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Introduction to Making Decisions with Data

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.

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Introduction to Making Decisions with Data

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  1. Introduction to Making Decisions with Data

  2. The Scientific Method • Formulate a theory • Collect data to test theory • Analyze the results • Interpret results and make a decision • Re-evaluate theory

  3. What is Statistics? • Most basic: A way to summarize information. • Real Purpose: A method for makingdecisions based upon data.

  4. What is a Theory? • Write down the definition of “theory.” • Share it with the persons next to you.

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. 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)

  11. 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?

  12. 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.

  13. 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?

  14. 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 innocentH1: Person is guiltyExplain what a type I and type II error would be in this case.

  15. Your Decision Based Upon the Data The Truth Null True Alternate True Null Accepted No Error Type II Error Alternate Accepted Type I Error No Error

  16. 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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