Introduction to Making Decisions with Data

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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 making decisions 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 Dont 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).
• H1Taking Glucosamine and Chondroitin will reduce
  joint pain in the majority of users (more than
  50 of users).
• (Well 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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Couldve 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 didnt work that we could be wrong?

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Types of Errors

• If we reject H0 when it was true weve made a
  Type I error
• If we fail to reject H0 when it is false, then
  weve made a Type II error
• For example, H0 Person is innocent H1 Person
  is guiltyExplain what a type I and type II error
  would be in this case.

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