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.

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

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

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

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

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

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 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.

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