# Chapter 1 by 39r8181

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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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