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Introduction to Making Decisions with Data The Scientific Method • Formulate a theory • Collect data to test theory • Analyze the results • Interpret results and make a decision • Re-evaluate theory What is Statistics? • Most basic: A way to summarize information. • Real Purpose: A method for making decisions based upon data. What is a Theory? • Write down the definition of “theory.” • Share it with the persons next to you. Fundamental Idea of Decision Making with Data • A theory is rejected if it can be shown statistically that the data observed would be very unlikely to occur if the theory were in fact true. A theory is accepted if it is not rejected by the data. Example • Theory: There are 4 blue balls and 1 yellow ball in the bag. • Collect Data: Pull a ball from bag, note color and replace it. • Analyze the Results: How many blue? How many yellow? • Interpret and make Decision My Daughters Guinea Pig • My daughters guinea pig started to get real fat. We were concerned that we had been over feeding her or that she had perhaps grown a tumor. • Out popped three baby guinea pigs. The pet shop owner had assured us that the other pig in the pen with her was a female. The Decision to Make • Competing Theories: The other guinea pig was female vs. the other guinea pig was male • Collect Data: Three baby guinea pigs • Analyze Results: The probability of the bunkmate being female is very small. • Interpret and Make Decision: Don’t call the Vatican just yet. Example of Hypotheses • Theory: A study suggests the taking Glucosamine and Chondroitin will reduce joint pain for the majority of users. • To test this theory we need to form competing hypotheses about the statement. • The Null Hypothesis is the status quo, or prevailing view. • The Alternate Hypothesis is the opposite of the null, the research hypothesis. State the Null and Alternate • The null hypothesis is denoted H0 and the alternate is given by H1 • H0: Taking Glucosamine and Chondroitin will not reduce joint pain for the majority of users (more than 50% of users). • H1:Taking Glucosamine and Chondroitin will reduce joint pain in the majority of users (more than 50% of users). • (We’ll let Glucosamine and Chondroitin be abbreviated as G/C from here) Based on Data, Make a Decision • If the proportion of subjects that report less joint pain is the same as with a placebo? • If 75% of the subjects taking G/C report significantly less joint pain and only 35% reported less pain that were taking the placebo? • If the difference between G/C and the placebo was 2%? • How large of a difference in proportion is needed for you to feel confident in rejecting the null hypothesis? Recall: Fundamental Idea • A theory is rejected if it can be shown statistically that the data observed would be very unlikely to occur if the theory were in fact true. A theory is accepted if it is not rejected by the data. Could’ve We Been Mistaken? • Is it possible that if we concluded from our data that G/C worked that we could be wrong? • Is it possible that if we concluded from our data that G/C didn’t work that we could be wrong? Types of Errors • If we reject H0 when it was true we’ve made a Type I error • If we fail to reject H0 when it is false, then we’ve made a Type II error • For example, H0: Person is innocent H1: Person is guilty Explain what a type I and type II error would be in this case. The Truth Null True Alternate True Your Null No Error Type II Decision Accepted Error Based Upon Alternate Type I No Error the Data Accepted Error Which Error is Worse? • H0: The water is contaminated. H1: The water is not contaminated. • H0: The parachute works. H1: The parachute does not work. • H0: A hostile country has weapons of mass destruction. H1: A hostile country does not have weapons of mass destruction. • H0: The infant pain reliever has the stated amount of acetaminophen. H1: The infant pain reliever has more than the stated amount of acetaminophen.
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