Introduction to Making Decisions with Data - PowerPoint PPT Presentation

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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.

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Introduction to Making Decisions with Data

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Introduction to making decisions with data l.jpg

Introduction to Making Decisions with Data


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The Scientific Method

  • Formulate a theory

  • Collect data to test theory

  • Analyze the results

  • Interpret results and make a decision

  • Re-evaluate theory


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What is Statistics?

  • Most basic: A way to summarize information.

  • Real Purpose: A method for makingdecisions based upon data.


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What is a Theory?

  • Write down the definition of “theory.”

  • Share it with the persons next to you.


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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.


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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


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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.


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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.


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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.


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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)


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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?


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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.


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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?


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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.


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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


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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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