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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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the scientific method
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
What is Statistics?
  • Most basic: A way to summarize information.
  • Real Purpose: A method for makingdecisions based upon data.
what is a theory
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
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
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
  • 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
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
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
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
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
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
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
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

which error is worse
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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