2 Level of significance = 0. 05 Step 3 Find Probability i. e. “p-value” Step 44 P < 0. 05 Significant results, reject H 0 P > 0. 05 Insignificant results, accept H 0

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 Ø Simple Ø Taught to be a rigid concept 1. Wrong emphasis 2. 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 Ø 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: ØCourts of law to show employment discrimination ØDrug 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 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) 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.

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